Symmetry capabilities and production-reduction status

The shared mathematical infrastructure is implemented and experimental. Production reduction is qualified separately for each numerical method, finite support, electronic state and retained space. There is no blanket completion or production-authorization claim for symmetry reduction.

Shared infrastructure

Capability	Implementation and boundary
Finite groups and lattice image cocycles	Native exact algebra checks, scalar antiunitary parity and point-group conjugacy classes are available. A valid table does not establish geometric completeness.
Compact space actions and orbit operations	Budgeted block actions, typed density/operator transport, stabilizers and adjoint scatter/gather are available without dense all-space matrices.
Molecular and periodic AO transport	Molecular compact actions support mixed pure/Cartesian shells through l=6, sharing the periodic polynomial kernel. Periodic AO/Bloch transport retains atom images, fractional translations, mesh wraps and scalar time reversal. The legacy dense molecular API requires pure shells beyond s.
State and retained-space diagnostics	Metric, group-law, operator and leakage checks can bind a native periodic state and selected spaces. A successful numerical witness does not certify a producer or authorize pair skipping.
Production method integration	An experimental SR/LR GDF retained-auxiliary tensor diagnostic compares independently built batches. Production GDF scheduling, PAO/PNO/TNO transport, reduced correlation execution and analytic derivatives retain separate implementation and acceptance gates.
Complex Abelian tensor execution	Experimental symmetry_abelian validates complete ordinary character tables and a supplied finite chemist ERI tensor, stores allowed blocks and contracts J/K on arbitrary complex densities. No source generation, production SCF dispatch, projective little groups or magnetic corepresentations are enabled.
Molecular representative integral execution	Experimental symmetry_quartets audits the complete finite MANTA P0 libint source, then evaluates shell representatives for arbitrary-density J/K. C2v and full C3v AO transport, real pure/Cartesian shells and stabilizers are tested. The optional symmetry_quartets_streaming schedule retains quadratic pair maps instead of the stored quartet inventory. Complete audits remain available; optional native Q/V bounds skip reads for omitted whole orbits while auditing retained members. Arbitrary-density contraction terms remain explicit. No production routing, complex integral source or reduced non-Abelian CC tensor is enabled.
Native quartet execution	Opt-in executor="native" compiles angular transport, member permutations and complex-density J/K contractions for either admitted schedule. Selected families share resolved matrix addresses across density channels; scalar shells bypass angular index loops. Integral generation, source digests and scientific tolerances remain unchanged; the chosen qualification policy controls audit reads. It is a provider-independent executor, not MANTA kernels or production SCF dispatch.
Shared-density quartet batches	jk_batch reuses each representative integral and angular transform for independent complex density channels. NumPy/native paths preserve per-channel J/K and source-error bounds, aggregate actual work, immutable density snapshots and whole-batch refusal. Optional per-channel J/K selectors skip unrequested contractions and output panels, with explicit compact-output mappings. An optional diagnostic checks method-assembled snapshots against the separate Fock-object draft. No spin/state selection or production driver dispatch is implied.
Fixed-orbit molecular screening	Opt-in QuartetScreening binds a density-independent whole-orbit mask to a stored or compact streamed P0 qualification. Both batch executors skip actual representative calls and contractions, retain separate source/policy identities and report per-input bounds. Optional MANTA Q/V envelopes omit orbits before reads; retained-only audits require that exact mask. Mutable callbacks, producer-side primitive screening and periodic sources remain outside this admission.
Native hierarchical bound candidates	Experimental symmetry_quartets_hierarchy consumes MANTA bubble traversal and order-zero full Gaussian-tail bounds. Native candidate blocks spend an ordered-AO tensor budget; only their intersection with complete quartet orbits may omit reads. Retained audits and fixed-mask requirements remain. No default dispatch, tree equivariance or periodic admission is inferred.
Explicit molecular HF bridge	symmetry_molecular_hf connects one admitted fixed P0 mask to native real RHF/UHF and method-owned HF FockBuild snapshots. symmetry_molecular_scf exposes explicit public RHF/UHF options and consistent evaluated density, energy, Fock and natural-orbital QVF output, including capped and NOITER states. Native UHF jointly requests total-density J and independent spin K; spatially broken states remain allowed. Default/job-deck dispatch, zero-copy native capture, periodic/complex-source/derivative admission remain separate.
Measured molecular route selection	Opt-in executor="auto" compares ordered retained-tile evaluation with representative reconstruction on nonsymmetric probes. Five bounded native HF signatures have separate cost decisions. Producer/audit/source/policy identities stay fixed; calibration is separately accounted. This does not bypass retained-source audits or enable default, periodic, RI/BUPO or complex-source SCF routing.
Explicit molecular job selection	run_job accepts the qualified RHF/UHF options or prepared source. Executable QVF records carry a strict fresh-source request, never saved audit authority. Normal output uses the physical evaluated state and labels natural orbitals; canonical frontier diagnostics refuse. Scientific job evidence is recorded below.
Exact terminal J/K reuse	Public qualified RHF/UHF keeps bounded method-local evaluations and assembles terminal FockBuild without more integrals when source, ordered channels and density bytes match. Separate native RHF J/K calls can be joined. Mismatches retain the cold path; prepared sources contain no state.
Reusable qualified molecular sources	prepare_molecular_symmetry owns one actual audit, fixed mask and checked one-electron source. Independent public RHF/UHF states can reuse it and its bounded scalar cost profiles after exact geometry/basis checks, with fresh state and physical counters. New sources still require qualification; changed geometry, radial content, overlapping use and cross-process reuse refuse.
Multi-k GDF exchange wedge	symmetry_reduce_k (driver ibz_native) builds exchange at wedge bras only and admits each transporting operation against the executed exchange source before any integral: every space-group operation, glides and screws included, on the pair-centred SR/LR fit; only equal-lattice-shift operations (the image shift computed with the fractional translation) on the origin-centred classic fit; none on other sources. A fractional translation is carried by the atom-image shift of the Bloch transport, with no separate exp(-i k.tau) factor in the AO-centred convention. Transported and directly built exchange agree to roundoff on nonsymmetric complex trial densities for diamond Fd-3m and hcp P6_3/mmc. Occupations are filled once per star on the wedge representatives, with levels split within the measured star spectral spread sharing their electrons, so a star-degenerate zero-temperature frontier receives the symmetric ensemble fill instead of a noise-selected one (#428). The state gate transports every representative through its little group as well as every member through its star operation, so a wedge-native run that passes it is invariant under every admitted operation (#470). Cartesian shells beyond s, a proof of electronic-state invariance (the SCF gate is a calibrated threshold) and floating-point membership of pairs lying exactly on a cutoff surface remain outside this admission.

The developer reference defines the implemented APIs and their resource contracts. The architecture page describes the remaining production gates. All shared-layer evidence retains production_reduction_authorized == False; a method must establish its own admission policy against an unreduced reference. Method-specific calculation acceptance of a particular change belongs to its tracker record, not to a general capability checkmark.

The multi-k GDF wedge also binds every executed k point and normalized weight to the declared full mesh before integral work. It preserves half-step shifts and reciprocal wraps, and refuses reordered or inconsistent point lists. This quadrature prerequisite does not strengthen the calibrated electronic state gate or qualify additional finite sources, local spaces or derivatives. For an already reduced input, the wedge path also validates the original representatives, orbit weights and full-grid mapping before expansion can replace them. Consistent representative reordering and reciprocal wraps are preserved; inconsistent reductions are refused before integral work.

October 2026 literature increment and measured results

The literature assessment covers Melega’s geometry supplement, the C3v scope of Hellmann and Gauss, the explicitly labeled Kitsaras and Stopkowicz preprint, MolSym’s two supplements and libmsym, with connections to the molecular and periodic foundations. The design specifies the non-Abelian tensor and MANTA/BUPO integration requirements. Only the bounded P0 reference-tile adapter below has been implemented; native MANTA kernels and BUPO symmetry execution are not supplied by this work.

Measured on the current matching native extension with Python 3.14 and NumPy 2.5.3, one requested OpenMP/BLAS thread, 31 alternating timed contractions after warmup, seed 6128, and source tolerance 1e-10. The density is complex Hermitian and not symmetry invariant. Both paths use the identical unreduced finite molecular integral source; the block path omits only forbidden entries below its recorded aggregate tolerance. All ERIs are computed first, then transformed with native compact actions and overlap-metric-normalized projectors. No geometry or final Fock matrix is symmetrized. These are development measurements, not speed guarantees.

Case / admitted group	AO count / irrep populations	Full / retained ERI values	Full / block J+K scalar products	Block calls	Median full / block time (ms)
NH3 STO-3G / C3 subgroup of C3v	8 / 4,2,2	4096 / 1376	8192 / 2752	54	0.0167 / 0.3525
NH3 cc-pVDZ / C3 subgroup of C3v	29 / 11,9,9	707281 / 235771	1414562 / 471542	54	2.8650 / 1.4416
H2O cc-pVDZ / C2v	24 / 11,4,2,7	331776 / 88456	663552 / 176912	128	1.3674 / 1.4425

Case	Full complex ERI / retained array payload (bytes)	Preparation / plan time (ms)	Process peak RSS (bytes)	Maximum J / K error against direct AO contraction	Trial RHF energy-functional error (hartree)
NH3 STO-3G	65536 / 22384	4.92 / 1.23	158433280	2.23e-15 / 4.71e-15	1.43e-14
NH3 cc-pVDZ	11316496 / 3773040	30.67 / 14.70	212959232	1.79e-13 / 1.53e-13	5.28e-13
H2O cc-pVDZ	5308416 / 1416096	18.55 / 9.90	212353024	2.67e-14 / 3.06e-14	1.15e-13

Retained payload includes indices and character tables, but excludes native group and Python metadata. RSS is for the whole fresh benchmark process, including imports and both reference and reduced arrays; it is not the incremental memory of the plan. Conservative setup byte reservations are 318150, 45421446 and 21401928, respectively. Forbidden ERI Frobenius norms are 8.53e-15, 1.75e-13 and 1.05e-13. Each case makes one full compute_eri call. Native primitive/shell-quartet evaluations are not instrumented here: no integral-work reduction is claimed.

Only the larger ammonia case is faster (about 1.99x for contractions), and its plan setup takes about 11 saved builds to amortize. Water is about 5% slower and the tiny ammonia case about 21x slower despite fewer arithmetic terms. Production dispatch needs a measured cost gate or a lower-overhead executor. The unreduced path remains necessary for both incompatibility and cost. There is no end-to-end SCF or CC speedup claim.

At independently converged native STO-3G RHF densities, water’s total reference energy is -74.96386817084978 hartree and ammonia’s is -55.450387020207344 hartree for the benchmark fixture geometries. Rebuilding with block J/K changes their electronic energy functionals by 2.85e-14 and 8.33e-17 hartree, respectively; maximum Fock differences from the native reference are 8.68e-15 and 8.89e-15. These terminal-density checks supplement, rather than replace, the nonsymmetric-density tests. The new adapter does not itself run the SCF iteration.

Focused regression coverage includes native molecular C2v/C3 ERIs, complex nonsymmetric Hermitian and non-Hermitian densities, Cartesian metric-aware actions, independently transformed AO J/K and energy functionals, native converged RHF Fock comparisons, density-energy finite differences, separate spin calls, dense within-irrep gauges, separately conjugated time-reversal data, displaced sources and rejection of unsupported non-Abelian/antiunitary/cocycle tables. All scientific tolerances and production defaults are unchanged.

Validation commands and completed results:

• pytest tests/test_symmetry_abelian.py -q: 17 passed.

• pytest tests/test_symmetry_shared.py tests/test_symmetry_gdf.py tests/test_periodic_k_symmetry.py tests/test_symmetry_salc.py -q: 468 passed (run together with the first 13 new tests: 481 passed).

• pytest tests/test_citation_database_integrity.py tests/test_citation_no_dead_entries.py -q: 1379 passed. These are citation/schema checks, not numerical chemistry cases.

• pytest tests/test_test_gate_lanes.py -q: 76 passed after explicitly excluding the new experimental T3 file from shipped/release lanes.

• pytest tests/test_periodic_ao_bloch_transport.py tests/test_periodic_orbital_sewing.py tests/test_periodic_mean_field_state.py -q: 312 passed in 2.45 s, with 16 existing spglib deprecation warnings. This bounded rerun covers odd/even meshes, nonsymmorphic phases, Cartesian metrics, degenerate retained spaces and native finite-Gaussian states independently of the incomplete larger run below.

• Candidate-byte privacy preflight and git diff --check: passed.

An additional six-file periodic/CCM run collected 633 cases and reached 90% progress without a reported failure, but did not finish a long native integral build. It was interrupted and then terminated when the native call did not return. This is incomplete validation, not a passing CCM lane. The attempted files were test_periodic_ao_bloch_transport.py, test_periodic_orbital_sewing.py, test_periodic_mean_field_state.py, test_periodic_k_gdf_ibz_nonsymmorphic.py, test_periodic_aiccm2026dev_b_symmetry.py and test_ccm_symmetry.py.

All commands use the matching .venv/bin/python -m interpreter and OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1. Native source provenance was checked before numerical work; that complex-Abelian increment changed no C++ code. The later MANTA provider integration was rebuilt as described below.

Next missing production capabilities, in order:

1. Scalable producer-side shell/factor schedules with orbit-consistent screening and cost-based dispatch through the shared Fock interface. The bounded reference-tile scheduler below supplies representative and stabilizer execution plus native call counters. The streaming alternative removes the full retained shell inventory. Q/V bounds can now skip some audit reads, but all-member bound queries, retained audits and repeated Python schedule generation are not a production planner.

2. Full non-Abelian partner/product/multiplicity and recoupling machinery; C3v energy and complete CC residual oracles before generalization.

3. Covariant auxiliary, frozen/occupied/virtual and PAO/PNO/TNO selections, momentum-aware periodic contraction schedules, with CCM and chi keeping separate source/support/weight admission.

4. Method-specific relaxed gradients and stress, including response, Pulay, fitting and finite-support derivatives, checked by displaced/strained finite differences. None is supplied by this J/K increment.

Molecular representative-tile increment

The subsequent experimental symmetry_quartets increment implements complete finite-source admission, real-ERI permutation/spatial orbits, stabilizers and streamed representative J/K execution over the coordinated MANTA P0 libint reference provider. The native extension was rebuilt after integrating that provider. C2v water, full C3v ammonia and nonorthogonal Cartesian s+d actions are tested. This is full-block AO transport, not non-Abelian reduced-product resolution. No production defaults, periodic sources or derivative capabilities are changed.

The following fresh-process measurements use the same immutable source, zero primitive-screening precision, one requested OpenMP/BLAS thread, seven timed builds after warmup and a complex Hermitian, noninvariant trial density (seed 679). none, permutation and spatial all use the same Python tile executor and a private reusable native session. These times include tile evaluation, receipt validation, digest checks, transport and J/K contractions. They do not compare with MANTA’s native J/K executor and do not establish a production or end-to-end SCF speedup. Other development work was active on the machine; timings are descriptive.

Case / group / AO count	Native shell calls, ordered / permutation / spatial	Requested primitive quartets, ordered / permutation / spatial	Median build ms, ordered / permutation / spatial	Full-source spatial admission ms
NH3 STO-3G / C3v / 8	1296 / 231 / 81	104976 / 18711 / 6561	33.754 / 12.775 / 11.171	44.30
NH3 cc-pVDZ / C3v / 29	50625 / 7260 / 1893	1874161 / 306834 / 125343	980.517 / 352.266 / 324.284	851.35
H2O STO-3G / C2v / 7	625 / 120 / 76	50625 / 9720 / 6156	11.009 / 4.163 / 3.939	16.45
One-center Cartesian s+d / C3v / 7	16 / 6 / 6	16 / 6 / 6	0.328 / 0.239 / 0.200	6.41

Every admission evaluates all ordered shell quartets once. The independent oracle makes another complete ordered pass, separately counted by the benchmark. Primitive counts describe requested primitive combinations, not instrumentation inside libint recurrences. These cases returned no null tiles. The one-center case saves no additional integral calls from spatial symmetry; its small timing difference is not a spatial speedup claim. For the larger ammonia case, charging the entire spatial admission against the measured saving over permutation-only builds requires about 31 subsequent builds to amortize. The setup cost is not omitted.

Case	J+K scalar products / block contractions, all modes	Extra spatial transport scalar products	Maximum spatial J / K error	Trial interaction energy error (hartree)
NH3 STO-3G	8192 / 2592	1800	5.33e-15 / 1.78e-15	1.81e-15
NH3 cc-pVDZ	1414562 / 101250	713398	4.31e-14 / 1.35e-14	1.20e-13
H2O STO-3G	4802 / 1250	711	3.11e-15 / 3.59e-15	3.67e-15
One-center Cartesian s+d	4802 / 32	0	4.48e-16 / 3.15e-16	6.67e-16

Arbitrary-density contraction work remains 2*n_AO**4, performed in 2*n_shells**4 blocks. The complex-Abelian block consumer above is the separate increment that omits forbidden contraction terms. Combining the two schedules without materializing a complete transformed tensor remains future work. No scalar orbit multiplicity substitutes for missing density blocks. Tests also use non-Hermitian densities and independent spin channels, checking U^dagger F[U D U^dagger] U = F[D] with metric-aware AO actions.

Spatial plan case	Factory logical bytes / completed-plan logical bytes	Action arrays / stabilizer-mask bytes	Native provider modeled bytes	Whole-process peak RSS bytes
NH3 STO-3G	11992280 / 10851544	728 / 486	8806200	159039488
NH3 cc-pVDZ	81872044 / 80102572	3920 / 11358	25527888	210714624
H2O STO-3G	10720544 / 9980704	464 / 304	8803256	158171136
One-center Cartesian s+d	10505444 / 9476324	1800 / 36	8698992	158564352

Logical bytes conservatively reserve inventories and scratch; they are not measured allocations or an RSS cap. Array and mask payloads exclude Python schedule objects. RSS includes imports, the schedule, provider and the independent dense oracle (32768, 5658248, 19208 and 19208 bytes respectively). The plan itself retains no complete AO ERI tensor. The largest spatial source residual is 2.07e-14 in Frobenius norm and the largest stabilizer residual is 2.78e-15, against an unchanged 1e-10 source tolerance. Roundoff remains separate from the exact-arithmetic source residual bound.

Reproduce with scripts/benchmark_symmetry_quartets.py; its JSON output contains separate setup/build/reference counts and each measured quantity. The focused quartet, complex-Abelian and MANTA reference tests pass 70/70. A combined run adding shared groups, AO/SALC/GDF, k symmetry, periodic AO transport, retained-space sewing, finite mean-field states, citation integrity and lane classification passes 2325 tests, with 16 existing spglib deprecation warnings. That count includes metadata/schema tests, not 2325 chemical systems. It preserves odd/even, fractional-translation, complex, degenerate-space and incompatible-domain coverage in the existing shared and periodic foundations. No CCM or chi Hamiltonian is modified or newly qualified by this run.

New regressions cover native ordered-source J/K oracles, actual call counts, asymmetric-source and displaced-source rejection, exact unreduced fallback, radial-source mismatch, ephemeral tile lifetime, reordered non-Abelian operations, energy density-direction finite differences and refusal of complex-AO/antiunitary/projective sources. An independent source review found a stabilizer storage underestimate; compact permutation-bit masks correct it. High-stabilizer regressions and exact/one-short factory budgets now pass, with insufficient caps refused before snapshots or native sessions. The review covered source algebra and resource admission, not independent physical reproduction. Analytic geometry gradients, stress, CC residuals, RI/CD and screened periodic sources remain separate acceptance targets.

Streaming pair-stabilizer increment

schedule="streaming" now selects an experimental pair-stabilizer enumeration behind the same MANTA factory. It retains pair maps and one aggregate representative digest, rather than every ordered quartet and every representative hash. Source admission remains complete. It does not infer producer equivariance from geometry or reduce the admission integral count. The default schedule="stored" and all three reduction modes remain available. No native MANTA code, periodic Hamiltonian or solver routing was changed by this increment.

Davidson’s double-coset intersection and inverse-pair redundancy now have an execution consumer. Independent S3 and S4 index models, including reordered identities, repeated shell orbits and fixed shells, compare the streaming enumeration with exhaustive quartet partitions. A Burnside census checks the orbit count separately. An index-only 60/120-shell test constructs schedules without expanding a quartet and observes quadratic array scaling; this is not a large-molecule numerical benchmark.

Fresh-process spatial-schedule comparisons use seven repeated builds after warmup and the same fixtures, source tolerance, density seed and one-thread settings as above. Both schedules have identical source/build receipts, residuals and J/K errors. The cc-pVDZ regression also requires bitwise equal J/K arrays, the same representative order and the same transporters.

Case	Factory logical bytes, stored / streaming	Streaming pair-array bytes	Whole-process peak RSS bytes, stored / streaming	Admission ms, stored / streaming	Median build ms, stored / streaming
NH3 STO-3G	11992280 / 10710212	2104	160317440 / 159023104	48.08 / 52.17	16.182 / 15.169
NH3 cc-pVDZ	81872044 / 29606236	10776	212140032 / 202194944	1753.34 / 2065.91	792.113 / 1138.456
H2O STO-3G	10720544 / 10112352	1240	160055296 / 160186368	50.31 / 46.61	11.328 / 13.213
One-center Cartesian s+d	10505444 / 10539676	408	161267712 / 159629312	14.41 / 14.88	0.705 / 0.991

These timings were taken under heavier concurrent development load than the previous table; they must not be used as a regression comparison with that earlier run or as a general dispatch threshold. Streaming regenerates topology per build and was slower in three of these four comparisons. Tiny systems need not save logical memory either. The option addresses retained schedule memory, not a universal speedup.

A separate --trace-admission-memory probe on NH3/cc-pVDZ measured 8198006 / 80630 bytes live and 9979706 / 125583 bytes peak for stored / streaming admission in Python’s allocation tracer. This excludes opaque native allocations and perturbs timing; the table above uses untraced runs. The completed streaming plan reserves 27836764 logical bytes, including 25527888 modeled provider bytes. RSS also includes imports and the independent complete-source oracle. A smaller logical budget is not an RSS guarantee.

Integral and contraction work is unchanged between schedules. For NH3/cc-pVDZ, each audits 50625 ordered shell tiles and 1874161 requested primitive quartets, then uses 1893 shell calls and 125343 requested primitive quartets per spatial build. Each build executes 1414562 J+K scalar products, 101250 block contractions and 713398 transport scalar products. Maximum J/K differences against the independent source remain 4.31e-14 / 1.35e-14; the trial interaction energy error is 1.20e-13 hartree. All counters are measured execution work; the pair-orbit census is not substituted for them.

Current validation: 1586 passed across quartet, complex-Abelian, MANTA-reference, citation integrity and lane-classification tests. This includes 80 quartet cases, running the source, covariance, Cartesian, non-Abelian, displaced-source, energy-density finite-difference, fallback, mutation and budget checks with both schedules. Citation and schema checks are included in the larger count. Full source audit and exact/one-short factory refusal remain enforced before snapshots or native sessions. A separate foundation run passed 797 tests across shared groups, AO/SALC/GDF, k symmetry, periodic AO transport, retained-space sewing and finite mean-field states, with 16 existing spglib deprecation warnings. The two disjoint runs therefore passed 2383 tests in total.

Independent source review compared the actual enumeration against 66 separate cyclic, dihedral, A4 and S4 cases covering 53028 ordered members. Synthetic finite-array tests, including a nonorthogonal angular action, found maximum J/K Frobenius error 9.33e-16 on arbitrary complex densities. The review checked late-representative mutation and exact/one-short factory boundaries, and found no actionable defect. This is source/index/finite-array review evidence, distinct from the native-provider measurements above.

Remaining production gates are producer-side source/screening admission, measured cost-based execution policy, and combination with selection-rule block contractions. The ordinary real-AO pair quotient does not supply complex integral conjugation, antiunitary corepresentations, non-Abelian reduced products, periodic image/momentum scheduling, local projector transport or relaxed derivatives. Existing separate contracts for those capabilities remain in force.

Native quartet executor increment

executor="native" now moves the four-leg inverse-action transport, permutation indexing and arbitrary-complex-density contractions into C++. One call consumes one representative and all its admitted members. The stored/streaming schedules, P0 integral provider, complete numerical audit, source identity and representative digest checks are preserved. Native construction snapshots density and angular matrices; checked tile buffers are borrowed only during each serial call. NumPy remains the default and explicit fallback. No screening, state projection, MANTA integral kernel, SCF routing, periodic support or derivative capability is enabled.

The native core was rebuilt and checked against all 603 native/build inputs before validation. Fresh-process measurements use seven timed builds after warmup, one requested OpenMP/BLAS thread, the same source and complex Hermitian noninvariant density (seed 679), and the unchanged 1e-10 source tolerance. Native times include allocation/packing, owned density snapshots, provider calls, receipt/digest checks, angular transforms, contractions and immutable result export. Complete admission is separate.

Case / mode / schedule	Shell calls	Median NumPy / native build ms	Native admission ms	Maximum native J / K entry error
NH3 cc-pVDZ / none / stored	50625	751.786 / 321.368	1374.11	1.12e-14 / 5.41e-15
NH3 cc-pVDZ / permutation / stored	7260	302.753 / 52.538	660.71	2.00e-14 / 1.24e-14
NH3 cc-pVDZ / spatial / stored	1893	310.821 / 25.368	770.93	2.82e-14 / 1.36e-14
NH3 cc-pVDZ / spatial / streaming	1893	366.755 / 78.003	797.81	2.82e-14 / 1.36e-14
NH3 STO-3G / spatial / stored	81	7.712 / 0.825	29.16	4.00e-15 / 9.94e-16
H2O STO-3G / spatial / stored	76	4.421 / 0.676	19.05	1.34e-15 / 1.41e-15
One-center Cartesian s+d / spatial / stored	6	0.168 / 0.100	6.36	2.78e-16 / 4.45e-16

For the larger ammonia spatial case, native execution is about 12.3x faster with stored topology and 4.7x with streaming topology in this run. Streaming still spends time regenerating Python orbit objects. These are tile-adapter comparisons under development load, not a comparison against MANTA’s native ordered J/K builder or an end-to-end SCF speedup. Earlier timing tables were taken under different load. No timing threshold selects this path automatically.

All integral receipts and contraction counts match the corresponding NumPy build. NH3/cc-pVDZ spatial execution requests 125343 primitive quartets, accumulates 1414562 J+K scalar products in 101250 blocks and performs 713398 transport scalar products. It still audits 50625 ordered shell tiles at setup. This increment accelerates the executed operations without claiming another integral or contraction-count reduction. Different floating-point accumulation order changes roundoff: the largest native trial interaction energy error in these measurements is 1.74e-13 hartree. The existing source-residual bound continues to exclude arithmetic roundoff.

Case / mode / schedule	Logical live plan / combined native execution bytes	Process peak RSS NumPy / native bytes
NH3 cc-pVDZ / none / stored	83398312 / 83615480	235929600 / 235749376
NH3 cc-pVDZ / permutation / stored	80102572 / 80319740	214679552 / 214548480
NH3 cc-pVDZ / spatial / stored	80102572 / 80319740	211910656 / 212041728
NH3 cc-pVDZ / spatial / streaming	27836764 / 28053932	200654848 / 200228864
NH3 STO-3G / spatial / stored	10851544 / 10943784	160841728 / 161480704
H2O STO-3G / spatial / stored	9980704 / 10066832	160104448 / 160415744
One-center Cartesian s+d / spatial / stored	9476324 / 9666276	159956992 / 161775616

The combined reservation includes the live admitted plan plus native input, owned target/export, packed action and tile-scratch allowances. It is checked before packing or native construction. RSS includes imports, provider, plan and the independent complete-source oracle, and is not bounded by the logical reservation. No complete AO ERI tensor is retained by the executor.

The corrected native artifact passes 171 focused tests, including 126 quartet cases. Coverage includes native/Python J/K and covariance on nonsymmetric Hermitian and non-Hermitian densities, metric-aware Cartesian actions, reordered non-Abelian groups, separate spin calls, density-energy finite differences, exact unreduced fallback, residual bounds, source mutations, strict array types/layout/alignment, checked integer overflow and exact/one-short native plus aggregate resource admission. An independent unequal-axis four-leg einsum checks every real-ERI permutation and ownership of captured density/actions.

Another 2258 compatibility tests pass across shared symmetry, fitting, k-point symmetry, SALCs, AO/Bloch actions, orbital sewing, mean-field state, citation integrity and test-lane classification. The two disjoint runs total 2429 passed; the compatibility run reports 16 existing spglib deprecation warnings. This preserves the earlier foundations without expanding the native executor’s admitted domains.

Independent source review identified a binding-error path that could export earlier partial accumulator contents after malformed input. Dispatched binding failures now invalidate the accumulator, as native arithmetic/index failures already did. Five permanent regressions submit a valid partial contribution followed by dtype, layout, rank, alignment or nonarray failure, then require both export and further accumulation to refuse. The final review found no additional issue; its separate index-arithmetic comparison covered 12 unequal-axis fixtures and 192 member visits with maximum relative J/K error 6.03e-16. That review is distinct from compiled runtime testing.

Next production work remains provider-qualified screening and scalable source admission, native schedule/producer batching to reduce Python callbacks, and measured dispatch through the shared Fock boundary. Complex integral tensors, irreducible-product CC contractions, periodic momentum and local-space transport, gradients and stress retain their separate gates.

Shared-density batch increment

The next coherent execution increment is jk_batch: a shared source traversal for independent spin or response trial densities. Stored and streaming schedules preserve the same complete admission, representative digests and 1e-10 source tolerance. No density is symmetrized, made Hermitian or assumed to be related to another channel. Each channel has its own J/K and residual bound; the actual integral and angular work is counted once for the batch. This follows linearity of the existing contraction and adds no new group or source admission.

The matching native extension was rebuilt and checked against all 603 native/build inputs. Fresh processes use seven timed builds after warmup, one requested OpenMP/BLAS thread and seed 679. Each separate/shared pair uses identical independent complex Hermitian noninvariant densities and the same unscreened MANTA P0 source. An independent all-ordered-tile tensor supplies each channel’s oracle. Timings include snapshots, allocation, source/digest checks and immutable result export. They exclude complete source admission and do not measure MANTA’s native J/K builder or SCF.

Case / executor / schedule / densities	Shell calls separate / shared	Primitive requests separate / shared	Median separate / shared ms	Maximum shared J / K entry error
NH3 cc-pVDZ / native / stored / 2	3786 / 1893	250686 / 125343	46.110 / 23.934	2.82e-14 / 1.43e-14
NH3 cc-pVDZ / native / stored / 8	15144 / 1893	1002744 / 125343	182.216 / 28.370	4.09e-14 / 2.81e-14
NH3 cc-pVDZ / native / streaming / 2	3786 / 1893	250686 / 125343	137.347 / 69.245	2.82e-14 / 1.43e-14
NH3 cc-pVDZ / NumPy / stored / 2	3786 / 1893	250686 / 125343	577.195 / 323.802	4.31e-14 / 1.97e-14
H2O STO-3G / native / stored / 2	152 / 76	12312 / 6156	1.252 / 0.635	1.36e-15 / 1.79e-15
One-center Cartesian s+d / native / stored / 2	12 / 6	12 / 6	0.161 / 0.086	4.58e-16 / 1.78e-15

The two/eight-channel stored native comparisons improve by about 1.93x/6.42x. Each reports the same maximum J/K errors as its separate-build comparison. Across native measurements the largest trial interaction-energy error is 1.74e-13 hartree. Full source admission remains mandatory: ammonia takes 0.728 to 0.807 s in these processes, still auditing 50625 ordered shell tiles and 1874161 primitive requests. Setup is paid once for either reuse policy.

Case / densities	J+K scalar products, both policies	Block contractions, both policies	Angular scalar products separate / shared
NH3 cc-pVDZ / 2	2829124	202500	1426796 / 713398
NH3 cc-pVDZ / 8	11316496	810000	5707184 / 713398
H2O STO-3G / 2	9604	2500	1422 / 711
One-center Cartesian s+d / 2	9604	64	0 / 0

Case / executor / schedule / densities	Live-plan + execution logical bytes separate / shared	Process peak RSS bytes separate / shared
NH3 cc-pVDZ / native / stored / 2	80319740 / 80400604	213401600 / 213221376
NH3 cc-pVDZ / native / stored / 8	80319740 / 80885788	213286912 / 213123072
NH3 cc-pVDZ / native / streaming / 2	28053932 / 28134796	202194944 / 201654272
NH3 cc-pVDZ / NumPy / stored / 2	80102572 / 80329836	213286912 / 213483520
H2O STO-3G / native / stored / 2	10066832 / 10071664	161529856 / 162201600
One-center Cartesian s+d / native / stored / 2	9666276 / 9671108	160972800 / 161054720

The separate execution budget covers one active call, while the shared budget covers the entire batch. The benchmark additionally owns density and collected result buffers: 80736 bytes for two ammonia channels, 322944 for eight, and 4704 for the smaller cases. RSS includes these buffers, imports, source, plan and the independent dense oracle. Logical reservation and RSS are distinct, and small RSS changes are not claimed as memory savings. Shared execution reserves O(batch*n**2) density/target storage; it does not retain a full ERI tensor or one angular tile per channel.

The focused quartet, complex-Abelian and MANTA reference run passes 225 tests, including 54 new batch cases. They cover both schedules and executors, C2v/C3v/metric-aware Cartesian actions, all reduction modes, non-Hermitian and zero channels, nonsymmetric-density covariance, singleton shape, independent ordered MANTA integrals, immutable outputs and density snapshots, exact/one-short caps, invalid/overflowing batch counts and a late tile/source failure. A failure in one native channel poisons the complete batch. Broken-spin UHF assembly agrees with the identical unreduced source; channel-resolved density-energy finite differences and linear J/K response agree without relaxing existing tolerances. These density derivatives are not nuclear gradients or stress.

Another 2258 compatibility, citation and lane-classification tests pass on this rebuilt core, for 2483 passed across the two disjoint runs. There are 16 existing spglib deprecation warnings. The compatibility run preserves the earlier shared, fitting, multi-k, AO/Bloch, SALC, orbital-sewing and retained-state foundations; it does not authorize those domains for the molecular batch executor.

Independent bounded source review found no actionable issue. A separate finite-array exercise ran 36 cases through the actual NumPy batch function with synthetic admitted-plan metadata (maximum relative J/K error 3.864e-16). Another 36 cases compared an independent transcription of the native channel/transport indexing with four-leg einsum (5.006e-16). These source/algebra checks cover budget/census arithmetic, ownership, per-channel bounds, whole-batch refusal and shared receipts; they are separate from the compiled molecular tests and timing measurements above.

Next production gaps are unchanged: provider-qualified screening/scalable source admission, native schedule/provider batching and method-owned Fock dispatch with measured costs. At this increment, batches computed both J and K for every channel; selective targets are implemented in the subsequent increment below. Complex integral sources, non-Abelian reduced CC products, periodic momentum/local-space transport and analytic derivatives require their own acceptance evidence. NumPy and separate-build fallbacks remain explicit; no solver default or production-authorization flag changes.

Selective J/K target increment, October 2026

jk_batch(..., targets=...) now accepts one immutable j, k or jk selector per input density. The default still requests both. NumPy and native execution skip unrequested contractions and target allocations; compact immutable outputs carry explicit input-channel mappings. J-only and K-only batches return an empty array for the absent family, rather than a matrix of zeros. Complete source admission, residual norms, covariance conventions and representative digests remain unchanged.

For an unrestricted build, three inputs [D_alpha+D_beta,D_alpha,D_beta] with ('j','k','k') replace four outputs from the two-spin both-target batch. This saves one quarter of the actual contraction terms and returned target bytes. The extra total-density input means total reservation is not reduced. Method-owned spin factors, Fock construction and energy assembly remain outside the executor; no production solver is enabled.

The final native artifact was rebuilt and checked against all 603 native/build inputs. The following fresh-process measurements use 11 timed builds after warmup, one requested OpenMP/BLAS thread, seed 679, the identical unscreened MANTA P0 source and unchanged 1e-10 source tolerance. Trial densities are complex Hermitian and noninvariant. Both-target native requests retain the original paired J/K loop. Timings include the full repeated-build adapter, but exclude mandatory admission. These measurements were made under development load and are not directly comparable with the earlier tables.

Case / executor / schedule	Request	Scalar products	Block contractions	Returned target bytes	Median build ms
NH3 cc-pVDZ / native / stored	8 densities, both	11316496	810000	215296	43.740
NH3 cc-pVDZ / native / stored	8 densities, J only	5658248	405000	107648	53.709
NH3 cc-pVDZ / native / stored	8 densities, K only	5658248	405000	107648	52.863
NH3 cc-pVDZ / native / stored	2 spins, both	2829124	202500	53824	44.925
NH3 cc-pVDZ / native / stored	Total-J and spin-K	2121843	151875	40368	48.259
NH3 cc-pVDZ / native / streaming	2 spins, both	2829124	202500	53824	130.453
NH3 cc-pVDZ / native / streaming	Total-J and spin-K	2121843	151875	40368	137.400
NH3 cc-pVDZ / NumPy / stored	2 spins, both	2829124	202500	53824	626.022
NH3 cc-pVDZ / NumPy / stored	Total-J and spin-K	2121843	151875	40368	713.182
H2O STO-3G / native / stored	2 spins, both	9604	2500	3136	1.239
H2O STO-3G / native / stored	Total-J and spin-K	7203	1875	2352	1.246
One-center Cartesian s+d / native / stored	2 spins, both	9604	64	3136	0.143
One-center Cartesian s+d / native / stored	Total-J and spin-K	7203	48	2352	0.194

The saved terms and output storage did not establish a wall-time gain: the stored native ammonia spin request is about 7.4% slower in this run, and its eight-density J-only and K-only requests are about 23% and 21% slower. Selected-target execution therefore remains explicit. These are execution/memory capabilities, not an automatic performance policy. Native selection specialization and stable cost measurements remain prerequisites for default dispatch. No timing threshold or scientific tolerance was relaxed.

All ammonia requests still make 1893 shell calls, request 125343 primitive quartets and execute 713398 angular scalar products per build. H2O uses 76 calls, 6156 primitive requests and 711 angular terms; the Cartesian case uses 6 calls, 6 primitive requests and no angular terms. No additional integral or angular reduction is claimed. Ammonia admission takes 1.188 to 1.610 s here and still evaluates 50625 ordered tiles and 1874161 primitive requests. Sampling or weakening that audit is not enabled by target selection.

Against independent all-ordered-tile references, the largest native J/K entry errors are below 4.09e-14/2.81e-14; the NumPy selected-spin errors are below 5.18e-14/1.97e-14. The largest measured native unrestricted interaction-energy error is 2.40e-13 hartree, with NumPy below 2.48e-13. J-only and K-only runs do not report a complete interaction energy. Source error bounds remain indexed by input density and exclude arithmetic roundoff.

Case / executor / schedule	Live-plan + execution bytes both / selected	Peak process RSS bytes both / selected
NH3, 8 densities / native / stored, J only	80885788 / 80670492	220512256 / 219152384
NH3, 8 densities / native / stored, K only	80885788 / 80670492	220512256 / 219348992
NH3, spin pair / native / stored	80400604 / 80400732	219594752 / 219119616
NH3, spin pair / native / streaming	28134796 / 28134924	207814656 / 208044032
NH3, spin pair / NumPy / stored	80329836 / 80329964	220561408 / 217989120
H2O, spin pair / native / stored	10071664 / 10071792	167788544 / 167575552
Cartesian s+d, spin pair / native / stored	9671108 / 9671236	167198720 / 167247872

One-family ammonia execution saves 215296 logical bytes, including the omitted targets and their immutable exports. For the selected spin request, an additional total-density snapshot replaces the omitted output storage; selector metadata raises the logical total by 128 bytes. RSS also includes imports, source, plan, the independent dense oracle and benchmark-owned buffers. The spin benchmark additionally retains its original two-spin input: 26912 bytes for ammonia and 1568 for the small cases. RSS differences are not attributed to the logical reservation or claimed as general savings.

The final core passes 259 focused quartet, complex-Abelian and MANTA tests, including 34 new target-selection cases. New coverage includes mixed channel mappings and nonsymmetric-density covariance for C2v/C3v and metric-aware Cartesian actions, J-only/K-only empty outputs, exact/one-short reservations before packing, invalid selectors and native descriptor types, selector ownership, and whole-result refusal after a late source mutation. A native test makes the omitted contraction overflow if evaluated: the selected request succeeds and the both-target request refuses. This checks actual omission, not just returned shapes or nominal counts. Independent dense integrals validate broken-spin Focks, unrestricted energies, empty beta channels, complex transition densities and channel-resolved density finite differences. These are not nuclear-gradient or stress tests.

Another 2258 compatibility, citation and lane-classification tests pass, for 2517 passed across the two disjoint final-core runs. There are 16 existing spglib deprecation warnings. Earlier shared, fitting, multi-k, AO/Bloch, SALC, orbital-sewing and retained-state foundations remain covered; their coverage does not admit those sources to the molecular target executor.

Remaining production gaps are source-qualified screening and scalable admission, native schedule/provider batching, and measured method-owned dispatch. Complex integral kernels, antiunitary/projective actions, non-Abelian reduced CC products, periodic momentum/local-space transport, gradients and stress still require their separate representation and source acceptance. The existing both-target, NumPy and unreduced-source fallbacks remain explicit; no production-authorization flag changes.

Selected native contractions and Fock-state compatibility, October 9, 2026

Native selected-target execution now resolves the J or K matrix strides once per member, shares those addresses across density channels, and handles scalar-shell tiles directly. It retains every finite-arithmetic check and each output’s accumulation order. The paired both-target path, complete source audit, source digests, tolerances, budgets and public API remain unchanged. No additional integral, transport or contraction reduction is claimed.

The comparison uses the previous native artifact and the rebuilt artifact in alternating fresh processes, with three processes per case/artifact and 21 timed builds after warmup. Both artifacts use the same Python adapter, seed 679, unscreened P0 source and 1e-10 source tolerance. One OpenMP/BLAS thread is requested. Timings include provider calls, transport, contraction and result export; mandatory source admission remains separate. Each table entry is the median of process medians, with their minimum/maximum in brackets. The benchmark also exports all individual build timings.

Native case / request	Previous build ms [min, max]	Current build ms [min, max]
NH3 cc-pVDZ stored, two spins both	23.323 [23.144, 24.132]	23.284 [23.130, 24.454]
NH3 cc-pVDZ stored, total-J/spin-K	23.749 [23.498, 23.990]	23.985 [23.537, 24.376]
NH3 cc-pVDZ stored, eight J targets	25.585 [25.551, 25.590]	25.091 [25.012, 26.278]
NH3 cc-pVDZ stored, eight K targets	25.685 [25.431, 25.823]	25.032 [24.911, 25.068]
NH3 cc-pVDZ streaming, total-J/spin-K	69.207 [68.898, 69.774]	69.187 [69.175, 69.388]
H2O STO-3G stored, total-J/spin-K	0.630 [0.626, 0.634]	0.635 [0.630, 0.639]
Cartesian s+d stored, total-J/spin-K	0.095 [0.092, 0.129]	0.092 [0.091, 0.094]

The eight-density J/K-only medians decrease about 1.9%/2.5%; the J ranges overlap. Mixed spin requests do not establish a timing improvement. Current stored selected-spin execution remains about 3.0% slower than both-target execution despite 25% fewer contractions. These bounded measurements do not justify automatic dispatch or a universal speedup. NumPy and unreduced-source fallbacks remain available, and scientific acceptance thresholds are unchanged.

For both artifacts, every ammonia build still evaluates 1893 representative shell tiles and 125343 primitive requests, with 713398 angular scalar products. Two-spin both/selected execution performs 2829124/2121843 scalar products and 202500/151875 block contractions. Eight J-only or K-only channels perform 5658248 scalar products and 405000 contractions. Admission still evaluates 50625 ordered tiles and 1874161 primitive requests; it took 0.705 to 0.764 s across these runs. H2O remains at 76 shell calls, 6156 primitive requests, 711 angular terms, 7203 selected scalar products and 1875 contractions. Cartesian s+d remains at 6 shell calls/primitive requests, no angular terms, 7203 selected scalar products and 48 contractions.

Case / request	Logical live-plan + execution bytes, unchanged	Peak RSS bytes, previous / current
NH3 stored, two spins both	80400604	217300992 / 217235456
NH3 stored, total-J/spin-K	80400732	217055232 / 217219072
NH3 stored, eight J targets	80670492	216940544 / 217038848
NH3 stored, eight K targets	80670492	217104384 / 216907776
NH3 streaming, total-J/spin-K	28134924	205340672 / 205340672
H2O stored, total-J/spin-K	10071792	165363712 / 165265408
Cartesian s+d stored, total-J/spin-K	9671236	165085184 / 165281792

RSS is the maximum over each artifact’s three fresh processes and includes the benchmark’s independent reference and Python/native runtime. Its small differences are not attributed to storage reduction. Returned target bytes are unchanged: ammonia both/selected spin 53824/40368, eight J-only or K-only 107648, and small selected-spin cases 2352. Source identities, receipts, counts, logical bytes and reference errors agree between compared artifacts. Maximum native J/K errors remain below 4.09e-14/2.81e-14 and the largest trial unrestricted interaction-energy difference below 2.40e-13 hartree.

The rebuilt core is newer than all 603 native/build inputs. 2539 tests pass, including 22 new cases for unequal shell axes and every ERI permutation, complex nonsymmetric transition densities, exact selected/both-target results, owned inputs and whole-result refusal on later-channel overflow. Existing source rejection, scalar-target omission, energy/density-response, fitting, Gamma/multi-k, AO/Bloch, sewing and retained-state checks remain covered. There are 16 existing spglib deprecation warnings. This coverage preserves the periodic foundations without admitting a periodic source to this executor.

scripts/check_symmetry_fock_contract.py also passes 24 optional snapshot crossings against explicitly supplied Fock-workstream source files. It reads only the draft operator/state modules into an isolated namespace and records their hashes, using this checkout’s native core. Water, NH3 and Cartesian s+d, both schedules/executors and full/empty beta channels agree with independent all-ordered P0 electronic-energy/Fock references. Maximum Fock/electronic-energy errors are 3.56e-15/7.11e-15. The diagnostic sets the nuclear component to zero and claims no converged total energy. Snapshots survive subsequent builds and input mutation and refuse write enablement. Reported retained state arrays are 4032 bytes for water/Cartesian and 5248 for NH3, additional to executor storage; this is not a bounded production memory admission.

The Fock object remains a separate, uncommitted draft with unresolved energy ownership/identity review findings. This crossing does not accept those semantics or enable production routing. The shared design now records the method-owned immutable density/Fock/energy boundary and PBC Parity’s physical AC/BD exchange support, wider K outputs, k weights, AO gauges, zero-mode and screening constraints. MANTA continues to own kernels, screening and bubble hierarchies. Next production capabilities remain scalable source-qualified admission/screening, provider/schedule batching and method-owned dispatch. Complex integral sources, non-Abelian reduced CC products, periodic/local space execution, nuclear gradients and stress require separate acceptance.

Source-qualified whole-orbit screening

The next increment adds QuartetScreening and jk_batch(screening=...). The literature assessment distinguishes measured finite-source omission norms from rigorous kernel bounds and empirical QQR/CSA estimates. The design specifies mask closure, correct density/operator variance, identities and the MANTA/Fock/PBC boundary. The developer reference gives the API, budgets and explicit fallbacks. Production defaults remain unchanged.

Each stored audit now records full ordered-source bytes in a digest and complete-orbit source/reconstruction norms. The immutable native P0 producer and session are required before future omitted reads can be skipped. A fixed mask contains whole orbits and has its own numerical-source identity; screen-policy identity and density-specific bounds stay separate. The existing 1e-10 source tolerance is unchanged. This is a bounded finite numerical certificate, with norm and contraction roundoff excluded, not a producer analytic error bound or scalable prescreening implementation.

Measurements below use three fresh processes per case and mask state, 21 timed native builds after warmup per process, alternating masked/unmasked order, one requested OpenMP/BLAS thread, seed 679 and total-J/alpha-K/beta-K channels. Both use the same immutable P0 source and the current stored audit. The explicit tensor omission budget is 1e-12. Timings include source calls, transport, contraction, receipt checks and exports; audit and mask creation are separate. The complete ordered reference is contracted both before and after applying the identical mask. These are trial-density measurements, not converged SCF, CC or gradient results.

Case	Actual representative calls, unmasked / masked	Requested primitive quartets, unmasked / masked	J/K scalar products, unmasked / masked	Block contractions, unmasked / masked	Median build ms, unmasked / masked
H2O STO-3G, C2v	76 / 68	6156 / 5508	7203 / 6267	1875 / 1755	0.6350 / 0.5774
NH3 cc-pVDZ, C3v	1893 / 1763	125343 / 104454	2121843 / 2059815	151875 / 149271	24.0571 / 22.6035
Cartesian s+d, C3v action	6 / 6	6 / 6	7203 / 7203	48 / 48	0.09337 / 0.09358

The three process medians span 0.631-0.645 / 0.574-0.582 ms for water, 23.600-24.411 / 22.111-22.766 ms for ammonia and 0.09317-0.09642 / 0.09358-0.09592 ms for Cartesian s+d. These measurements show about 9% and 6% lower build medians in water and ammonia; the Cartesian case omits nothing and has no demonstrated speedup. No automatic dispatch policy follows from this small set. Ammonia angular scalar products change from 713398 to 712318. Water’s 711 and Cartesian s+d’s zero are unchanged.

Case	Logical live-plan/execution bytes, unmasked / masked	Total process peak RSS range, bytes	Complete audit tiles / primitive requests	Audit ms range	Mask creation ms range
H2O STO-3G	10087152 / 10110704	167247872-168083456	625 / 50625	18.2-28.6	0.057-0.073
NH3 cc-pVDZ	81330012 / 81818716	219578368-220528640	50625 / 1874161	973-1086	0.887-0.899
Cartesian s+d	9672004 / 9677636	167182336-167542784	16 / 16	5.08-5.89	0.019-0.028

The full stored inventory remains live. Masks increase the conservative reservation; they do not reduce output storage or claim an RSS saving. Target arrays remain 2352, 40368 and 2352 bytes respectively. RSS includes imports, provider, plan, densities, targets and independent dense references. The new per-orbit norms/digest increase admission work relative to the earlier audit measurements; complete source evaluation counts are unchanged. This setup cost is never included in a claimed repeated-build saving.

Water omits 40 ordered tiles containing numerical zeros. Ammonia omits 868 ordered tiles and 20676 scalar ERI values, with independently checked omitted Frobenius norm 4.15022e-16; Cartesian s+d omits none at this cap. Maximum J/K differences against the identical masked ordered source are 8.92e-15 / 1.79e-15, 3.52e-14 / 1.43e-14 and 8.96e-16 / 1.78e-15. The unscreened comparisons stay inside the same rounded envelopes. The largest trial UHF interaction-energy difference is 2.43e-13 hartree against the masked reference and 2.42e-13 against the unscreened reference. Ammonia per-input matrix bounds are approximately 1.771e-12, 1.266e-12, 1.191e-12; these include retained reconstruction residual and omission, with arithmetic roundoff still separate.

Regression tests also use deliberately large diagnostic budgets to exercise nonzero omissions, never as proposed production tolerances. They verify identical-source integrals/J/K, per-density and method-weighted energy bounds, broken-spin assembly, non-Hermitian covariance, density-energy finite differences, selected and absent targets, all-omitted zero-work execution, immutable receipts, exact/one-short budgets and incompatible-domain refusal. A three-center Cartesian-d fixture measures an orbit norm of 0.544744, where a representative norm times square-root multiplicity gives 0.516083. The latter would wrongly admit a 0.52 tensor budget; the implemented complete-orbit norm refuses that omission. This is separate from the smaller Cartesian s+d timing fixture above.

The matching native core was unchanged and newer than all 603 native/build inputs. Validation with Python 3.14 and NumPy 2.5.3 completed 2560 passed, 9 skipped, with 16 existing spglib warnings. The focused quartet, Abelian and MANTA suite contributes 302 passed, 9 skipped; skips are explicitly inapplicable streaming-screen cases, and streaming refusal is tested. The larger run repeats the shared, AO/SALC, fitting, periodic k/Bloch, orbital-sewing, retained-state, citation and test-manifest files from the previous increment. It preserves odd/even meshes, fractional translations, complex actions and degenerate-space evidence without admitting a periodic screened source. Fitting factors, CC residuals and nuclear derivatives are unchanged and are not acceptance claims for this mask. The Sphinx documentation build and staged privacy preflight pass; Sphinx retains the two pre-existing unrelated cross-reference warnings.

Coordination confirmed that MANTA owns kernel bounds, screening and bubble hierarchies; its current source/tile seam has no general rigorous omission certificate. The Fock workstream consumed 24 original and 12 screened snapshot crossings against its updated energy-owning draft. Maximum screened Fock/electronic-energy errors are 1.78e-15 / 1.07e-14. Fixed mask receipts travel in source provenance; per-density bounds remain separate. This optional crossing is not a dependency or production memory certificate. PBC Parity confirmed unchanged physical AC/BD support, wider exchange output support, metric-domain sensitivity, weights, image gauges and Ewald rules.

Complete screened molecular SCF acceptance

On 2026-10-11 a complete RHF calculation through vq exercised the native screened quartet executor at every iteration on runtime commit ed9bfb42, which contains the symmetry landing 5857803f. The case is neutral singlet NH3, pure cc-pVDZ, 29 AOs and 15 shells. In bohr, N is at (0,0,0.3) and the three H atoms are at (1.7 cos(t),1.7 sin(t),-0.7), with t = 0, 2*pi/3, 4*pi/3. The calculation starts from an orbital-rotated core guess. The immutable P0 source, 1e-10 source tolerance and explicit 1e-12 tensor omission budget are unchanged.

Three complete SCF calculations use the screened native executor, an independently evaluated ordered tensor with the identical mask, and that ordered tensor without the mask. The latter two are dense correctness oracles, not timing baselines. All converge in 16 iterations without averaging the produced J/K or Fock matrices.

Reference	Total energy, hartree	Absolute difference from screened SCF, hartree
Screened native quartet SCF	-56.18855210065033	0
Identical-mask ordered tensor SCF	-56.18855210065026	7.11e-14
Unmasked ordered tensor SCF	-56.18855210065033	0 at reported precision
Native full-source RHF driver	-56.18855210065040	7.11e-14
ORCA 6.1.1 RHF/cc-pVDZ, VeryTightSCF, NoRI	-56.188552099947	7.03e-10

The existing ORCA calculation was reused; its energy difference passes the declared 1e-8 hartree comparison threshold. ORCA uses its own integral and screening conventions, so this chemical reference does not replace the identical-source checks. Final same-mask density/J/K differences are 8.78e-14 / 2.13e-14 / 1.15e-14. Reassessment of the saved S/H/D/J/K arrays gives ten electrons to 4e-15, maximum D S D - 2 D residual 2.00e-15, Fock Hermiticity residual 5.55e-17, metric-orthogonalized commutator norm 3.35e-10 and density closure 8.57e-11. The energy-change, commutator and closure gates remain 1e-11, 1e-9 and 1e-10 respectively.

An arbitrary complex non-Hermitian trial density also passes the raw operator checks: same-mask J/K errors are 1.78e-14 / 6.40e-15, and the maximum covariance error over the six C3v operations is 2.98e-14, using D' = U D U^dagger and U^dagger F[D'] U = F[D]. These checks are separate from the converged state. The independently measured omitted tensor norm is 5.51e-16; the retained reconstruction residual is 2.25e-14.

Each screened SCF build performs 1763 shell calls, 104454 requested primitive quartets, 1373210 J/K scalar products and 99514 block contractions. The 16 builds total 28208 shell calls and 1671264 primitive requests. Qualification separately evaluates 50625 ordered tiles and 1874161 primitive quartets. With one requested OpenMP/BLAS thread, the single-run admission takes 2.608 s, mask creation 1.578 ms, median screened build 45.19 ms and the screened SCF loop 0.731 s. The entire acceptance job, including all oracles and trial-density checks, takes 10.84 s and peaks at 313028608 bytes RSS. The logical execution reservation is 81737738 bytes; the two dense tensor oracles alone retain 11316496 bytes. These are measured costs, not a new cross-machine speedup or memory-saving claim.

This accepts the bounded opt-in molecular screened SCF experiment. It does not enable production dispatch or extend admission to native MANTA kernels, periodic sources, fitting, CC residuals, nuclear gradients or stress.

Next production capabilities are scalable producer-issued bound/support certificates, compact streaming mask evidence, native provider/schedule batching and method-owned acceptance/dispatch. Density-dependent screening, complex integral sources, RI/CD and retained local spaces, non-Abelian reduced CC tensors and periodic/BIPOLE/CCM/chi screening require their own source and representation admission. Analytic gradients and stress remain separate method targets including response, Pulay, fitting and support/mask derivatives. The unscreened, NumPy and existing streaming fallbacks remain available with unchanged scientific tolerances.

Native molecular HF bridge acceptance

The explicit symmetry_molecular_hf consumer now runs the admitted fixed P0 mask through the existing native RHF/UHF drivers and constructs method-owned FockBuild snapshots. This closes the standalone-diagnostic-to-native-host integration gap. It remains opt-in and experimental; no default runner, periodic producer, fitting, CC or derivative admission changes.

Fourteen focused regressions passed. They cover C2v water, full C3v ammonia, nonunitary Cartesian s+d actions, nonsymmetric real densities, NumPy/native execution, byte admission, complex-input and unsupported-kernel refusal, owned H/D/frame states, rectangular retained frames, independent spin channels, and finite differences of the HF energy with respect to density. These are density-response checks, not nuclear-gradient or stress acceptance.

A complete queued calculation used the candidate Python module with a healthy already-built native development runtime. Loaded runtime files were hashed before and after the calculation and stayed unchanged. This is candidate-module acceptance, not evidence of installed default production dispatch. The same NH3 geometry, cc-pVDZ basis, source tolerance 1e-10, fixed omitted tensor budget 1e-12, native energy tolerance 1e-11 and gradient tolerance 1e-9 as the preceding acceptance were retained. The existing ORCA reference was reused. Two additional UHF/STO-3G calculations used H2 at 4.00 and 4.02 bohr with opposite atom-localized initial spin densities.

Calculation	Energy, hartree	Difference from full-source native SCF, hartree	Ordered identical-mask Fock max error
NH3 RHF/cc-pVDZ	-56.188552100650256	7.11e-14	3.42e-14
H2 UHF, 4.00 bohr	-0.9358423283198118	4.45e-16	1.39e-17
H2 UHF, 4.02 bohr	-0.9357442504982110	2.23e-16	1.12e-16

The NH3 ORCA difference is 7.03e-10 hartree, below the unchanged 1e-8 comparison gate. Re-evaluated native energy, common HF state energy and the independent identical-mask ordered contraction agree within 5.69e-14 hartree. H2 converges in five iterations at each geometry, with final ||Da - Db||_F = 1.39525 / 1.39596 and one electron in each spin to roundoff. The integral reduction therefore does not force the electronic state to obey atom-exchange symmetry. No separate ORCA reference was acquired for these broken-spin finite-source H2 checks.

NH3 qualification costs 50625 ordered shell calls and 1874161 requested primitive quartets. A terminal fused J/K build uses 1763 shell calls, 104454 primitive requests, 1373210 scalar products, 99514 block contractions and 712318 angular-transport scalar products. The native driver makes 68 actual J/K calls over 15 iterations, including its additional solver work, for 119884 shell calls, 7102872 primitive requests, 56988215 scalar products and 4129831 block contractions. The counts are not inferred from iteration count. Each H2 native UHF run makes 24 calls, 96 shell calls and 7776 primitive requests. Its separate terminal three-channel HF-state evaluation shares four representative calls instead of the native driver’s three separate traversals.

With one requested OpenMP/BLAS thread, the NH3 audit takes 8.010 s and native SCF 9.324 s; the terminal fused build takes 72.96 ms. The two H2 SCFs take 8.60 and 5.27 ms. These single-run integration timings are not isolated speedup benchmarks and are not compared across machines with earlier results. Peak RSS for the combined tests and acceptance is 253706240 bytes. NH3’s maximum J/K logical reservation is 81964746 bytes; the evaluated-state array storage is separately 27144 bytes. For H2 those values are 9193288 and 224 bytes, with 9194568 bytes reserved for the terminal three-channel batch. Full-audit/stored-inventory cost remains a production scaling limitation.

Next work is compact producer-bound screening and method dispatch with source and accuracy admission, plus native UHF channel batching and terminal/output state integration. MANTA owns rigorous bounds, support receipts and bubble hierarchies. Fock unification owns shared evaluated-state semantics; this adapter supplies only molecular HF factors and its source receipt. Periodic Seitz, full image shifts, reciprocal wraps, phases, weights and finite-domain qualification, as well as distinct CCM/chi sources, retained-space transport, non-Abelian reduced CC tensors, gradients and stress retain their own gates.

Compact streamed screening acceptance

The streaming pair-stabilizer plan now accepts an explicit maximum_omitted_norm during its complete source audit and exposes a fixed plan.screening certificate. It retains one packed bit per orbit and one retained-representative digest, instead of complete quartet member lists, norms and hashes. The schedule-order first-fit policy can differ from the stored smallest-first policy; each result is checked against its own exact masked source. Full actual-member norms preserve the Cartesian metric boundary. The unchanged molecular JKBuilder and HF FockBuild adapter consume either certificate. Default dispatch remains experimental and off.

Twenty-eight focused regressions passed, comprising fourteen new compact screen tests and the fourteen existing HF bridge tests. New coverage includes C2v water, C3v ammonia, nonunitary Cartesian s+d and three-center Cartesian d shells, general complex non-Hermitian density covariance, native and NumPy execution, all/zero omission, selected channels, HF density finite differences, resource refusal before reads, mutable-source refusal, foreign audits and changed retained-tile digests. No final-matrix symmetrization substitutes for these operator checks.

A queued calculation used candidate Python modules with a healthy already-built native runtime; all 375 loaded files hashed before and after stayed unchanged. The NH3 geometry, cc-pVDZ basis, source tolerance 1e-10, omitted tensor budget 1e-12, native energy/gradient tolerances 1e-11 / 1e-9 and ORCA comparison gate 1e-8 were unchanged. The two H2 UHF/STO-3G cases retain opposite atom-localized initial spin densities and the 4.00/4.02 bohr separations. Each case ran reduced, independent ordered identical-mask, and full-source native SCFs, followed by independent terminal Fock and energy checks.

Calculation	Energy, hartree	Identical-mask SCF difference, hartree	Full-source SCF difference, hartree	Terminal identical-mask Fock max error
NH3 RHF/cc-pVDZ	-56.188552100650256	4.27e-14	7.11e-14	3.42e-14
H2 UHF, 4.00 bohr	-0.9358423283198118	0	4.45e-16	1.39e-17
H2 UHF, 4.02 bohr	-0.9357442504982110	2.23e-16	2.23e-16	1.12e-16

NH3 again agrees with the existing ORCA reference within 7.03e-10 hartree and converges in 15 iterations. Both H2 cases converge in five iterations, retain spin-density differences 1.39525 / 1.39596, and have one electron per spin to roundoff. The displaced calculation is an energy check; nuclear gradients and stress remain unqualified. The H2 reference is the independently contracted identical source, with no separate external-program parity claim.

NH3’s 1893 orbits need 237 mask payload bytes and 10776 retained pair-schedule array bytes. These exclude object overhead; the full conservative J/K logical reservation is 28289620 bytes, including source, plan, native accumulator and bridge buffers. HF state arrays separately occupy 27144 bytes. The mask’s worst-case storage remains quartic in shell count despite its compact encoding. Whole-job peak RSS, including tests, source oracles and all SCFs, is 282673152 bytes; neither the mask payload nor the logical reservation is an RSS bound.

The audit still evaluates 50625 ordered shell tiles and 1874161 requested primitive quartets. The mask omits 130 representatives, 868 ordered tiles and 20676 integral values, with omitted norm 4.15e-16 and retained reconstruction residual 2.06e-14. Each terminal fused J/K uses 1763 actual shell calls, 104454 primitive requests, 1373210 scalar products, 99514 block contractions and 712318 angular-transport products. The native NH3 solver’s 68 actual J/K builds total 119884 shell calls, 7102872 primitive requests, 56988215 scalar products and 4129831 block contractions. Each H2 solver uses 24 builds, 96 shell calls, 7776 primitive requests and 384 scalar/block contractions; its terminal three-channel evaluation shares four representative calls.

With one requested OpenMP/BLAS thread, the single-run NH3 audit takes 2.825 s, native screened SCF 12.634 s, and terminal J/K 133.0 ms. H2 SCFs take 23.83 and 20.26 ms. These include streaming schedule regeneration and are not an isolated speedup comparison with the preceding stored-plan measurements. The change reduces retained schedule metadata; it does not claim faster SCF.

Next production capabilities remain rigorous MANTA-issued bound/support certificates that avoid a full numerical audit, source/accuracy-qualified public dispatch, native UHF channel batching and terminal/output state integration. MANTA owns kernel bounds and BUPO/bubble construction; symmetry supplies compatible representatives, stabilizers and mask closure. Periodic Seitz/images/wraps/phases/weights/momentum, distinct finite CCM/chi sources, RI/CD and local retained spaces, reduced non-Abelian CC tensors, complex integral kernels/antiunitary actions, gradients and stress keep their separate admission and acceptance requirements. The unmasked and NumPy fallbacks remain.

Producer-bound audit screening acceptance

MolecularCoulombBounds now binds MANTA’s existing native full-space Q/V product envelopes to the immutable molecular P0 source. It supplies bounds for complete ordered AO shell tiles without evaluating Coulomb integrals. The compact streaming scheduler can omit entire orbits before numerical reads; every retained member and stabilizer still passes the unchanged equivariance audit. This avoids the full quartet integral audit when bounds are sufficiently small. It is an opt-in experimental molecular HF capability, with no default dispatch or new periodic admission.

The adapter uses the native envelope producer, not a second implementation of MANTA kernels or BUPO. Its receipt records kernel, normalization, source, precision, pair work and memory. Equal extent-search radii avoid unused search; the selected radius is not a cutoff. The inequality bounds analytic integrals with floating-point headroom and excludes an interval proof of arithmetic roundoff. The source receipt distinguishes retained-orbit qualification and upper-bound omission from a measured full-source audit. Unmasked reconstruction from a partial plan refuses; the original provider and complete audit remain explicit fallbacks.

Thirty-seven focused regressions pass, including nine new envelope/admission checks and the existing compact-screening and HF-bridge tests. Coverage includes C2v and C3v molecular sources, nonunitary Cartesian shells, all-ordered integral bounds, native and NumPy contractions on nonsymmetric complex non-Hermitian trial densities, raw operator covariance, actual skipped-read instrumentation, source/basis displacement refusal, immutable ownership, resource refusal and positive-underflow/overflow behavior. The bridge’s existing density-response finite differences remain passing. These are not nuclear derivative tests.

A queued acceptance calculation used the candidate Python modules with an already-built healthy native runtime. All 377 loaded files watched before and after remained unchanged. Source tolerance 1e-10, fixed omitted tensor budget 1e-12, native SCF energy/gradient tolerances 1e-11 / 1e-9 and the NH3 ORCA comparison gate 1e-8 were unchanged. Each case ran reduced, independent ordered identical-mask and full-source native SCFs, then terminal Fock/energy checks. H4 contains two H2 fragments with 1.4 bohr bonds and 30 bohr between centers; its admitted group is D2h. H2 UHF retains the broken spin seeds from preceding acceptance.

Calculation	Energy, hartree	Identical-mask SCF difference	Full-source SCF difference	Terminal identical-mask Fock max error
NH3 RHF/cc-pVDZ	-56.18855210065033	2.85e-14	0	5.13e-14
H4 separated RHF/STO-3G	-2.2334286410805104	8.89e-16	8.89e-16	4.45e-16
H2 UHF, 4.00 bohr	-0.9358423283198118	0	4.45e-16	1.39e-17
H2 UHF, 4.02 bohr	-0.9357442504982110	2.23e-16	2.23e-16	1.12e-16

NH3 converges in 15 iterations and differs from the existing ORCA reference by 7.03e-10 hartree. H4 converges in two iterations. Both H2 cases converge in five, retain ||Da-Db||_F = 1.39525 / 1.39596 and one electron per spin to roundoff. H4 and broken-spin H2 use the independent identical-source oracle; no separate external-program parity is claimed for them. The displaced H2 calculation tests source-dependent energies, not gradients or stress.

Actual setup work	NH3	Separated H4
Native bound shell pairs / primitive pairs	120 / 771	10 / 90
Envelope evaluations / integral calls for bounds	240 / 0	20 / 0
Ordered-member bound queries	50625	256
Audit shell calls / full ordered count	50625 / 50625	64 / 256
Audit primitive quartet requests	1874161	5184
Omitted representatives / ordered tiles	0 / 0	11 / 192
Measured omitted tensor norm / reported upper bound	0 / 0	1.17e-34 / 2.01e-33
Bound arrays / packed mask bytes	2040 / 237	192 / 3
Retained pair-schedule array bytes	10776	1312
Conservative J/K logical reservation, bytes	62621129	26680564

The H4 audit avoids 75% of actual ordered integral calls. Its terminal fused J/K uses eight representative calls, 648 primitive requests and 128 scalar products/block contractions, compared with 256 calls, 20736 primitive requests and 512 products/blocks in the independent ordered full-source contraction. The native screened SCF makes 19 actual J/K calls totaling 152 shell calls, 12312 primitive requests and 1344 products/blocks. Bound visitation is still quartic; neither subquartic planning nor an SCF speedup is inferred.

NH3 bounds omit nothing at the unchanged cap, so its terminal J/K retains all 1893 representatives, with 125343 primitive requests, 1414562 scalar products, 101250 block contractions and 713398 angular-transport products. Its 68 solver calls total 128724 shell calls, 8523324 primitive requests, 58704323 scalar products and 4201875 block contractions. This policy can retain more work than the preceding measured-norm mask; bound-only omission is deliberately explicit. Each H2 solver uses 24 builds, 96 shell calls, 7776 primitive requests and 384 scalar products/blocks. Bounds omit no H2 orbit.

With one requested OpenMP/BLAS thread, bound construction takes 0.529 ms for NH3 and 0.152 ms for H4. Their audits take 2.891 s and 12.24 ms, native reduced SCFs 13.904 s and 59.12 ms, and terminal J/K 191.68 ms and 1.320 ms. H2 SCFs take 5.57 and 6.78 ms. These are single-run integration timings, including Python scheduling, not isolated speedup measurements. Whole-job peak RSS including tests and independent source oracles is 300482560 bytes. Logical reservations conservatively retain producer/bound construction costs and are not RSS guarantees; state array storage is separately 27144 bytes for NH3, 544 for H4 and 224 per H2 case.

Next capabilities are tighter producer bounds and hierarchical screening, producer-issued equivariance/support attestations, measured cost-aware public dispatch, native UHF channel batching and terminal/output state integration. MANTA owns envelope/kernel/bubble construction; symmetry owns whole-orbit closure and qualification; the shared FockBuild contract is unchanged. Periodic finite domains, Seitz/image/wrap/phase/weight/momentum data, distinct CCM/chi Hamiltonians, auxiliary rank cuts, local retained spaces, non-Abelian reduced CC tensors, complex kernels, gradients and stress keep their existing separate gates. No scientific tolerance or fallback was relaxed.

Native hierarchical screening acceptance

The optional MolecularHierarchicalBounds adapter consumes MANTA’s existing native bubble traversal and order-zero error model. A node magnitude takes the minimum of Q/V and a monopole magnitude plus all compact, penetration and full-moment-tail errors. Ordered AO dimensions and pair orientations weight each disjoint candidate block. Only complete quartet orbits contained in accepted blocks are omitted. A generic native tree need not be symmetric; it supplies bounds, not an operator-equivariance certificate.

Two queued acceptances pass 36 distinct focused regressions: thirteen new hierarchy tests, nine existing producer-bound tests and fourteen molecular HF-bridge tests. Separated H8 accepts internal-node blocks covering multiple pair interactions, and deliberately tight H4 caps produce partially covered orbits that must remain retained. These two additional checks and the complete H8 SCF run use a pinned source/native snapshot. Independent ordered integrals check both the hierarchy’s own bound and the Q/V minimum, including C2v, C3v and nonunitary Cartesian sources. Native/NumPy arbitrary complex non-Hermitian density contractions, raw operator covariance, actual omitted-read instrumentation, foreign and displaced sources, changed caps, resource refusal and immutable ownership are covered. The existing HF density-response tests remain passing.

Five complete reduced, independently contracted identical-mask and full-source native SCFs pass with unchanged source/omission tolerances 1e-10 / 1e-12, native SCF energy/gradient tolerances 1e-11 / 1e-9 and ORCA gate 1e-8. The candidate numerical module bytes match those executed on the healthy existing native runtime; all 378 watched loaded files stayed unchanged.

Case	Energy, hartree	Identical-mask / full-source SCF differences, hartree	Terminal Fock max error
NH3 RHF/cc-pVDZ	-56.18855210065033	2.85e-14 / 0	5.13e-14
H4 separated RHF/STO-3G	-2.2334286410805104	8.89e-16 / 8.89e-16	4.45e-16
H2 UHF, 4.00 bohr	-0.9358423283198118	0 / 4.45e-16	1.39e-17
H2 UHF, 4.02 bohr	-0.9357442504982110	2.23e-16 / 2.23e-16	1.12e-16
H8 separated RHF/STO-3G	-4.466857260869869	1.78e-15 / 0	6.67e-16

NH3 agrees with the reused matching ORCA reference within 7.03e-10 hartree. H2 retains the broken spin states and one electron per spin. H4, H8 and H2 comparisons use independent contractions of the same finite source, without external-program parity. The displaced H2 result is an energy check, not nuclear-gradient or stress acceptance.

Measured setup work	NH3	Separated H4
Native tree nodes / depth	199 / 5	15 / 3
Envelope evaluations / integral calls for envelopes	6734 / 0	350 / 0
Native node visits / bound queries	12462 / 7260	79 / 69
Far-error calls / tightened node bounds	0 / 0	14 / 14
Accepted candidate blocks / ordered AO entries	0 / 0	34 / 192
Orbit-member coverage requests / ancestor-map probes	1893 / 59178	200 / 300
Actual audit calls / full ordered count	50625 / 50625	64 / 256
Audit primitive quartet requests	1874161	5184
Actual omitted norm / upper bound	0 / 0	1.17e-34 / 2.01e-33
Q/V/size arrays / candidate-block payload, bytes	2040 / 0	192 / 816
Ancestor index payload / fixed mask, bytes	5424 / 237	256 / 3
Conservative maximum J/K logical reservation, bytes	71041033	26815268

H4 still skips 192 ordered audit calls and eleven representatives; this case does not skip more integrals than the preceding Q/V-only policy. The hierarchy performs fewer native node-bound queries than flat ordered-member bounds, but also incurs extent searches, traversal and coverage lookups. These are separate counts, not a claimed net work or wall-time speedup. NH3 has no far candidates or omissions and illustrates the need for a dispatch cost gate.

Terminal H4 J/K uses eight calls, 648 primitive requests and 128 scalar products/block contractions; its 19 native solver calls total 152 shell calls, 12312 primitive requests and 1344 products/blocks. NH3 terminal J/K retains 1893 calls, 125343 primitive requests, 1414562 scalar products, 101250 blocks and 713398 angular-transport products. Its 68 native calls total 128724 shell calls, 8523324 primitive requests, 58704323 scalar products and 4201875 blocks. Each H2 solver uses 24 builds, 96 shell calls and 7776 primitive requests.

With one requested OpenMP/BLAS thread, NH3/H4 bound construction takes 18.21 / 0.843 ms, audits 1.828 s / 12.55 ms, native reduced SCFs 8.829 s / 25.41 ms and terminal J/K 99.02 / 1.307 ms. H2 SCFs take 6.07 and 6.69 ms. Whole-job peak RSS is 302579712 bytes. Payload counts exclude object overhead; logical admission reserves worst-case candidate storage and native construction workspace. These single-run measurements are not isolated comparisons with prior runs. Worst-case storage remains quadratic in pair count; orbit iteration and retained-source audits remain explicit costs.

The H8 extension consists of four H2 fragments with centers at (x,y,0), x,y = +/-15 bohr, and hydrogen offsets z = +/-0.7 bohr. Its 351 accepted blocks cover 588 unordered pair interactions, including 107 blocks containing an internal node. Thus the hierarchy compresses actual candidate interactions, rather than only representing a theoretical orbit count. Closure permits omission of 3840 of 4096 ordered audit calls and 90 representatives. The actual omitted tensor norm is 2.56e-34, below its 6.28e-33 recorded bound and the unchanged 1e-12 cap.

Additional H8 measured work/storage	Value
Tree nodes / depth; envelope evaluations / integral calls	58 / 4; 732 / 0
Native node visits / bound queries; far calls / tightened bounds	667 / 500; 250 / 81
Member coverage requests / ancestor-map probes	3856 / 15069
Retained audit calls / primitive quartet requests	256 / 20736
Terminal J/K calls / primitive requests / products / blocks	16 / 1296 / 512 / 512
SCF builds / shell calls / primitive requests / products / blocks	28 / 448 / 36288 / 7680 / 7680
Q/V/size arrays / candidate blocks / ancestor payload, bytes	640 / 8424 / 1296
Mask / schedule arrays / state arrays, bytes	14 / 4096 / 2112
Conservative maximum J/K logical reservation, bytes	28081834

With one requested thread, H8 bounds/audit/reduced SCF/terminal J/K take 0.0514 / 3.507 / 29.121 / 0.538 seconds; whole-job peak RSS is 239697920 bytes. The two focused checks take 46.93 seconds in this queued run versus 0.52 seconds in their separate focused invocation, so these loaded-run timings do not establish a speedup or a scaling comparison. The candidate implementation and test bytes match the landed source, and all 378 watched loaded files remain unchanged during this run. The H8 reference is the same finite source with independent ordered contractions, not an external code.

The shared FockBuild and native molecular HF interfaces are unchanged. Production defaults stay off. Further work includes measured cost-aware routing, tighter source-specific bounds and efficient orbit/hierarchy joins, producer equivariance/support attestations and native channel/output-state integration. Periodic finite domains and Seitz/image/wrap/phase/weight/momentum handling, distinct CCM/chi sources, auxiliary rank cuts, local projectors, complex integral kernels, reduced non-Abelian CC products, gradients and stress retain their separate qualification requirements.

Joint native UHF symmetry builds

JKBuilder.build_jk_uhf(Da, Db) returns independent physical (J[Da + Db], K[Da], K[Db]) matrices. Native NOITER, ordinary iterations and the terminal rebuild use this additive boundary. Its default executes the original incremental slots in order: J0, K-alpha0, K-beta1. The opt-in ScreenedMolecularJK implementation shares one retained representative read and angular transport across the three selected channels. Neither density is projected, and equality of spin densities is not required.

The new focused checks exercise arbitrary nonsymmetric independent densities with C2v, C3v and metric-aware Cartesian actions in both NumPy and native executors. They compare raw J/K against ordered identical-mask contractions and check covariance. Other checks preserve incremental slot results bit for bit across resets and threshold changes, cover NOITER/capped/converged UHF, and reject malformed inputs or insufficient three-channel resources before integral work. Direct incremental UHF, terminal F/D energy consistency and DF closed-shell/doublet regressions cover the inherited sequential fallback.

Thirty distinct regressions pass across focused queued runs on the rebuilt native core. Five complete UHF calculations compare the joint and sequential builds, an independently contracted identical mask and the full P0 source. All 3457 recorded source/test files and the loaded core remain unchanged through the final run; 377 loaded module files are recorded. Source/omission caps remain 1e-10 / 1e-12, SCF energy/gradient tolerances 1e-11 / 1e-9 and the reused ORCA gate 1e-8.

UHF case	Energy, hartree	Identical-mask / full-source energy difference	Terminal Fock max error
NH3/cc-pVDZ	-56.18855210065030	2.85e-14 / 4.27e-14	1.98e-14
Separated H4/STO-3G	-2.2334286410805104	0 / 8.89e-16	4.45e-16
H2/STO-3G, 4.00 bohr	-0.9358423283198118	0 / 4.45e-16	1.39e-17
H2/STO-3G, 4.02 bohr	-0.9357442504982110	2.23e-16 / 2.23e-16	1.12e-16
H doublet/STO-3G	-0.46658184955727544	0 / 0	0

Joint and sequential builds return identical energies for all five cases. NH3 retains equal spin densities and matches the existing ORCA closed-shell reference within 7.03e-10 hartree. Both H2 cases retain broken spin densities with norms of Da - Db above 1.39. H4 starts from broken spin seeds but converges to equal spin densities; its 192 omitted ordered tiles remain bounded by 2.01e-33, with actual omitted norm 1.17e-34. The H doublet has zero beta density and agrees with its one-electron generalized eigenvalue within 1e-11 hartree. H4/H2 use same-source numerical references, not an external program. The displaced H2 energy is not a gradient or stress acceptance.

Whole native solver work, joint / sequential	NH3	H4	Each H2	H doublet
Joint invocations / other builds in joint path	16 / 45	8 / 18	6 / 6	3 / 0
Shell calls	115473 / 176049	208 / 336	48 / 96	3 / 9
Primitive quartet requests	7645923 / 11656899	16848 / 27216	3888 / 7776	243 / 729
Angular transport products	43517278 / 66346014	0 / 0	0 / 0	0 / 0
Density scalar products, equal in both paths	65777133	2688	384	9
Block contractions, equal in both paths	4708125	2688	384	9
Maximum logical reservation, bytes	71202761 / 70987209	26818596 / 26814244	26366892 / 26365612	26313524 / 26313012

One terminal NH3 joint build evaluates 1893 shells and 125343 primitive quartets, with 713398 angular transport products, 2121843 density products and 151875 blocks. The corresponding sequential calls require exactly three times its integral and transport work, with equal density contractions. NH3/H4 mask, schedule and evaluated-state arrays occupy respectively 237 / 10776 / 40832 and 3 / 1312 / 832 bytes. Whole-job peak RSS is 263979008 bytes; logical reservations are conservative buffer admissions, not measured peak allocation or complete runtime RSS.

With one requested thread, joint/sequential SCFs take 81.506 / 109.461 seconds for NH3, 0.376 / 1.106 for H4, 0.160 / 0.0124 and 0.103 / 0.0121 for the two H2 cases, and 0.00444 / 0.00326 for H. NH3 bound construction/audit take 0.979 / 29.540 seconds; H4 takes 0.000676 / 0.314 seconds. These shared-host observations include scheduling variation and show no consistent wall-time speedup. The measured savings are actual integral/transport counts, with slightly higher joint buffer reservations; cost-aware routing remains needed.

Post-convergence stability analysis and stateless Hessian/response builds retain their existing separate calls. Joint builds therefore save two representative traversals each; total solver work also includes those other calls and must be measured separately. Density contraction terms remain unchanged. UKS, periodic drivers and native output-state migration are outside this increment. Source masks, scientific tolerances, default dispatch and the shared FockBuild contract remain unchanged.

This completes the joint native UHF consumer increment. Next production work is measured cost-aware routing, efficient orbit/hierarchy joins and stronger producer source/support attestations, followed by native terminal/output-state integration with FockBuild. Further response batching requires its own cache and source contract. MANTA retains ownership of integral kernels and bounds; its separate finite periodic remainder API does not qualify this molecular adapter for periodic sources. Complex-source SCF, reduced non-Abelian CC products, auxiliary/local retained spaces, gradients and stress still require their separate method admissions.

Orbit-local hierarchical coverage reuse

The bounded candidate audit now reuses coverage results for identical unordered real-ERI shell-pair labels within one orbit. It does not equate spatially related members or alter MANTA’s tree, envelopes or candidate blocks. Every ordered member still contributes to the norm in the original order. The 128-entry cache is discarded after each orbit; exhausted capacity falls back to actual queries. Empty candidate sets require no ancestor-map probes. A conservative 36864-byte reservation covers cache construction and objects.

Nineteen focused regressions pass on a healthy native runtime with the exact changed Python modules. They cover independent ordered integrals, C2v/C3v and metric-aware Cartesian actions, arbitrary complex nonsymmetric density J/K and raw covariance, partial-orbit refusal, displaced/foreign sources, resource refusal, and exact cached/uncached bounds, masks, source identities and audit work. Multi-pair leaves and cache capacities zero, one and two preserve the same results. Instrumented coverage calls agree with request-minus-hit counts.

Three complete native UHF cases pass against independently contracted identical-mask and full-source references. Source/omission tolerances remain 1e-10 / 1e-12, SCF energy/gradient tolerances 1e-11 / 1e-9, and the ORCA gate 1e-8. Cached and uncached qualification produce identical source identities, masks, omitted norms, retained integral work and member counts.

Case	Energy, hartree	Identical-mask / full-source energy difference	Terminal Fock max error
NH3/cc-pVDZ	-56.18855210065030	2.85e-14 / 4.27e-14	1.98e-14
Separated H8/STO-3G	-4.466857260869869	1.78e-15 / 0	5.56e-16
Broken-spin H2/STO-3G, 4.00 bohr	-0.9358423283198118	0 / 4.45e-16	1.39e-17

NH3 retains equal spin densities and agrees with the matching reused ORCA reference within 7.03e-10 hartree. H8 and H2 use same-source numerical references, without external-code parity. No gradient/stress claim follows.

Measured admission work	NH3	H8	H2
Ordered member requests, unchanged	1893	3856	4
Actual coverage calls / cache hits	1893 / 0	604 / 3252	4 / 0
Ancestor-map probes, cached / original	0 / 59178	2218 / 15069	0 / 16
Peak cache entries	1	8	1
Candidate blocks / native bound queries, unchanged	0 / 7260	351 / 500	0 / 6
Retained audit shell calls / primitive requests, unchanged	50625 / 1874161	256 / 20736	16 / 1296
Native UHF shell calls / primitive requests	115473 / 7645923	384 / 31104	48 / 3888
UHF density products / block contractions	65777133 / 4708125	7680 / 7680	384 / 384
Maximum J/K logical reservation, bytes	71239625	28131242	26403756

H8 avoids 3252 actual coverage calls and 12851 ancestor-map probes. The cache does not reduce integral calls or density contractions beyond the already admitted mask. Cache-key construction and dictionary operations add work; the probe reduction is not a claim that all setup work falls equally. No new persistent quartet inventory or leaf-pair expansion is retained.

With one requested thread, bound construction takes 0.01760 / 0.00294 / 0.000212 seconds for NH3/H8/H2. Cached versus original audits take 1.985 / 1.416, 0.02564 / 0.02885 and 0.001307 / 0.001136 seconds. Reduced SCFs take 5.576 / 0.1181 / 0.002421 seconds. Whole-job peak RSS is 311820288 bytes. These single-run timings show no general wall-time speedup. Logical memory reservations increase by 36864 bytes; the cache occupancy is reported separately from total RSS. All 678 recorded runtime/candidate files remain unchanged through acceptance, with 409 loaded modules recorded.

This completes bounded reuse in the existing molecular coverage audit. Default dispatch remains off. Next production work is cost-aware source routing and producer-issued equivariance/support attestations, followed by terminal/output-state integration with the shared FockBuild. MANTA still owns integral/bound generation and bubble traversal. Its periodic finite/infinite source work, multi-k phase/domain contracts, distinct CCM/chi sources, auxiliary/local projector transport, complex-source SCF, reduced non-Abelian CC products, gradients and stress retain separate method acceptance targets.

Same-source cost routing and producer qualification

The explicit molecular bridge now admits ordered and auto execution in addition to the existing native and NumPy choices. The ordered route evaluates every retained ordered tile from the same immutable MANTA P0 session, without angular transport or final symmetrization. Both routes preserve the exact mask, source/policy identity, selected density channels and error budget. Qualification combines the exact native constructor contract, per-tile provider/kernel/range checks and the existing complete or retained-only audit. It is not a new algebraic producer attestation or permission to skip retained audits. Default method entry points remain unchanged.

Calibration probes are nonsymmetric and alternate the two execution orders. Five native HF channel signatures have separate bounded decisions. The fastest ordered minus slowest reduced sample must repay complete calibration cost over the caller’s expected remaining builds; otherwise ordered execution remains selected. Timing noise can change the choice but cannot change the source. Only scalar diagnostics are cached, with a 131072-byte reservation. Probe work never counts as physical SCF builds or enters FockBuild provenance.

Numerical implementation 3c80e0aa passes 36 focused regression cases. A subsequent receipt-only addition labels each probe executor explicitly; its focused calibration functionality check passes without changing algebra. Queued acceptance first exercises both routes and full unmasked references, then reuses those accepted arrays for the bounded multi-signature fix, with ten routing regressions and three complete UHF calculations. This preserves the independent ordered-source and external-reference evidence without repeating those solves. The native extension is unchanged: runtime source 203393d4, native SHA-256 851b221a8b2fb1e13e55159448c39576d2dead6438d5586e183be6af5a2c0116. Seven candidate Python modules load explicitly; 684 recorded files remain unchanged through the final calculation, with 410 loaded modules recorded.

Case	Final routed energy, Eh	Maximum energy difference between routes, Eh	Full-source energy difference, Eh	Final Fock maximum error, Eh
NH3 cc-pVDZ, C3v	-56.18855210065030	5.69e-14	4.27e-14	1.98e-14
Four separated H2 fragments, STO-3G	-4.466857260869869	1.78e-15	0	5.56e-16
H2 at 4 bohr, broken-spin STO-3G	-0.9358423283198127	1.78e-15	1.34e-15	2.23e-16

NH3 agrees with the matching ORCA 6.1.1 UHF/cc-pVDZ VeryTightSCF NoRI reference -56.188552099947 Eh within 7.033e-10 Eh, below the unchanged 1e-8 gate. H8 and H2 use independent same-source numerical references; no new external parity for those cases is claimed. Source tolerance remains 1e-10, omission cap 1e-12, and SCF energy/gradient convergence 1e-11/1e-9. Broken-spin H2 remains broken. C2v/C3v, Cartesian shells, complex nonsymmetric J/K, retained-frame physical Focks, unsupported kernels/images, budget refusal and calibration disagreement are covered. No gradient or stress is accepted.

Actual physical SCF work	NH3	H8	H2
Ordered shell calls	3088125	6144	192
Routed shell calls	115473	384	120
Ordered primitive requests	114323821	497664	15552
Routed primitive requests	7645923	31104	9720
Density scalar products, both routes	65777133	7680	384
Block contractions, both routes	4708125	7680	384
Routed angular scalar products	43517278	0	0
Routed maximum logical bytes	71370697	28262314	26533548

Ordered execution has zero angular transport. Symmetry saves integral work here, not density scalar products. The final route selects native for NH3/H8 joint UHF, J and K. H2’s joint batch stays ordered because the timing intervals overlap; its standalone J/K select native. Unmeasured signatures remain ordered and require their own calibration to claim a benefit.

Setup and calibration, separate from SCF	NH3	H8	H2
Source/bound setup seconds	1.0881	0.02742	0.001606
Retained audit shell calls	50625	256	16
Calibration seconds, three signatures	2.7424	0.06589	0.003293
Calibration shell calls / primitive requests	315108 / 11997024	1632 / 132192	120 / 9720
Calibration density products / blocks	14145620 / 1012500	5120 / 5120	320 / 320
Calibration angular products	4280388	0	0
Calibration maximum logical bytes	71759177	28352426	26601900
Routed SCF seconds	5.1572	0.11256	0.003634
Earlier identical-mask ordered SCF seconds	30.0159	0.17784	0.002900

One thread was requested. Final whole-job peak RSS is 237027328 bytes. Timing rows come from successive acceptance runs, not a controlled speedup benchmark. H8’s calibration consumes its observed saving and H2 is too small to amortize calibration in this run. Expected reuse is an estimate, not a performance guarantee. The initial one-signature implementation passed numerically but routed standalone calls poorly: NH3 took 21.63 seconds and 2308413 shell calls. The bounded signature cache resolves that measured problem; explicit native execution remains available without calibration.

Remaining production capabilities are pre-audit cost admission, reusable producer-issued operation/support attestations, and native terminal FockBuild capture without an additional build. MANTA owns immutable kernel/domain descriptors, bounds and bubble hierarchies. No molecular cost decision admits periodic BIPOLE, MANTA finite/infinite domains, CCM or chi; their supports, weights, image shifts, Seitz products, reciprocal wraps, Bloch phases and momentum remain separate. Complex-source SCF, reduced non-Abelian CC products, covariant auxiliary/local projectors, analytic gradients and stress also remain separate.

Public molecular HF method and output acceptance

The explicit symmetry_reduction=MolecularSymmetryOptions(...) public RHF/UHF entry is available for qualified all-electron real molecular P0 sources. It remains opt-in and experimental. It checks the actual molecule/basis and one-electron operator, qualifies the fixed screened source, and uses the existing native solver. Execution selection changes neither the Hamiltonian nor the source identities. Analytic gradients explicitly refuse this result.

Seventeen focused regressions passed through the calculation queue on source 4ab94c28, using native runtime 203393d4 with explicitly loaded and hashed candidate Python modules and the shared QVF orbital-label change. All 692 expected files stayed unchanged; 394 loaded modules were recorded. Tests cover native and ordered RHF/UHF at convergence, one iteration and NOITER, fractional READ densities, rotated degenerate retained coordinates, metric leakage refusal, incompatible sources, one-electron covariance rejection and actual QVF writing. Density-defining natural orbitals preserve the evaluated state without a state-symmetry assumption or next-step extrapolation.

Five complete public-method calculations also passed. Source tolerance 1e-10, omission cap 1e-12, SCF energy 1e-11 and gradient-norm 1e-9 thresholds are unchanged. Each calculation was compared with an independent unmasked native P0 SCF and explicit J/K contractions of the complete AO ERI tensor. The hierarchy omitted no source elements in the compact examples; H8 omitted 3840 of 4096 ordered quartets with bound 6.273e-33.

Case / method	Energy (hartree)	Energy difference from full source	Maximum Fock element difference from independent ERIs	Density reconstruction error
C3v NH3 cc-pVDZ / UHF	-56.18855210065031	2.843e-14	2.243e-14	6.912e-15
Four separated H2 fragments, STO-3G / RHF	-4.466857260869866	1.777e-15	6.662e-16	3.775e-15
Broken-spin H2, 4 bohr, STO-3G / UHF	-0.9358423283198123	0	2.165e-15	2.221e-16
NH3 with N displaced 0.02 bohr along z, cc-pVDZ / RHF	-56.18712146664339	2.843e-14	6.040e-14	2.343e-14
He with Cartesian s+d test shells / RHF	-2.300337779324880	0	8.882e-16	1.555e-15

The same-geometry NH3 ORCA 6.1.1 UHF/cc-pVDZ VeryTightSCF NoRI reference is -56.188552099947 hartree. The difference 7.0331e-10 passes the existing 1e-8 gate. Other cases use the independent same-source checks above; no new external reference, CC residual, analytic gradient or stress acceptance is claimed. The displacement tests a newly qualified source, not a derivative. Maximum converged density difference from the unmasked runs is 4.838e-14.

The following are actual integral and contraction counts, including native stability requests in the SCF totals. NH3 used measured automatic routing; the other cases selected native execution explicitly. Terminal costs are additional to SCF, audit and calibration; no theoretical orbit count is substituted for work performed.

Work / storage	NH3	H8	Broken H2	Displaced NH3	Cartesian He
Source-audit shell calls	50625	256	16	50625	16
SCF shell calls	115473	448	48	128724	150
SCF primitive quartet requests	7645923	36288	3888	8523324	150
SCF density scalar products	65777133	7680	384	58704323	72030
SCF block contractions	4708125	7680	384	4201875	480
Additional terminal shell calls	1893	16	4	1893	6
Additional terminal density scalar products	2121843	512	48	1414562	4802
Maximum J/K logical bytes	71370697	28118698	26403756	71077897	26950975
Additional method reservation bytes	926720	131072	69632	926720	115712
Owned FockBuild state bytes	40832	2112	224	27144	1624
Source setup seconds	0.98868	0.01935	0.001152	0.99239	0.005103
SCF J/K seconds	4.32545	0.09749	0.001511	4.69549	0.006321
Additional terminal J/K seconds	0.07428	0.003478	0.000132	0.06870	0.000248
Total public method seconds	7.72271	0.12213	0.003789	5.76480	0.01297

NH3 calibration separately used 315108 shell calls, 14145620 density scalar products and 2.32266 seconds; all three host signatures selected native representatives. Earlier identical-mask ordered SCF evidence records 3088125 shell calls for the same NH3 61-build workload. Contraction products are not reduced by this representative-tile schedule; integral generation is. One-electron qualification additionally builds S/T/V once each and performs 585336, 16384, 64, 585336 and 8232 scalar products, respectively. Maximum overlap and Hcore covariance residuals are 3.576e-15 and 2.240e-14. One thread was requested; whole-job peak RSS was 278495232 bytes, including the independent references and QVF serialization. Logical workspace counts are not a process-memory cap, and these timings are not a scaling benchmark.

The method consumes Fock unification’s existing frame/source/build/run_fields interfaces and method-declared QVF orbital labels. MANTA’s separately landed periodic exchange bounds certify fixed-mesh evaluated-density errors, not symmetry; they are not admitted by this molecular route. Periodic source support, Seitz composition, full integer image shifts, reciprocal wraps, Bloch phases, k weights, momentum and distinct CCM/chi Hamiltonians retain their existing boundaries. Next production work is job-deck admission, pre-audit cost selection, producer-issued operation/support qualification and direct native terminal-state capture. RI/CD, complex-source SCF, non-Abelian reduced CC tensors, local/auxiliary subspaces and method-specific derivatives remain separate capabilities.

Prepared-source reuse acceptance

Explicit preparation now removes repeated qualification work for independent HF calculations on the identical all-electron molecular source. It owns the actual immutable producer, audited mask and checked one-electron matrices; no source hash alone authorizes reuse. Full nuclei/order, centers, shell representation and radial content are checked before tile reads. Charge, spin, density and retained-space choices remain method-owned. One process-local lease protects the native workspace, and each method receives fresh physical counters and state. Only the five bounded scalar cost profiles may persist.

Source a9d4b1e8 passed 22 regressions and six complete HF calculations through the calculation queue, using the same identified native runtime 203393d4 with explicit candidate Python modules. All 695 expected files stayed stable; 394 loaded modules were recorded. The tests include neutral RHF followed by charged UHF and another fresh RHF state using native, ordered and automatic execution. Changed geometry, nuclei, same-size radial content and basis size refuse before reads. Overlapping use, cross-process reuse and pickling refuse; an invalid READ state releases the lease for the next valid calculation.

Each of NH3 cc-pVDZ UHF, separated H8 STO-3G RHF and broken-spin H2 at 4 bohr STO-3G UHF was run twice from explicitly supplied initial conditions. The second H2 calculation swaps the alpha/beta READ densities. Complete independent AO ERIs again check physical J/K and energies; the prior accepted full-source SCF arrays and ORCA reference are reused after exact geometry/S/H matching. All six results match the prior energy, density and Fock arrays exactly, with the expected spin-channel swap for H2. Maximum independent ERI Fock and energy differences are 2.243e-14 and 4.264e-14. NH3 retains the ORCA energy difference 7.0331e-10 hartree under the unchanged 1e-8 gate. The source, omission and SCF tolerances are unchanged. QVF source and preparation identities are checked on all six written artifacts.

Actual work / storage	NH3	H8	Broken H2
Once-paid source audit shell calls	50625	256	16
First-call calibration shell calls	315108	0	0
Second-call audit / calibration shell calls	0 / 0	0 / 0	0 / 0
Physical SCF shell calls, each calculation	115473	448	48
Physical SCF primitive quartet requests, each	7645923	36288	3888
Physical SCF density scalar products, each	65777133	7680	384
Physical SCF block contractions, each	4708125	7680	384
Additional terminal shell calls, each	1893	16	4
Additional terminal density scalar products, each	2121843	512	48
Persistent S/H bytes	13456	1024	64
Geometry/basis signature reservation bytes	70144	57344	23552
Maximum J/K logical bytes	71370697	28118698	26403756
Preparation seconds	1.69886	0.03265	0.002221
First-call calibration seconds	4.26287	0	0
First / second SCF J/K seconds	8.27719 / 8.90774	0.15994 / 0.16159	0.002510 / 0.002520
First / second total method seconds	12.69907 / 9.06118	0.16826 / 0.16964	0.004310 / 0.004192

Relative to preparing and calibrating independently twice, reuse avoids 365733 NH3 shell calls, 256 H8 calls and 16 H2 calls. Preparation makes three one-electron calls, one each for S/T/V, and either prepared method call makes zero. NH3’s first calibration performs 14145620 density scalar products; its second call reuses all three host signatures and performs no probes. The independent-state regressions fill all five allowed signatures without keeping densities or adding an unbounded cache. The whole-job peak RSS is 293666816 bytes, including independent references and QVF serialization. One thread was requested. These wall times reflect current load and are not a controlled cross-run speedup benchmark; skipped calls provide direct work evidence. Physical SCF and terminal work are unchanged.

A fresh geometry/basis/policy still needs a new source audit. There is no new producer-issued algebraic attestation, periodic source admission or derivative acceptance. MANTA owns the missing producer operation/support contract; pre-audit cost admission for unseen sources, public job-deck selection and native terminal capture remain production increments. This explicit reuse interface provides a place to consume stronger producer evidence without weakening the current audit or confusing source and electronic state.

Historical reduction milestones

The following inventory records the original implementation milestones as of 2026-05-23. It is retained to explain module names and legacy APIs. It is not a current all-method validation matrix, and its checks do not override the limitations below. In particular, force symmetrization is not an analytic gradient implementation, and non-symmorphic transport support does not qualify every finite integral domain or reconstruction path.

#	Milestone	Status
M1	symmetry=True primitive reduction	✅
M2	1e compute reduction (S, T)	✅
M2a	Wire M2 into 5 drivers	✅
M3	build_jk_gamma_molecular_limit_explicit	✅
M3b	build_jk_2e_real_space_explicit	✅
M3b	build_jk_pair_contributions (C++)	✅
M3b	compute_jk_gamma_reduced (Python)	✅, origin-fixed cells only
M4	IBZ-native SCF (4 drivers)	✅
M5	symmetry_scf.py	✅
M5a	symmetry_stabilize in GDF	✅
SYM5	symmetrize_forces()	✅
-	Non-symmorphic support	✅, diamond Fd-3m validated
SYM6	Character tables (Oh, Td, D4h, C6v)	✅

Legacy reduction limitations

1. M3b: origin-fixed cells only. compute_jk_gamma_reduced works for single-atom primitive cells (Mg, He) but not multi-atom cells (NaCl), per-atom lattice shifts break cell-pair Wigner-D reconstruction. The historical single-atom checks do not establish a general multi-atom or multi-k reduction.

2. M2a: S/T template workaround. The GDF driver computes full S/T as a template when using the symmetry-reduced path, because pybind11’s LatticeMatrixSet has read-only nbf/cells/blocks. The ERI compute reduction is unaffected.

Module map

Module	Purpose
symmetry_shared.py, native symmetry_shared	Shared group, space, orbit and qualification contracts
symmetry_abelian.py	Experimental complex Abelian selection and finite-ERI block J/K
symmetry_quartets.py	Experimental source-audited molecular representative-tile execution
symmetry_quartets_screening.py	Fixed complete-orbit masks and finite-source omission receipts for stored or compact streamed P0 batches
symmetry_quartets_bounds.py	Source-bound adapter to native MANTA Q/V envelopes, whole-orbit omission before reads and retained-only audit admission
symmetry_quartets_hierarchy.py	Native bubble/error-model candidates intersected with complete quartet orbits before retained-source auditing
symmetry_quartets_ordered.py	Same-mask ordered fallback and descriptive immutable-producer qualification evidence
symmetry_molecular_scf.py	Explicit qualified molecular RHF/UHF entry and evaluated FockBuild/QVF state
symmetry_core.py	Real Wigner rotations, including stable near-pole extraction
symmetry_ao.py	Compact pure/Cartesian molecular actions and legacy dense pure-shell matrices
native periodic_ao_bloch_transport, periodic_orbital_sewing	Periodic AO/Bloch transport and state/retained-space audits
symmetry_lattice.py	Lattice-cell orbits (SYM2b)
symmetry_lattice_c.py	Atom-pair orbits (SYM2c)
symmetry_integrals.py	Storage-reduced 1e integrals (SYM3a)
symmetry_integrals_reduced.py	Compute-reduced 1e integrals (SYM3b)
symmetry_fock_reduced.py	Compute-reduced 2e Fock (M3b)
symmetry_scf.py	Group-averaging + force symmetrization (M5, SYM5)
symmetry_salc.py	Character tables + irrep projection (SYM6)
periodic_runner.py	symmetry/reduce_to_primitive/symmetry_reduce_fock kwargs
periodic_rhf_gdf.py	GDF driver with M2a/M5a/M3b integration
pbc_bipole*.py	BIPOLE drivers with M2a/M4 integration

Native legacy entry points

File	Addition
lattice_integrals.cpp	compute_1e_lattice_matrix_explicit + wrappers
periodic_fock.cpp	build_jk_gamma_molecular_limit_explicit, build_jk_2e_real_space_explicit, build_jk_pair_contributions
bindings.cpp	pybind11 for all above

Qualified molecular jobs and executable source requests

Source 60936dd9 connects the existing cost-aware fixed-source RHF/UHF entry to run_job. It adds no new integral formula, source certificate or symmetry representation. The literature-to-code gap here was consumer integration: Davidson/Dupuis-King representative execution and MANTA-owned bounds were already available, but the normal job could not select them or preserve their source request. The new job interface retains exact source guards, physical FockBuild output and a fresh-qualification QVF recipe. Producer-owned operation/support attestations and cost admission before an unseen-source audit remain missing; none of the recent molecular or periodic literature justifies inferring those from a geometry group or a serialized identity.

The queue acceptance ran 130 focused regressions and four complete HF jobs using candidate Python modules and identified native runtime 203393d4. All 707 expected files stayed stable and 426 loaded modules were recorded. The tests exercise real RHF/UHF output, prepared reuse, strict operation and budget records, fresh QVF execution, unsupported method refusal, and a stopped calculation that cannot enter the legacy SAD retry. Existing canonical orbital and cube tests also pass. Natural-orbital tables now report actual occupations and physical-Fock Rayleigh quotients without false canonical frontier gaps.

The larger jobs were NH3 cc-pVDZ UHF through both run_job and an executable QVF, separated H8 STO-3G RHF through a prepared source, and broken-spin H2 at 4 bohr STO-3G UHF from same-basis READ arrays. The direct jobs reproduce the previous accepted full-source D/F/E arrays exactly. NH3 is -56.18855210065031 Eh; the retained ORCA 6.1.1 UHF/cc-pVDZ VeryTightSCF NoRI reference is -56.188552099947 Eh, an error of 7.0331e-10 Eh below the unchanged 1e-8 gate. Independent complete AO ERIs give Fock and energy errors no larger than 2.243e-14 and 4.264e-14 Eh respectively. The source tolerance 1e-10, omission cap 1e-12, energy convergence 1e-11 and gradient norm 1e-9 were unchanged.

The QVF Angstrom-to-bohr round trip changes a coordinate by 2.22e-16 bohr. It therefore correctly produces a fresh source identity instead of reusing an old audit. A separate queued reference reconstructs that exact source, confirms its prepared identity, and contracts full AO ERIs with the returned densities: Fock error 1.577e-14, energy error 1.422e-14 Eh. Relative to the original geometry the exported D/F differences are at most 1.99e-14 and 3.56e-14; energy is identical. The tiny change affects native stability work, so the two jobs do not claim identical build counts.

Calculation	Physical J/K builds	SCF shell calls	Primitive quartets requested	Density scalar products	Block contractions	SCF seconds	Complete job seconds
NH3 direct job	61	115473	7645923	65777133	4708125	12.5425	23.5831
NH3 QVF execution	67	126831	8397981	70020819	5011875	12.6568	23.0585
H8 prepared job	28	448	36288	7680	7680	0.27468	1.08543
H2 broken-spin job	12	48	3888	384	384	0.01203	0.30662

Each NH3 additionally pays 50625 audit calls, 315108 calibration calls and 14145620 calibration scalar products. Setup takes 3.24660/3.19407 seconds; calibration takes 6.89984/6.39517 seconds. All three measured signatures select native reconstruction and agree with their nonsymmetric ordered probes within 2.101e-14. The corresponding ordered SCF traversals would request 3088125/3391875 shell tiles with the same density contraction counts. Terminal capture separately costs 1893 calls and 2121843 scalar products per NH3 job. This integration adds no further integral or contraction reduction beyond the already accepted execution path.

H8 preparation pays 256 audit calls once (0.05598 seconds); its job pays none. H2 pays 16 audit calls. Their terminal captures cost 16/4 calls and 512/48 scalar products. Maximum logical J/K reservations are 71370697 bytes (NH3), 28118698 (H8) and 26403756 (H2); NH3 calibration reserves up to 71759177 bytes. Owned output states occupy 40832/2112/224 bytes. Whole-job peak RSS is 475365376 bytes including tests, full reference ERIs and normal output analysis. These observations are not a controlled timing speedup or a hard SCF memory limit. Default populations, localization, Molden and QVF exports are validated but their work is not counted as symmetry savings.

This remains an explicit experimental all-electron molecular P0 route. MANTA owns producer bounds, bubble hierarchies and future attestations; the job parser cannot issue them. The incoming cutoff-selected periodic BUPO source work is independent and supplies no molecular or periodic symmetry permission. Fock unification’s source/frame/state fields are reused unchanged. PBC/CCM/chi sources, complex-source SCF, non-Abelian reduced CC products, local/auxiliary/frozen projectors and method-specific gradients/stress retain their separate production acceptance targets.

Exact terminal evaluation reuse acceptance

Source 0804b885 removes the redundant terminal quartet traversal when the native method has already evaluated exactly the returned density. This is reuse of an actual fixed-source evaluation, not a new group-theory theorem, a geometry/state-symmetry assumption or a source audit bypass. Full UHF channels preserve total-density J and alpha/beta K order. The native RHF convergence path calls J and K separately; their exact source/density bytes can be joined before the method assembles its FockBuild. Standalone response requests do not authorize a different state. Single-bit density changes, spin permutations, absent/reset captures and failed replacements cannot reuse that evaluation; the existing counted cold path remains available.

The method owns at most one full-channel snapshot and one pending J request. Immutable byte owners isolate them from native input changes and returned writable J/K matrices. Prepared sources still own no density, J/K or Fock history. An additional 4096 + 128*n_AO**2 byte reservation is admitted before new calibration probes. Only immutable scalar route receipts can return to the prepared source. The reused terminal receipt reports zero new integral, contraction and transport work and names its original method-local build numbers in reused_from_builds.

The queued acceptance ran 101 regressions and four complete calculations on candidate Python source and identified native runtime 203393d4. All 708 expected files stayed stable; 418 loaded modules were recorded. Regression coverage includes exact FockBuild identity against cold evaluation, native and ordered execution, separate RHF J/K, nonsymmetric inputs, Cartesian shells, retained spaces, caps/NOITER and fractional READ states, spin ordering, owned buffers, changed-bit/signed-zero misses, reset/failure fallback, and resource refusal before new cost probes. All scientific tolerances remain unchanged. Ordinary job/QVF source and output checks also pass.

The complete jobs repeat NH3 cc-pVDZ UHF via normal job and executable QVF, prepared separated H8 STO-3G RHF, and broken-spin H2 at 4 bohr STO-3G UHF. Energies and direct-job D/F arrays match the preceding full-source acceptance exactly. NH3 remains -56.18855210065031 Eh, 7.0331e-10 Eh from the existing ORCA 6.1.1 UHF/cc-pVDZ VeryTightSCF NoRI reference, below the unchanged 1e-8 gate. Independent complete AO ERIs give maximum Fock/energy errors of 2.243e-14/4.264e-14 Eh. The QVF check uses its actual reloaded geometry: its full-source Fock/energy errors are 1.577e-14/1.422e-14 Eh. Physical error bounds, source identities and spin-broken densities are preserved.

Calculation	Original builds reused	Avoided terminal shell calls	Avoided primitive requests	Avoided density scalar products	Retained capture bytes	Capture seconds	Complete job seconds
NH3 direct job	16	1893	125343	2121843	40368	0.000575	15.4488
NH3 QVF execution	16	1893	125343	2121843	40368	0.000688	17.6643
H8 prepared job	3 and 4	16	1296	512	2560	0.000929	0.82694
H2 broken-spin job	6	4	324	48	192	0.000138	0.22879

Every terminal receipt contains zero additional shell/primitive calls, density scalar products, block contractions and angular transport products. The avoided block counts are 151875 per NH3, 512 for H8 and 48 for H2; each NH3 also avoids 713398 angular transport scalar products. The original physical SCF work stays 115473/126831 shell calls and 65777133/70020819 density products for the two NH3 jobs, 448/7680 for H8 and 48/384 for H2. The work is reused, not removed from the original SCF counters. The capture copies 80736 values in 16 snapshots per NH3, 1600 values in H8 and 144 in H2. H8’s retained bytes include its 1024-byte pending response J capture.

Logical J/K reservations increase by 111744 bytes for NH3, 12288 for H8 and 4608 for H2, reaching 71482441/28130986/26408364 bytes respectively. Whole-job peak RSS is 426328064 bytes including tests, complete reference ERIs and normal output. NH3 still pays 50625 audit and 315108 calibration calls per fresh source; setup takes 2.34352/2.22801 seconds and calibration 4.28323/5.04610 seconds. SCF times are 8.36332/9.88929 seconds for NH3, 0.22127 for H8 and 0.00977 for H2. These timings come from a different load than the prior acceptance and do not establish a controlled wall-clock speedup. Avoided source work is established by zero-work receipts and tests that reject any additional quartet execution on an exact match.

The bridge remains explicit and experimental. Its bounded capture closes the redundant terminal-build gap in these admitted RHF/UHF paths without changing native solver loops or FockBuild ownership. Zero-copy native capture could reduce copying further. MANTA producer-issued operation/support and roundoff attestations, cost admission before fresh audits, complex/fitted/ periodic sources, reduced non-Abelian CC products, covariant local/frozen/ auxiliary spaces and method-specific derivative acceptance remain open.

Ordered-source qualification and short-use routing acceptance

The next increment separates a producer-qualified fixed mask from permission to reconstruct its angular images. Hierarchical ordered preparations read zero integral tiles. Auto requests with one or two expected builds also skip paired calibration and choose that admission before the audit. Longer-use auto requests retain the existing measured routes and retained-orbit audit. All reduced entry points reject an ordered-only certificate. The actual producer/mask identity is independent of audit and cost evidence; integral and molecular Fock source hashes use version 2. Stored historical identities are not rewritten. Geometry, numerical-operator, electronic-state and retained-subspace symmetry remain separate.

Numerical source commit e2e3384d passed 154 regressions and four complete queued HF calculations using an explicitly overlaid Python candidate and the previously healthy native runtime. Exact source/native hashes, loaded module inventory, queue identity, outputs and arrays are retained outside the product checkout. All 711 expected files and the loaded runtime were checked before and after execution. The native molecular kernels were unchanged by this increment; no new periodic or derivative acceptance is inferred. Tests include Abelian water, non-Abelian C3v ammonia, metric-aware Cartesian actions, complex nonsymmetric densities, exact ordered/reduced mask and Fock-source identity, producer/kernel refusal, resource admission, impossible probe repayment and attempts to invoke reduced executors without an audit.

Complete calculations used NH3/cc-pVDZ UHF through both run_job and executable QVF, separated H8/STO-3G RHF with a prepared source, and broken-spin H2/STO-3G UHF at 4 bohr from the existing READ state. Source tolerance 1e-10, omission cap 1e-12, energy convergence 1e-11 and SCF gradient norm 1e-9 are unchanged. NH3 energies are -56.188552100650256 and -56.18855210065030 hartree. The existing ORCA 6.1.1 UHF/cc-pVDZ VeryTightSCF NoRI reference is -56.188552099947 hartree; differences are at most 7.0330e-10, below the unchanged 1e-8 acceptance limit. Independent full AO-ERI contractions of each actual final density, including the QVF’s reloaded geometry, differ by at most 3.2863e-14 in Fock entries and 2.8422e-14 hartree in energy. Maximum density difference from previous accepted results is 1.2144e-13. H8 and H2 use the independent full-integral reference; no external comparison is added for those cases.

All four preparations performed zero audit tile/shell/primitive calls, and all short-use route receipts contain zero probe samples and zero probe work. Each NH3 preparation avoided the previous 50,625 audit calls and 315,108 calibration calls. H8 and H2 avoided 256 and 16 audit calls. Source setup times were 0.25157/0.31331 seconds for NH3, 0.06560 for H8 and 0.00231 for H2. These are measured times under current load, not a controlled speedup ratio. Native envelope/hierarchy work remains explicitly reported in producer receipts and is not counted as zero setup work.

Case	Physical J/K builds	Shell calls	Primitive requests	Density products	Block contractions	Maximum logical J/K bytes	SCF seconds / complete job seconds
NH3 job	61	3,088,125	114,323,821	65,777,133	4,708,125	71,465,881	96.0524 / 97.3653
NH3 QVF	67	3,391,875	125,568,787	70,020,819	5,011,875	71,465,881	98.8094 / 100.1143
H8 prepared job	28	7,168	580,608	7,680	7,680	28,115,754	0.4701 / 1.4329
H2 broken-spin job	12	192	15,552	384	384	26,406,284	0.0140 / 0.3040

All angular-transport counts are zero, and exact terminal reuse adds zero integral/contraction calls. H8 omits 3,840 of 4,096 ordered tiles per build with an aggregate bound of 6.2726e-33; actual physical requests fall from 114,688 for the unmasked ordered source to 7,168. Logical reservations remain conservative; whole-batch measured peak RSS is 428,834,816 bytes, including tests, full-integral references and output work.

The deliberately short NH3 estimate is not its actual converged workload: ordered execution makes more physical integral calls than the previously accepted reduced route and is slower overall. This increment removes unnecessary setup for explicitly ordered/short-use requests; it does not establish a new default or promise an overall speedup. A better estimate must request a newly audited handle. A numerical source identity or bound-only receipt cannot upgrade ordered qualification into angular equivariance.

Supported execution remains experimental real molecular P0 all-electron RHF/UHF with explicit fixed masks. Producer operation/support/roundoff attestation for cheap reduced-source admission is still missing. MANTA owns that extension and its kernels, envelopes and bubble hierarchy. FockBuild continues to separate source, frame and evaluated state. Periodic finite supports, Seitz/image/wrap/phase and momentum conditions, distinct CCM/chi Hamiltonians, complex kernels and separate antiunitary actions, non-Abelian reduced products/recoupling, covariant local/auxiliary spaces, CC residuals, gradients and stress retain their separate acceptance requirements.

Source-qualified molecular RI block execution

Numerical source cfee8c49 passed 89 focused regressions and four complete queued RI-HF cases using a candidate Python overlay and unchanged healthy native runtime. All 709 expected files and the 396 loaded module files were recorded; the inputs/runtime hashes were unchanged after execution. Queue, host, full runtime identity, outputs and factor/density arrays are retained outside the product tree. This acceptance adds an explicit developer API; normal method/job defaults do not change.

The source uses native MANTA metric factorization with its lower-triangle convention and unchanged absolute/relative cut. It evaluates all ordered three-center tiles once, then retains only allowed complex-Abelian factors. Complete auxiliary spaces may mix through unitary matrices; split partner spaces, noninvariant metrics, non-Abelian character tables, antiunitary transport and an artificially perturbed finite coupling on symmetric geometry are rejected. Cartesian and pure-shell actions, nonsymmetric complex trial densities, rank cuts, immutable source snapshots, resource refusals, HF density finite differences and the existing P0 Fock bridge are covered. No metric projector or electronic density is repaired by symmetrization.

The complete calculations use water/STO-3G RHF, NH3/cc-pVDZ UHF restricted to the C3 Abelian subgroup, H2/STO-3G UHF at 4 bohr with independently localized spin seeds, and water with symmetric x displacements of 0.001 bohr. Auxiliary and orbital bases are deliberately identical in these finite-source tests; this is not an accuracy qualification of those small fitting bases. Source tolerance remains 1e-10, SCF energy tolerance 1e-11 and gradient norm 1e-9. Broken-spin density survives. The displaced case validates requalification, not an analytic gradient or finite-difference derivative implementation.

Case	RI-HF energy / hartree	Native full RI energy difference	Same-factor dense SCF difference	Independent libint Fock maximum error
Water	-74.89503754718201	0	2.8422e-14	1.5877e-14
NH3	-56.45804593400345	1.4211e-14	7.1055e-14	2.8422e-14
Broken-spin H2	-0.9530462725814317	0	0	2.2205e-16
Displaced water	-74.89507584326651	5.6844e-14	0	1.0659e-14

The independent reference recomputes metric and three-center integrals with libint and independently diagonalizes the metric using the identical cut. Maximum independent energy error is 1.4211e-13 hartree; maximum complex nonsymmetric J/K error is 7.0346e-14. Same-selected-factor dense density error is at most 1.2491e-14. The existing ORCA reference uses NoRI and therefore a different Hamiltonian. No matched external RI result is available; comparison with ORCA/CRYSTAL for this auxiliary/rank convention remains unclaimed.

Case	Metric / three-center setup calls	Stored / dense complex factors	J/K complex products, blocked / dense	Block contractions	Median J/K ms, blocked / dense / native streaming
Water	25 / 125	124 / 343	1,888 / 5,488	48	0.487 / 0.126 / 6.692
NH3	225 / 3,375	8,135 / 24,389	488,100 / 1,463,340	72	1.453 / 2.457 / 121.894
Broken-spin H2	4 / 8	4 / 8	24 / 48	24	0.132 / 0.034 / 0.154
Displaced water	25 / 125	124 / 343	1,888 / 5,488	48	0.183 / 0.048 / 3.404

The corresponding metric/three-center primitive requests are 225/3,375, 1,369/50,653, 36/216 and 225/3,375. All repeated symmetry J/K builds make zero integral calls. One native streaming J/K benchmark requires 375, 20,250, 24 and 375 coupling calls, respectively (3, 6, 3 and 3 passes); its primitive requests are 10,125, 303,918, 648 and 10,125. The saving against native streaming includes caching and is not attributed entirely to symmetry. No four-center integrals are evaluated by this RI source.

NH3 retained-factor storage is 130,160 bytes versus 390,224 bytes for a dense complex factor array; orbital/auxiliary transforms add 26,912/13,456 bytes, and retained native metric/factor arrays add 13,456 bytes. Setup reserves 42,439,624 logical bytes; the method maximum is 43,889,384. Whole acceptance peak RSS is 262,832,128 bytes, including Python, tests and independent dense references. Source setup took 0.01247, 0.03603, 0.00285 and 0.00693 seconds. Blocked SCF times were 0.01782, 0.08133, 0.00231 and 0.01054 seconds; NH3’s dense-factor/native-streamed SCF times were 0.15255/9.95887 seconds. Timings are measured under current load with five warmed fixed-density samples, not a general performance guarantee. Python block overhead loses to dense contraction on the smaller cases, so both explicit executors remain available.

This closes bounded fitted-source execution and auxiliary-space transport for molecular complex-Abelian factors, not scalable default routing. Still missing are producer-issued operation/support/roundoff authority and reduced fitting generation, measured automatic RI cost routing, bounded native block digestion, production-sized auxiliary sets and matched external RI evidence. Non-Abelian reduced products/multiplicities/recoupling, periodic finite-domain and Seitz/ Bloch/momentum admission, distinct CCM/chi sources, covariant frozen/local correlation spaces, CC residuals, analytic gradients and stress remain separate experimental or unimplemented capabilities as described above. No periodic or derivative gate is relaxed by this molecular acceptance.

Finite native RI Gram preservation and larger fitting bases

Larger auxiliary spaces exposed a false refusal in the initial RI adapter: water and NH3 with def2-SVP/def2-universal-JKFIT have native retained-factor Gram defects of 3.2779e-10 and 2.5777e-10. Comparing those factors to an ideal identity at the 1e-10 source tolerance rejected them before checking the actual fitted tensor. Whitening the factors or loosening the cutoff would change the source and is not an acceptable fix.

Numerical source 1637c38c instead keeps G = F^dagger M F as supplied by MANTA. A QR coordinate solve measures transport and leakage in the original factor span. The complete assembled irrep rotation receives a unitary polar correction; this preserves F F^dagger rather than normalizing F. Original partner relations and the final selected-factor tensor error are then checked at the unchanged tolerance. AO orthonormal-panel auditing is unchanged. The native Gram defect is descriptive evidence, separate from isometry, leakage and source-error acceptance. No native factorization or rank-cut implementation changes.

The queued candidate passed 49 regressions plus three complete calculations, each with blocked, same-selected-factor dense, and native unreduced RI SCF. There are now matched ORCA 6.1.1 RI-JK references for these cases, also run through the queue. The external inputs explicitly supply the same QVF orbital/AuxJK primitive data and bohr coordinates, all-electron charge zero and multiplicity one. ORCA uses spherical functions, RI for both J and K, no point-group reduction, and VeryTightSCF with energy 1e-12, RMS/max density 1e-10/1e-9, DIIS error 1e-9 and integral thresholds 1e-14/1e-15. Its printed auxiliary dimensions are 113, 131 and 139. ORCA uses a Cholesky metric inverse; MANTA’s eigenfactor retains every auxiliary column in these cases. Thus the external comparison is of the same full-rank fitted approximation, with different numerical inverse algorithms, not identical floating-point source bytes. Native and independent-libint checks establish the latter boundary. The ORCA manual, Sections 2.7.6 and 2.8.5, was used to match custom auxiliary input and RI-JK semantics; no derivative capability is inferred.

Case	Orbital / auxiliary dimensions	Blocked energy / hartree	ORCA energy / hartree	Absolute difference
Water RHF, def2-SVP / def2-universal-JKFIT	24 / 113	-75.95160765116219	-75.951607651057	1.0519e-10
NH3 UHF, def2-SVP / def2-universal-JKFIT	29 / 131	-56.140538613389054	-56.140538613308	8.1052e-11
NH3 UHF, cc-pVDZ / cc-pVDZ-JKFIT	29 / 139	-56.188539942151536	-56.188539942070	8.1535e-11

All differences pass the unchanged 1e-8 external energy limit. Molecular source tolerance remains 1e-10, SCF energy convergence 1e-11 and gradient norm 1e-9. Maximum native unreduced energy difference is 5.3291e-12 hartree; same-selected-factor dense energy and density differences are at most 7.1055e-14 hartree and 5.7455e-15. Independent libint metric/three-center integrals and an independent eigendecomposition at the same cut give maximum energy, Fock and complex nonsymmetric J/K errors of 5.4144e-12 hartree, 2.2454e-12 and 2.2574e-12. This includes complete native RI calculations, not only agreement at a symmetry-projected state. Earlier broken-state, Cartesian/pure, rank-split and incompatible-source refusals remain covered. A synthetic nonidentity Gram test explicitly detects any accidental whitening.

The auxiliary isometry residuals are 1.4056e-11, 3.8146e-11 and 1.0402e-11; coefficient leakage is at most 1.0220e-15. Final tensor error bounds are 5.4421e-12, 1.3743e-11 and 8.3266e-12. These remain below the original 1e-10 cap and explicitly exclude arithmetic roundoff. Metric ranks are unchanged.

Case	Metric / coupling setup calls	Stored / dense complex factor values	J/K products, blocked / dense	Median J/K milliseconds, blocked / dense / native streaming
Water	1,369 / 5,328	17,834 / 65,088	891,700 / 3,254,400	2.111 / 4.345 / 244.307
NH3 def2	1,849 / 9,675	36,745 / 110,171	2,204,700 / 6,610,260	3.168 / 8.211 / 436.912
NH3 cc	2,601 / 11,475	38,985 / 116,899	2,339,100 / 7,013,940	3.408 / 8.617 / 586.532

Metric/coupling primitive requests are 2,401/23,716, 3,249/41,553 and 2,601/69,819. Repeated symmetry builds perform zero integral calls; one native streamed J/K uses 90,576, 183,825 and 229,500 calls across 17, 19 and 20 coupling passes. Native primitive requests per benchmark are 403,172, 789,507 and 1,396,380. Block calls are 160, 72 and 72 versus four dense calls. Saving against native streaming includes cached factors, not just symmetry. Complex factor arrays occupy 285,344, 587,920 and 623,760 bytes; the dense complex comparison occupies 1,041,408, 1,762,736 and 1,870,384 bytes. Native unrotated factors are real, so these complex-array ratios are not claimed as native storage ratios. Transform and retained native arrays remain separately reported in the receipts.

Setup times are 0.04785, 0.08675 and 0.07760 seconds. Blocked SCF times are 0.10322, 0.19520 and 0.22186 seconds, against dense-factor times 0.21371, 0.53025 and 0.58251 seconds. Conservative method reservations peak at 98,440,936, 126,641,928 and 134,823,240 bytes; whole acceptance RSS is 301,416,448 bytes, including independent references and tests. Fixed-density timings are medians of five warmed samples under current load. No default routing threshold is inferred from these three cases.

Candidate Python source and the unchanged native runtime were recorded with 710 input files and 396 loaded modules; before/after hashes match. Queue identities, reference inputs/outputs, arrays and native hashes are archived outside the product checkout. This supersedes the earlier absence of matched external RI evidence for these three full-rank molecular sources only. Automatic RI cost routing, native bounded block digestion, producer-owned factor export and reduced fitting generation remain next capabilities. Periodic source/image/phase/momentum admission, non-Abelian reduced products, local/frozen spaces, CC residuals, gradients and stress retain separate gates.

Measured routing for prepared RI factors

Numerical source fec402ba adds explicit executor='auto' to the RI native JKBuilder bridge. Dense and blocked routes consume the identical selected factor source; unknown signatures use dense. The same conservative payback rule as quartet routing compares the minimum dense time with the maximum blocked time and charges all calibration overhead. Fixed nonsymmetric probes alternate order, are checked at the unchanged source tolerance, and produce only bounded scalar profiles. Short-use requests skip all probes when even the baseline halves cannot repay. No timing evidence changes factor selection, producer qualification, metric rank, physical Fock identity or state symmetry. Preparation work is no longer incorrectly charged again in each contraction’s work reservation. Its full costs remain in the source receipt.

The queued candidate passed 79 focused regressions and four complete RI-HF calculations against explicit dense contraction. The suite also retains quartet routing and physical Fock bridge coverage. It checks each native channel signature, independent profiles, bounded calibration storage, resource refusal before work, corrupted-probe rejection, zero-work short requests, immutable source identity and profile reuse with fresh counters. There is no online retuning or method default change.

Water/def2-SVP/def2-universal-JKFIT RHF and NH3/cc-pVDZ/cc-pVDZ-JKFIT UHF use the exact source identities accepted in the preceding increment. Their existing ORCA 6.1.1 explicit-basis RI-JK and native unreduced evidence is reused. Energies remain -75.95160765116219 and -56.188539942151536 hartree, with ORCA differences 1.0519e-10 and 8.1535e-11, below the unchanged 1e-8 limit. Small water/STO-3G with the same auxiliary basis and broken-spin H2/STO-3G at 4 bohr additionally run fresh native RI references. Their energies are -74.8950375471821 and -0.9530462725814317 hartree; native energy differences are 8.5266e-14 and zero. Broken spin remains present.

All auto/dense energy differences are zero in the reported calculations; maximum density difference is 4.8850e-15. Independent libint metric/three-center references give maximum energy and Fock errors of 5.4144e-12 hartree and 2.2454e-12. Same-source calibration differences are at most 9.4330e-15. Source tolerance remains 1e-10 and SCF energy/gradient criteria remain 1e-11/1e-9. The routed and explicit FockBuild source identities agree, and forked profile reuse evaluates the same physical state with fresh counters.

Five signatures were calibrated with two probe pairs each and an estimate of 100 future builds per signature, except H2’s explicit short-use estimate of two. These estimates are cost inputs, not measured iteration counts. Every selected signature chose blocked for the large cases and dense for small water. H2 selected dense with no probe calls. Preparing unused signatures is included in the measured overhead below; applications can request only the signatures they expect to use.

Case	Calibration seconds	Auto SCF seconds	Dense SCF seconds	Calibration plus auto SCF seconds	Physical J/K builds
Water large	0.07417	0.11155	0.23174	0.18572	73
NH3 large	0.16351	0.25371	0.59635	0.41722	68
Water small	0.00349	0.00408	0.00296	0.00757	42
Broken-spin H2	0	0.00113	0.00092	0.00113	13

Both large runs recover the complete five-profile calibration cost in this measured workload. Small water pays to discover that dense execution is faster, and auto therefore costs more than an explicit dense request. H2 avoids that probe overhead but still has ordinary dispatch overhead. These are individual runs under current load, not guaranteed speedup ratios. Source preparation takes another 0.04906, 0.07976, 0.00598 and 0.00276 seconds respectively, equally applicable to either executor.

Case	Probe complex products / block calls / AO transport products	Physical complex products / block calls / AO transport products	Maximum logical bytes, including calibration
Water large	48,758,136 / 1,764 / 1,880,064	47,509,776 / 8,064 / 4,506,624	98,969,320
NH3 large	110,365,872 / 792 / 3,316,904	156,407,820 / 4,284 / 9,950,712	135,342,792
Water small	82,908 / 528 / 46,648	163,268 / 104 / 64,484	26,538,280
Broken-spin H2	0 / 0 / 0	720 / 54 / 864	25,847,464

All routing and repeated physical builds perform zero integral calls. Native setup remains 1,369/5,328, 2,601/11,475, 25/125 and 4/8 metric/coupling calls; primitive requests are 2,401/23,716, 2,601/69,819, 225/3,375 and 36/216. Actual physical counts were independently summed from per-build receipts; probe work never enters those totals. The largest paired-calibration work reservation is 5,244,979,584 modeled units, charging execution rather than repeated preparation. Source-factor and transform storage are unchanged. Whole acceptance peak RSS is 301,121,536 bytes including tests and independent references. All 710 expected files and 396 loaded modules were recorded with matching before/after hashes; exact queue/runtime provenance and outputs are archived outside the checkout.

This closes bounded measured routing for the prepared RI developer bridge. Normal method/job/QVF integration, automatic workload estimates, native bounded block digestion and producer-owned factor export/reduced fitting generation remain next execution capabilities. Molecular source qualification does not supply periodic finite-support, Seitz/Bloch/momentum, non-Abelian reduced-product, local/frozen-space, CC residual, gradient or stress acceptance. Those original goal requirements and their explicit fallbacks remain separate.

Qualified RI methods, jobs and QVF

Numerical source a9e45532 connects the existing finite complex-Abelian RI source and measured routing to explicit molecular RHF/UHF, run_job, and executable QVF requests. It reuses PreparedMolecularSymmetry, native SCF, and the shared evaluated MolecularSymmetryResult/FockBuild. The actual S/H pass covariant invariance before admission. The auxiliary basis, native rank cutoffs and complete characters are explicit immutable inputs. Fresh jobs requalify; serialized requests carry neither audit authority nor profiles. The ordinary job bibliography now includes the executed RI symmetry papers.

Queued acceptance passed 159 regressions and three complete ordinary jobs, with same-factor dense method comparisons. Water and ammonia also passed fresh executable QVF replay. The suite covers both native method spin routes, complex characters, capped and zero-step states, independent integral/Fock checks, nonsymmetric trial-density covariance, prepared reuse with fresh counters, changed geometry, incompatible one-electron operators, resource refusal and malformed/unqualified request schemas. Existing quartet, native bridge and cost-routing regressions remain passing. Scientific tolerances stay at 1e-10 source qualification and 1e-11/1e-9 SCF energy/gradient.

Case	Job energy / hartree	Dense method energy difference	External/native energy difference	Independent Fock maximum error	QVF replay energy difference
Water/def2-SVP/def2-universal-JKFIT RHF	-75.95160765116213	1.4211e-14	1.0514e-10 (ORCA)	2.2454e-12	6.7218e-12
NH3/cc-pVDZ/cc-pVDZ-JKFIT UHF	-56.18853994215148	2.8422e-14	8.1478e-11 (ORCA)	2.8245e-13	7.8160e-13
Broken-spin H2/STO-3G, same auxiliary, 4 bohr	-0.9530462725814317	0	0 (native RI)	2.2205e-16	Not repeated

The two large sources exactly match their earlier ORCA 6.1.1 RI-JK/native qualified source identities, allowing reuse of those matched references. Maximum independent energy error is 5.4428e-12 hartree. H2 retains distinct spin densities. QVF unit conversion can change geometry’s last bits, so replay qualifies its actual producer; equality of a copied digest is not an acceptance criterion. The unchanged external energy limit is 1e-8 hartree. No matched external reference is claimed for the broken-spin minimal case.

Case	Source setup / calibration / SCF / terminal seconds	Physical complex products / block calls / AO transport products	Probe complex products / block calls / AO transport products	Maximum source/J-K logical bytes
Water	2.11202 / 1.44030 / 6.18560 / 0.32815	125,148,764 / 3,366 / 4,340,736	32,505,424 / 1,176 / 1,216,512	98,821,864
NH3	0.12651 / 0.09378 / 0.32218 / 0.00777	156,407,820 / 4,284 / 9,950,712	55,494,704 / 416 / 1,951,120	135,342,792
H2	0.00395 / 0 / 0.00935 / 0.00014	720 / 54 / 864	0 / 0 / 0	25,847,464

Physical counts include the cold terminal FockBuild contraction; this RI consumer has no terminal matrix capture yet. Routing probes are separate. All repeated J/K builds perform zero integral calls. Source setup uses 1,369/5,328, 2,601/11,475 and 4/8 metric/coupling shell calls respectively, with 2,401/23,716, 2,601/69,819 and 36/216 primitive requests. Stored selected complex factor arrays occupy 285,344, 623,760 and 64 bytes; conservative logical source/J-K reservations include much more staging/workspace. Separate method/signature reservations are 655,360/54,272, 926,720/70,144 and 69,632/23,552 bytes. Whole acceptance peak RSS is 406,421,504 bytes. One-electron preparation makes three calls per source plus the overlap call inside RI qualification, and checks at most 7.5247e-14 operator residual.

Only method-needed signatures are calibrated. Water chose dense for standalone K and blocked for its other signatures; ammonia chose blocked; H2’s short-use estimate skipped every probe and chose dense. These decisions and timings reflect this loaded run, not a speedup guarantee. The earlier isolated routing measurement remains the relevant performance comparison; no new speed claim is made from job/output timings. Full job times were 15.8793, 0.8494 and 0.1900 seconds, including non-SCF output work.

Validation used the healthy native runtime with an explicit candidate Python overlay. All 714 expected files and 420 loaded modules retained their recorded hashes. The compatibility overlay omits only unrelated newer periodic BUPO exports absent from that runtime; no periodic runtime acceptance is inferred. Queue, runtime, native hash, exact input/output and overlay provenance are archived outside the product checkout.

Supported here is explicit all-electron molecular RHF/UHF over this qualified finite RI source, including normal output and fresh QVF execution. It remains experimental and opt-in. Producer-owned factor export, reduced fitting construction, native bounded block execution, automatic workload estimates and RI terminal capture remain next capabilities. Non-Abelian products, periodic Seitz/Bloch/momentum and CCM/chi sources, CC residuals, frozen/local projectors, response, gradients and stress retain their separate qualification and acceptance requirements. This method entry does not promote any of them.

Producer-owned RI factors

Numerical source 917dd74d, validated on main b16999d2, moves fitted-factor construction into MANTA’s existing RIJKBuilder. The factory-owned export binds the actual retained metric factor, coupling source, rounded payload and executed census. Its plan admits arrays and integral/contraction work before allocation. The symmetry consumer uses the export by default, keeps complete retained-space and tensor-selection qualification, and offers the previous ordered-tiles construction explicitly. Methods, prepared handles and QVF carry that choice through the existing FockBuild interface.

This removes the consumer’s full raw three-center array. It does not reduce the ordered coupling census or certify a spatial operation. The native auxiliary rotation remains unconjugated; complex AO variance, reconstructed four-index conjugation, actual finite Gram and native rank are unchanged. Different contraction order can change rounded factors and their selected source identities. Reduced/dense comparisons use the same selected payload; the independent exporter comparison requires identical parent producer, coupling and metric-factor identities, not identical rounded exports.

All 206 focused checks pass, covering independent fitted integrals, native streamed J/K, real and complex nonsymmetric trial densities, Cartesian/pure actions, full/reduced/zero native rank, resource refusal before export work, owned-copy lifetime and mutation isolation, foreign-source rejection, and method/job/QVF admission. Native zero-rank export performs no coupling work; the symmetry consumer continues to refuse an empty retained space. Seven initial job checks encountered a stale generated basis overlay before any calculation; rebuilding that overlay resolved them. The five acceptance basis files were byte-identical to the earlier accepted inputs.

Queued scientific acceptance completed three ordinary jobs, same-payload dense controls, independent ordered-tile controls and two fresh QVF replays. The two large systems retain the earlier qualified parent source, coupling and metric-factor identities, so their matched ORCA 6.1.1 RI-JK references were reused. Independent libint metric/three-center reconstruction checks the actual terminal Fock matrices and energy. No external reference is claimed for the broken-spin minimal case; native RI supplies its control.

Case	Energy / hartree	Same-payload dense energy difference	Ordered-tile energy difference	ORCA/native energy difference	Independent Fock maximum error
Water/def2-SVP/def2-universal-JKFIT RHF	-75.95160765116752	1.4211e-14	5.4002e-12	1.1052e-10 (ORCA)	7.5496e-14
NH3/cc-pVDZ/cc-pVDZ-JKFIT UHF, complex C3	-56.188539942151195	0	3.1264e-13	8.1194e-11 (ORCA)	1.1547e-13
Broken-spin H2/STO-3G, same auxiliary, 4 bohr	-0.9530462725814317	0	0	0 (native RI)	2.2205e-16

Maximum independent energy error is 1.4211e-13 hartree; replay differences are 3.4107e-13 and 1.8475e-13 hartree. H2 retains distinct spin densities. Source tolerance 1e-10, SCF energy/gradient thresholds 1e-11/1e-9 and external energy limit 1e-8 hartree remain unchanged. Arithmetic roundoff is still excluded from the selection-error bound.

Case	Coupling shell calls / primitive products / integral values	Export products / compensated accumulations	Real exported factor bytes	Raw coupling bytes avoided
Water	5,328 / 23,716 / 65,088	7,354,944 / 2,408,256	520,704	520,704
NH3	11,475 / 69,819 / 116,899	16,248,961 / 5,961,849	935,192	935,192
H2	8 / 216 / 8	16 / 16	64	64

Both exporters use these same coupling calls. Metric construction separately uses 1,369/2,401, 2,601/2,601 and 4/36 shell calls/primitive products. Export is one coupling pass, with no independent Python fitting provider. Repeated J/K uses zero integral calls. Selected complex factor storage remains 285,344, 623,760 and 64 bytes respectively.

Case	Source setup / calibration / SCF / terminal seconds	Physical complex products / block calls / AO transport products	Probe complex products / block calls / AO transport products	Maximum source/J-K logical bytes
Water	0.07074 / 0.06340 / 0.16064 / 0.00255	47,509,776 / 8,064 / 4,506,624	32,505,424 / 1,176 / 1,216,512	100,472,288
NH3	0.09553 / 0.08636 / 0.29348 / 0.00853	156,407,820 / 4,284 / 9,950,712	55,494,704 / 416 / 1,951,120	138,535,482
H2	0.00296 / 0 / 0.00408 / 0.00012	720 / 54 / 864	0 / 0 / 0	25,804,188

Physical counts include the cold terminal contraction. Water and NH3 selected blocked execution for their requested signatures; H2’s expected-use estimate of two skipped every probe and selected dense. Routing remains measured and source-preserving. Full job times were 1.06812, 0.83770 and 0.15758 seconds.

Three alternating-order preparation samples measured the following. These times include Python allocation tracing and varied substantially under load; they do not establish an uninstrumented speedup.

Case / exporter	Preparation seconds, median (range)	Python-traced peak bytes, median
Water / producer	2.10592 (0.08196-3.10736)	10,022,600
Water / ordered tiles	14.15873 (3.04529-16.42959)	10,544,578
NH3 / producer	0.43900 (0.30827-3.06279)	17,794,757
NH3 / ordered tiles	3.87049 (1.88787-21.98737)	18,731,578

Python tracing excludes native and BLAS allocations. Whole scientific acceptance peak RSS was 476,905,472 bytes, not a controlled exporter memory comparison. Producer source reservations are 97,869,280/133,994,330 bytes versus ordered-tile 95,969,000/130,413,160 bytes for water/NH3: the conservative producer plan explicitly reserves compensation, binding and digest copies. Removing the raw array therefore does not imply a smaller logical reservation or a demonstrated process-RSS reduction.

The refreshed native module contains the implementation directly, without a compatibility overlay. All 1,457 expected input/source/native hashes and 424 loaded module hashes remained consistent; unchanged molecular source/object hashes justify reuse of the focused checks across the unrelated main merge. Queue, build, core hash, exact input/output and comparison evidence are archived outside the product checkout.

Explicit molecular Coulomb RI RHF/UHF remains experimental and opt-in. The native exporter also has focused Coulomb/erf/erfc coverage; that does not admit range-separated kernels through this symmetry method. Next production capabilities are producer-issued operation/roundoff and screening-closure certificates for representative fitting generation, native bounded block execution, automatic workload estimates and shared RI terminal capture. MANTA/BUPO owns producer screening and hierarchy bounds. Fock unification continues to consume the same evaluated source/density result. PBC Parity, non-Abelian products, CC residuals, local/frozen projectors, response, gradients and stress keep their separate source and acceptance requirements.

Shared exact-input RI terminal capture

Source 2eee59fe extends the existing method-local quartet capture to MolecularRIJK through one shared implementation. It retains one owned full-channel evaluation and at most one pending RHF J evaluation. Full UHF uses ordered total/alpha/beta inputs; separately evaluated RHF J and K can join only when their source and density bytes match. The selected fitted source identity is required, not merely its parent producer or metric factor. No state symmetry, tolerance-based density match or spin permutation is used.

Public RI method forks enable capture after resource admission and before new route probes. Reusable prepared sources remain free of densities and Fock matrices; forks inherit only source ownership and scalar cost profiles. The shared FockBuild still assembles the evaluated energy, physical Focks, frames and output state. Successful reuse reports zero new integral, factor-contraction and AO-transport work with original build numbers. Missing or changed inputs, reset state and failed full replacements keep the cold path. This does not change factor construction, integral counts, metric rank, selection rules, SCF tolerances or source/state admission.

All 178 focused checks pass. The exact-input capture tests now run against both quartet and fitted sources: independent input/output ownership, nonsymmetric trial densities, bit changes including signed zero, spin order, cross-source capture rejection, response calls, split RHF joining, reset and failed replacement, and budget refusal before work. RI method tests cover converged, capped and zero-step results and prepared reuse without state retention. Existing complex-factor covariance and native/ordered quartet checks remain passing. No native code changed; validation reused the prior qualified producer-export binary with unchanged native source/core hashes.

The queued RI phase completed three ordinary jobs, same-selected-source dense controls, explicit ordered-tile controls, independent integral/Fock checks and two fresh QVF replays. Capture-enabled and capture-disabled dense SCF controls had exactly equal FockBuild identities and energies. The two large sources match their prior qualified identities and ORCA 6.1.1 RI-JK references; broken-spin H2 retains distinct spin densities and its native RI control. All external and source tolerances remain unchanged.

Case	Energy / hartree	ORCA/native energy difference	Independent Fock maximum error	Reused physical builds
Water/def2-SVP/def2-universal-JKFIT RHF	-75.95160765116754	1.1054e-10 (ORCA)	7.1721e-14	17 and 18
NH3/cc-pVDZ/cc-pVDZ-JKFIT UHF	-56.188539942151195	8.1194e-11 (ORCA)	1.1547e-13	16
Broken-spin H2/STO-3G, same auxiliary, 4 bohr	-0.9530462725814317	0 (native RI)	2.2205e-16	6

Maximum independent energy error is 1.4211e-13 hartree. Water/NH3 QVF replay energy differences are 3.4107e-13/1.8475e-13 hartree. Ordered-tile control differences are at most 5.4144e-12 hartree. The selected factor source is unchanged by capture; different qualified exporter rounding remains separate from exact-input reuse.

Case	Dense control’s terminal products / block calls / AO transport products, all avoided by capture	Captures / copied values / compared values	Retained snapshot + pending bytes / reserved bytes	Capture seconds / terminal reuse seconds
Water	3,254,400 / 4 / 82,944	17 / 50,112 / 21,888	13,824 + 9,216 / 77,824	0.0027244 / 0.0000061
NH3	13,794,082 / 6 / 292,668	16 / 80,736 / 2,523	40,368 + 0 / 111,744	0.1128835 / 0.0000168
H2	80 / 6 / 96	6 / 144 / 12	192 + 0 / 4,608	0.0517244 / 0.0000117

The avoided counts are measured in the explicit dense cold controls; capture counts, storage and timing are from the ordinary jobs, which can choose different routes. All three ordinary terminal receipts report zero new contractions and transport. Their original physical SCF products remain counted: 86,216,928, 154,456,666 and 640 respectively, with 4,423,680, 9,658,044 and 768 AO-transport products. Fitting preparation and route calibration are unchanged. Maximum J/K logical reservations are 100,550,112, 138,647,226 and 25,808,796 bytes, including the additional 4096 + 128*n_AO**2 capture reservation. RI acceptance peak RSS was 389,283,840 bytes; it is not a controlled memory comparison.

Loaded-run source/calibration/SCF times were 9.39177/6.98070/14.59322 seconds for water, 7.16153/7.03748/19.26765 for NH3 and 0.03132/0/0.92151 for H2. Capture-disabled dense terminal contractions took 0.60665, 1.19599 and 0.12276 seconds. Scheduling variation is large; these observations do not establish an end-to-end speedup. The bounded byte copies and comparisons are reported rather than treated as free work.

The shared quartet path also completed NH3/cc-pVDZ UHF and an exact cold-versus-captured FockBuild comparison. Its energy is -56.18855210065031 hartree, 7.0331e-10 from the matched ORCA no-RI reference. The saved result has exactly the earlier accepted density and Fock bytes, verified against its complete density/FockBuild digests with current source metadata. Its unchanged producer, complete audit and zero-omission mask justify reuse of the independent full-ERI errors: 2.2427e-14 for Fock and 4.2633e-14 hartree for energy. Terminal evaluation reuses build 16 with zero new quartet, primitive, density-product and angular-transport work. Its 61 physical SCF builds retain 115,473 shell calls, 7,645,923 primitive requests, 65,777,133 density products and 43,517,278 angular products. Sixteen captures copy 80,736 values and compare 2,523, retaining 40,368 bytes within a 111,744-byte reservation. Capture and terminal-reuse times are 0.0007918 and 0.0000272 seconds; source preparation and SCF took 50.68368 and 219.93979 seconds in this loaded run.

The initial queue run reached its wall limit after all RI checks passed; only the unfinished quartet phase was submitted again. That calculation passed convergence and exact cold/captured equality, then stopped at a stale harness comparison between v1 and v2 source digests. The already landed e2e3384d source-format change explains that difference. A corrected queued assessment of the saved output passed without repeating SCF: producer/full audit and omitted mask matched, and exact D/F bytes matched the accepted independent reference. Original failure records and outputs are retained. All 1,478 pinned input/source/native hashes were checked unchanged after the interrupted phases and during the successful result assessment. Queue, runtime, references and detailed provenance are archived outside this tree.

The current molecular quartet and RI entries share exact terminal reuse; this closes that execution gap. Native bounded RI block contractions, automatic workload estimates, and producer-issued operation/roundoff and screening-closure certificates remain next capabilities. RI remains explicit and experimental. MANTA/BUPO producer ownership, FockBuild state ownership, and PBC Parity’s finite-domain/Seitz/Bloch/momentum contracts are unchanged. No new non-Abelian CC, local/frozen-space, periodic, response, gradient or stress acceptance is claimed.

Native execution of qualified RI blocks

Source 3822f763 replaces repeated Python block dispatch in the existing blocked route with an immutable native factor layout and one auxiliary exchange panel. The source factory still qualifies the complete producer export, retained Gram/rank, orbital and auxiliary representations and selection-error bound. The numerical source identities match the earlier accepted producer exports exactly. Neither integral generation nor source, state or retained-space admission changes. The low-level numpy executor preserves the former blocked implementation; dense uses the identical selected factors. Public method options and measured route selection retain their existing interfaces.

All 166 focused checks passed, including independent arbitrary complex rectangular factors, nonsymmetric densities, empty irrep groups, input/output ownership, overflow and resource refusal, failed calls, complex covariance, Cartesian/pure shells, retained-space cuts, source isolation and method-owned terminal Fock reuse. The first queue attempt failed at import before any calculation because an incoming periodic binding required a refreshed native module. After rebuilding, both binding checks passed; unchanged molecular object hashes justify reuse of the focused numerical checks. The corrected queued acceptance completed successfully. It ran explicit native-block RHF and UHF jobs, same-source dense SCF controls, independent integral/Fock/energy checks, two fresh QVF replays and alternating-order contraction benchmarks. No scientific tolerance was changed.

Case	Energy / hartree	ORCA/native energy difference	Independent Fock maximum error	Dense SCF energy difference
Water/def2-SVP/def2-universal-JKFIT RHF	-75.95160765116749	1.1049e-10 (ORCA)	7.7050e-14	4.2633e-14
NH3/cc-pVDZ/cc-pVDZ-JKFIT UHF, complex C3	-56.18853994215115	8.1152e-11 (ORCA)	1.1192e-13	4.2633e-14
Broken-spin H2/STO-3G, same auxiliary, 4 bohr	-0.9530462725814317	0 (native RI)	2.2205e-16	0

The matched ORCA 6.1.1 RI-JK references and exact producer/factor identities were reused. H2 retains distinct spin densities; it has a native RI control, not an external-program comparison. Maximum independent energy error is 1.7054e-13 hartree. Water/NH3 QVF replay errors are 3.5528e-13/1.2790e-13 hartree. All 1,482 pinned input/source/native hashes and 424 loaded module hashes agree with the recorded runtime before/after evidence.

The following benchmark contracts a fixed nonsymmetric complex AO density, including its AO/adapted transport. It uses one requested OpenMP/BLAS thread, one warmup and eight timed trials with alternating executor order. These are same-process measurements on the identical selected source, not comparisons against earlier jobs under different host load.

Case	Complex products, native/NumPy blocks vs dense	Native panel / NumPy batched / dense contraction calls	Median native / NumPy / dense time (ms)	Maximum executor difference
Water	891,700 vs 3,254,400	4,520 / 160 / 4	1.0559 / 2.3816 / 4.5019	3.9721e-15
NH3	2,339,100 vs 7,013,940	3,336 / 72 / 4	3.3712 / 3.9344 / 9.5978	2.2645e-15
H2	24 vs 48	24 / 24 / 4	0.02335 / 0.12044 / 0.03727	0

Native execution is 2.26/1.17/5.16 times faster than the previous NumPy block path in this measurement, and 4.26/2.85/1.60 times faster than dense factors. The scalar-product reduction is unchanged from the qualified block algebra; the new improvement removes Python dispatch and full-rank exchange intermediates. Panel and batched contraction-call counts have different granularity, explicitly shown above. Separate nonsymmetric real HF probes selected native blocks for water J/K and NH3 total-J/two-spin-K at expected use 100; calibration took 0.01152/0.05191 seconds. Expected use two for H2 skipped all probes and retained dense execution, preserving the cost gate.

Case	Additional owned native factor bytes	Native layout logical reservation	Physical SCF products / panel calls / AO transport products	Maximum J/K logical bytes
Water	285,344	721,600	44,870,344 / 215,152 / 4,257,792	101,140,640
NH3	623,760	1,432,160	142,607,130 / 180,978 / 9,072,708	139,948,314
H2	64	67,520	320 / 320 / 768	25,745,244

The physical runs used explicit native blocks for 69/61/12 builds; automatic probe costs above are separate. Terminal reuse retained zero new products, integrals and AO transport. Fitting still uses 5,328/11,475/8 coupling shell calls and 23,716/69,819/216 primitive-product requests respectively. No integral-work reduction is attributed to this increment. Peak process RSS was 471,515,136 bytes for the complete acceptance, including controls and references; it is not an incremental-memory comparison. Additional native factor ownership is charged, not treated as free or as a memory saving. Source setup / physical SCF times were 0.06093/0.06589 seconds for water, 0.08927/0.21575 for NH3 and 0.00273/0.00447 for H2. Ordinary job wall times were 0.50018/0.59204/0.14787 seconds. No end-to-end speedup over previous loaded-host runs is inferred from these timings.

MANTA received the reusable contraction interface; its producer-owned operation/roundoff and screening-closure certificates remain the next requirement for omitting factor-generation work. Automatic workload estimates also remain missing. FockBuild continues to own the evaluated physical state, and PBC Parity retains its separate source, Seitz/image/Bloch/momentum and quadrature requirements. Molecular RI remains explicit and experimental; this acceptance adds no periodic, non-Abelian CC, local-projector, response, gradient or stress capability. Original failure evidence, exact runtime, queue records and comparisons are archived outside the product tree.

Demand-driven molecular route calibration

Source 0d98618a removes eager calibration of unrequested RHF/UHF channel signatures. Each actual first request obtains or reuses its own scalar cost profile. Native NOITER has an exact single-evaluation horizon and skips new probes; that temporary baseline decision is not saved onto a prepared source for future iterative runs. Already paid profiles remain reusable. Source, spin state, retained spaces and FockBuild ownership keep their distinct admission rules. This increment does not predict general iterative workloads or replace producer qualification with timings.

All 192 focused checks passed. After adding the explicit targets field to zero-probe receipts, 93 relevant cases passed again; these are included in the 192, not additional unique tests. Coverage includes arbitrary nonsymmetric trial densities, actual-request-only probes, failed and invalid probes, resource refusal before calibration, prepared-source reuse, and NOITER followed by iterative use for both quartet and RI builders. Existing complex, Cartesian/pure, source/rank and physical-state checks remain in the focused set. The source was landed before queued acceptance; the compatible native module was rebuilt from 955ec2c8, whose native inputs are unchanged by this Python-only increment. All 2,288 pinned files and 425 loaded module hashes passed the runtime before/after check.

Queued acceptance completed in 31.954 seconds with one CPU and a 2 GiB reservation. It exercises ordinary auto-routed jobs, same-source dense RI SCFs, independent integral/Fock/energy references, two fresh QVF replays, three NOITER calculations and cold versus reused terminal evaluation. Matched ORCA references were reused; H2 uses an independent native RI control and has no external reference here. All existing tolerances are unchanged.

Case	Energy / hartree	ORCA/native energy difference	Independent Fock maximum error
Water/def2-SVP/def2-universal-JKFIT RHF	-75.95160765116749	1.1049e-10 (ORCA)	7.7050e-14
NH3/cc-pVDZ/cc-pVDZ-JKFIT UHF, complex C3	-56.18853994215115	8.1152e-11 (ORCA)	1.1192e-13
Broken-spin H2/STO-3G, same auxiliary, 4 bohr	-0.9530462725814317	0 (native RI)	2.2205e-16
NH3/cc-pVDZ quartet UHF, full C3v	-56.18855210065031	7.0331e-10 (ORCA)	2.2427e-14

Maximum dense RI SCF energy difference is 4.2633e-14 hartree; maximum independent energy difference is 1.7054e-13. Water/NH3 QVF replay errors are 3.5528e-13/1.2790e-13 hartree. Fresh NOITER energy differences from their accepted RI densities are zero, with exactly one physical build and zero new probes in each case. Terminal reuse performs zero new integral, contraction or AO-transport work throughout.

The former eager signature schedule was reproduced on each identical source. The following counts include both baseline and candidate probes. Timings are single calibration observations, including transport and comparisons, not a paired end-to-end speedup measurement. Automatic routing selected native RI blocks for water/NH3, native quartet reconstruction for NH3, and the dense fallback without probes for H2’s declared two-use workload.

Case	Probes, eager to demand	Probe scalar products, eager to demand	Probe AO-transport products, eager to demand	Calibration seconds, eager to demand
Water RI RHF	16 to 12	32,505,424 to 16,584,400	1,216,512 to 774,144	0.05937 to 0.04565
NH3 RI UHF	12 to 12	55,494,704 to 55,494,704	1,951,120 to 1,951,120	0.13730 to 0.15587
H2 RI UHF	0 to 0	0 to 0	0 to 0	0 to 0
NH3 quartet UHF	12 to 12	14,145,620 to 14,145,620	4,280,388 to 4,280,388	5.05519 to 4.88062

Water never requests the separate two-K signature: its removal saves 15,921,024 scalar products and four probes. Both UHF cases with probes request all three signatures, so there is no probe-count reduction. The quartet probes still perform 315,108 shell calls and 11,997,024 primitive-quartet requests. RI probe integrals remain zero because the selected factors already exist. A fresh NOITER uses only its physical baseline build; its source setup and qualification are still paid.

Case	Physical SCF products / contraction calls / AO transport products	Maximum physical J/K logical bytes	Source setup / physical SCF / elapsed SCF seconds
Water RI	44,870,344 / 215,152 / 4,257,792	101,271,712	0.09818 / 0.11863 / 0.16428
NH3 RI	142,607,130 / 180,978 / 9,072,708	140,079,386	0.18181 / 0.43077 / 0.58665
H2 RI	640 / 48 / 768	25,876,316	0.00401 / 0.00590 / 0.00590
NH3 quartets	65,777,133 / 4,708,125 / 43,517,278	71,482,441	2.08186 / 8.78897 / 13.66959

Elapsed SCF includes demand calibration; physical SCF excludes that separately recorded cost. There were 69/61/12/61 physical builds respectively. Maximum calibration logical reservations were 101,447,840 / 140,467,866 / 25,876,316 / 71,870,921 bytes. The RI acceptance portion, including controls and references, peaked at 442,744,832 bytes RSS; this is not an incremental memory comparison or the later quartet peak. Prepared sources store only bounded scalar profiles; method-local capture remains charged. No memory reduction is claimed.

RI coupling calls remain 5,328 / 11,475 / 8, with identical producer, coupling, metric-factor, rank and selected-source identities to the accepted exports. The quartet source pays a fresh 50,625-call audit, then 115,473 physical shell calls and 7,645,923 primitive-quartet requests. Qualification records separately bind producer, audit, source and screening policy. No source-audit or factor-generation savings are attributed to this change.

The Fock consumer handoff records the changed route/timing receipt semantics. MANTA still owns source generation, bounds and screening closure; its current screening work does not itself certify symmetry-compatible omission. PBC Parity keeps separate finite supports, full image shifts, wraps, Bloch phases, weights, momentum and state admission. The next missing producer capability is an operation- and pair-bound certificate including arithmetic error and screening closure for reduced factor generation. General workload prediction, non-Abelian reduced CC products, local/frozen projectors, periodic source reduction and method-specific derivatives remain separate. These molecular routes remain explicit and experimental. Queue/runtime/reference evidence is archived outside the product tree.

Incoming MANTA source 9c396ff6 separately adds fixed-metric periodic coupling-only screening, with paired actions, reference-source identity and fixed-density J/energy bounds. Its contract explicitly excludes integral, factor, phase and contraction roundoff and supplies no operation closure. That native change is outside this molecular acceptance runtime; its own producer evidence is recorded in the linked MANTA contract. It is not an admission to molecular RI reduction or a reason to repeat unchanged molecular checks.