χ-CCM / aiccm2026dev-b decisions and open questions

Last updated: 2026-07-16.

Decisions

ID	Decision	Reason
D1	Define the method as a finite BvK torus constrained to primitive-translation-invariant RHF determinants.	Gives a precise Hamiltonian, variational space, and finite-size problem.
D2	Evaluate the cyclic Gamma-supercell problem through the full unreduced Gamma-centred character mesh.	Exact finite-group Fourier equivalence; reuses the validated SCF/integral infrastructure.
D3	Use Wigner–Seitz weights only to partition tied minimum-image representatives of one translation class.	Weights sum to one and preserve one- and two-electron permutation symmetries.
D4	Reject the historical pair-product four-centre weighting.	Its displayed factors are not generally invariant under bra–ket interchange, so a conventional RHF scalar functional does not follow.
D5	In 3D use the common neutral periodic Ewald/GDF gauge, remove the Hartree (G=0) mode, and apply the BvK-supercell exchange Madelung correction.	Keeps electron–electron, electron–nuclear, nucleus–nucleus, and exchange finite-size conventions consistent in the 3D route.
D6	Reject charged cells and smearing in Phase 1.	Both require a different explicitly stated variational functional/background convention.
D7	Keep the existing CCM untouched and expose aiccm2026dev-b as a new PeriodicJKMethod.	Allows head-to-head comparison with no behaviour change to the peer implementation.
D8	Reuse native GDF, Ewald, basis, lattice, canonical orthogonalisation, DIIS, and output infrastructure.	These are not AICCM-specific; duplicating them would reduce comparability and correctness.
D9	Accept only the pair-resolved RSGDF or MDF fit; reject the q-only compcell fit.	The latter is not a consistent four-centre finite-torus Hamiltonian on tight cells and has known non-physical fixed points.
D10	Initialise the existing periodic citation flag for non-KPoints inputs.	The repo-wide gate exposed an unrelated unbound local in citation output. The false default restores the intended existing behaviour and does not alter any SCF result.
D11	Refresh two stale k-point recommender assertions found by the repo-wide gate.	They still expected the retired ungated-model error and Fermi–Dirac default, while the shipped implementation and changelog specify the environment gate and Methfessel–Paxton default. Production behaviour is unchanged.
D12	Expose three independently selectable integral backends: four_center, ri, and rijcosx.	They allow direct-versus-three-centre consistency tests when their dimensional Coulomb gauges are matched.
D13	Reuse the corrected-gauge BIPOLE Fock engine for four_center; do not use the legacy multi-k Ewald direct-exchange path.	The former contains direct four-centre short-range J/K plus the reciprocal long-range and BvK exchange correction. The legacy path is documented upstream as missing the exchange correction. This identifies the intended corrected-gauge algebra; D82 separately records that the current short-range internal traversal is not yet basis-independently converged.
D14	Permit production χ-CCM-B SCF only for 3D cells until a shared 1D/2D mixed-boundary Coulomb kernel is derived.	The finite group is dimension independent, but the Coulomb kernel is not. The current lower-dimensional four-center path uses a direct-truncated BIPOLE fallback rather than a neutral finite-torus wire/slab gauge, and the shared neutral-RI/GDF mesh collapses transverse Fourier components to (G_\perp=0), giving a transverse-uniform sheet term rather than (1/r). Returning lower-dimensional absolute energies from either family would be silent scientific corruption.
D15	Fail closed for RI/RIJCOSX RKS and RIJCOSX RHF at a one-cell mesh.	The native Gamma-only RKS GDF path is not pair-resolved and the COSX bridge is multi-k only; silently falling back would mislabel the backend.
D16	Audit the 2008 deMon2k KS-ADFT CCM separately from the 2014 four-center formula.	Janetzko et al. use multiplicative occurrence weights, but their Eq. (20) explicitly averages both AO-center orderings. The same bra–ket diagnosis cannot be copied without checking that symmetrization; quotient-space adjoint consistency and long-range truncation remain open.
D17	Superseded by D88. Transpose the repository’s row-lattice array when constructing the mathematical lattice generator.	This historical decision incorrectly asserted that PeriodicSystem.lattice stores lattice vectors as rows. The core and bindings define its columns as the direct-lattice vectors. D88 repairs the implementation and fingerprints affected records.
D18	Build χ-CCM MP2 from the χ-CCM RI-RHF character-mesh reference, not the existing toroidal Gamma-supercell HF helper.	The two references differ by 4.6408868 mHa per cell on the two-cell 8 x 12 x 12 bohr H2 control, so substituting the latter changes the finite zeroth-order Hamiltonian.
D19	Use a truncated metric inverse square root expressed in the original auxiliary-AO basis for post-HF momentum blocks.	Compact eigenspace factors have arbitrary phases and rotations independently at (q) and (-q). The canonical matrix function removes that gauge from cross-block MP2 contractions.
D20	Expose canonical RI-MP2 initially for 3D neutral closed-shell systems and fail closed for 1D/2D.	The 3D two-point H2 result agrees with external KRHF/KMP2 below one nanohartree per cell. The lower-dimensional long-range convention remains O1 and cannot yet support a single reference Hamiltonian.
D21	Transform the pair-resolved RI Hamiltonian to a real finite torus before local correlation.	The derived (N_c^{-2}) inverse transform reproduces the momentum-space RI integral normalization exactly and preserves the χ-CCM reference instead of substituting the legacy Gamma-supercell Hamiltonian.
D22	Count every occupied pair and ordered triples contribution on the finite torus, then divide the total correlation energy by (N_c).	This is unambiguous and passes the exact-limit oracle. Translation-reduced pair/triple orbits require an orbit-stabilizer derivation and are not approximated by occurrence weights.
D23	Use PBC-safe Pipek–Mezey occupied localization; reject molecular Foster–Boys localization.	Mulliken populations do not require the ordinary position operator, which is discontinuous on the torus boundary.
D24	Keep pair-distance screening, finite occupied-coupling radii, and local fitting disabled in the B local-correlation route.	The existing molecular algorithms use Euclidean distances. Minimum-image Wannier and auxiliary domains are required before those approximations can preserve translation symmetry. PNO truncation itself remains available.
D25	Localize one complete finite-torus occupied space, never independent k blocks.	A single unitary rotation preserves the occupied projector, density, and SCF energy exactly and produces translationally related occupied orbitals for local correlation.
D26	Label the present periodic spread as a projected circular AO-centre approximation, not an exact Marzari–Vanderbilt spread.	Exact continuum localization needs cross-k exponential-position matrix elements that the integral API does not yet expose.
D27	Construct B-specific PAOs with the metric projector and canonical Gram orthogonalization, and construct PNOs from a Hermitian positive-semidefinite pair density.	The algebra removes occupied leakage and PAO redundancy and gives nested PNO ranks as the occupation threshold is tightened. MP2 energy errors are not variational and need numerical validation.
D28	Enumerate occupied-pair orbits by closure under measured localization translation permutations, but do not skip representative pairs yet.	Orbit multiplicities are exact only after translation covariance is proven. The current Wannier control passes, while finite-supercell IAO cross overlaps leave a residual near (10^{-5}). Representative-only amplitude scattering has no energy-parity gate yet.
D29	Expose space-group symmetry as an off-by-default diagnostic and fail closed for integral reduction.	The compatible finite-cluster subgroup, nonsymmorphic atom/cell maps, irreducible k orbits, and primitive shell-pair/quartet orbit partitions are derived. General-k AO sewing matrices and representative scatter are not yet proven in every backend convention.
D30	Before the real local solver, construct and verify a full-rank real time-reversal gauge; at the complete-domain, zero-PNO-threshold MP2 limit, audit the result with an independent rotation-invariant full-space DF-MP2 contraction.	The first integration exposed unsafe complex-to-real casts in a solver whose equations are real. Explicit realification preserves the occupied projector. The public result reports both the raw value and any full-space correction. No correction is applied to truncated calculations.
D31	Make the real-space lattice extension the primary user parameter and derive the full Gamma-centered character net from it.	The method is a finite BvK torus, not two independently converged real- and reciprocal-space approximations. A shell radius (s_i) means (N_i=2s_i+1); the old mesh tuple remains only an exact compatibility alias.
D32	Extend UHF and UKS with independent alpha and beta idempotent projectors on the same declared finite Hamiltonian.	Spin changes the variational ranks and exchange contractions, not the translation quotient, Wigner–Seitz partition, or finite-torus convention. Separate density, electron-count, and spin-contamination audits make this explicit.
D33	Build unrestricted post-HF from the exact real transform of the χ-CCM RI-UHF Hamiltonian.	Reusing a molecular or legacy Gamma reference would change the finite zeroth-order Hamiltonian. The supercell multiplicity is (N_c(M-1)+1), preserving the spin difference in every primitive cell.
D34	Treat the present unrestricted DLPNO-UCCSD(T) engine as an O(N^6) correctness oracle.	Full-domain projection proves the PNO exact limit, but translation-representative amplitude propagation and minimum-image domains are not implemented. Calling it production reduced scaling would be false.
D35	Expose only gauge-invariant SCF properties derivable from the finite-net one-particle density.	Electron/spin counts, Mulliken populations, finite-net gaps, idempotency, and ⟨S²⟩ are defined. Cell dipoles, Berry-phase polarization, analytic response, and correlated properties need additional theory and fail closed.
D36	Move the B post-HF finite-torus setup kernels to native OpenMP code, but keep the equations and parity tests in Python-visible form.	The inverse RI-factor transform and AO-to-MO contractions are performance and memory bottlenecks. The native RI transform streams directly to the final real tensor instead of materialising the former six-dimensional complex temporary. The public method semantics do not change.
D37	Fail closed for 1D/2D four-center absolute energies rather than preserving the old vacuum-H2 molecular-limit shortcut.	The shortcut geometry did not test the uniform h-chain/lih-chain/polyethylene F1 class. The benchmark wave confirmed a mesh-independent, (Z)-scaled Madelung-size over-binding in real chain inputs, so the lower-dimensional four-center route is disabled until its neutral Green function is derived and tested.
D38	Surface SCF residuals and accelerator settings in every χ-CCM SCF diagnostic record.	The c-diamond and si-diamond RKS/PBE/RI queue failures reached the iteration cap with clean density idempotency and electron count, but the old JSON did not preserve the final commutator norm, energy step, or effective accelerator controls. Without those residuals one cannot distinguish a physical/gauge error, a true two-cycle, or an accelerator that is simply outside its basin. This is diagnostic hardening only; it does not change the finite Hamiltonian or mark the failed jobs as acceptable.
D39	Make the RSGDF reciprocal mesh respect the declared periodic dimensionality.	Low-dimensional χ-CCM routes embed chains and slabs in large vacuum-padding axes. The previous RSGDF dense mesh treated those inactive axes as periodic and built a full 3D sphere, so h-chain/lih-chain RI jobs appeared to hang at the per-pair (L_{P\mu\nu}) cache. The fix freezes inactive reciprocal indices at zero for dim < 3; 3D crystals retain the original full reciprocal sphere.
D40	Stream the canonical χ-CCM RI-MP2 energy contraction in native OpenMP code.	The earlier Python loop materialised one (O(n_o^2 n_v^2)) oovv scratch tensor per virtual k block for every occupied k pair. The new kernel contracts each momentum-conserving quartet directly from the pair-resolved (L_{Pia}(k_i,k_a)) factors, preserving the same spin expression while reducing scratch memory from (O(n_k n_o^2 n_v^2)) to scalar accumulators plus cache-resident slices.
D41	Build multi-k RKS XC from the full inverse-Bloch real-space density and Bloch-fold (V_\mathrm{xc}(R)) back to each k point.	A local or semilocal XC functional is periodic in the primitive cell, but its AO matrix elements are lattice matrices. Collapsing the finite-torus density to one Gamma AO block and adding the same (V_\mathrm{xc}) to all k points is exact only in the molecular/vacuum limit and is not a variational KS map for tight crystals.
D42	Attach an explicit finite-torus convention descriptor to χ-CCM SCF and post-HF results: coulomb_kernel="3d-periodic-g0", exchange_q0="bvk-ewald", the boundary model, the character mesh, and the BvK Madelung supercell.	Finite-N HF, MP2, CCSD(T), and DLPNO denominators depend on the exchange q=0 seam through the reference orbital energies. A strict-zero-mode reference is a different finite Hamiltonian with the same thermodynamic target, so it must not compare silently as the production χ-CCM Hamiltonian. The non-rank-1 Madelung remainder is finite-size physics of the same (v_E), not RI error or gauge freedom.
D43	Carry the same finite-torus convention descriptor into χ-CCM SCF properties, band structures, and Mayer bond analyses.	Electron counts, Mulliken charges, finite-net gaps, spin diagnostics, interpolated bands, and Mayer bond orders are one-particle analyses of the declared finite Hamiltonian. The formulas do not gain an extra convention factor, but the outputs must keep the Hamiltonian label so QVF, JSON, and manuscript comparisons cannot mix BvK-Ewald exchange with strict-zero-mode or low-dimensional kernels silently.
D44	Treat ECP electron and background bookkeeping as part of the finite Hamiltonian descriptor, not as a backend detail.	A periodic ECP removes core electrons from the variational space and replaces bare nuclear charges by (Z_\mathrm{eff}). χ-CCM now validates that ecp_total_ncore, per-atom effective nuclear charges, the effective electron count, and the neutral background are mutually consistent before SCF. Diagnostics, bands, Mayer analysis, and Mulliken charges use the effective counts rather than bare all-electron (Z).
D45	Contract χ-CCM Mayer bond orders from finite-torus residue blocks in native OpenMP code and fold the compact residue tensor directly.	The dense reference formula first materialises full AO supercell density and overlap matrices, multiplies them, and then folds a full atom-supercell pair matrix. The block-circulant identity ((PS)(\Delta)=\sum_G P(G)S(\Delta-G)) gives the same residue-resolved atom-pair tensor (M_{AB}(\Delta)) while storing only (N_c n_\mathrm{AO}^2) intermediate data plus (N_c n_\mathrm{atom}^2) Mayer data. The full-matrix path remains only as a compatibility and regression oracle.
D46	Build the χ-CCM post-HF momentum-conservation table in native OpenMP code.	RI-MP2 and local-correlation setup need the finite-group map (k_b=k_i-k_a+k_j) modulo reciprocal lattice vectors. The mathematical object is unchanged, including duplicate-character and non-closed-mesh rejection, but the (O(N_k^3)) loop no longer runs in Python.
D47	Reuse the native finite-character matrix transform for localization overlap and Fock matrices.	Occupied localization needs real finite-torus overlap and Fock matrices before the unitary gauge search. The old Python einsum path is retained as a test oracle, but production now uses the same OpenMP transform as post-HF and fails closed if a non-negligible imaginary residue would otherwise be discarded.
D48	Back-transform canonical χ-CCM occupied Bloch coefficients to Wannier coefficients in native OpenMP code.	The formula (w_{Rn}=\frac{1}{N}\sum_k e^{ikT}C_{kn}e^{-ikR}) is unchanged, but the old Python einsum materialised a four-index temporary over target cell, AO, home cell, and band. The native route streams directly into the final real-torus coefficient matrix and keeps the einsum path as a regression oracle.
D49	Expose the RSGDF kinetic-energy cutoff at the high-level periodic runner and print it in the χ-CCM log.	RI and RIJCOSX finite-N energies depend on the declared fitting representation and reciprocal auxiliary mesh. The direct B APIs already had rsgdf_ke_cutoff; the public run_periodic_job(..., jk_method="aiccm2026dev-b") surface now forwards the same keyword and writes gdf_method, rsgdf_ke_cutoff, and mdf_ke_cutoff to the .out file. The default remains 200 Ha, so existing inputs are unchanged. Recording the base cutoff does not attest a high-G tail completion or prove dense-core absolute-energy convergence.
D50	Stream canonical χ-CCM RI-MP2 pair factors from AO-space Lpq to MO-space Lov.	Canonical character-space MP2 only needs (L_{Pia}(k_i,k_a)), not the full AO-space (L_{P\mu\nu}(k_i,k_a)) cache. The MP2 route now builds one pair-resolved Lpq, transforms it with the native AO-to-MO kernel, then releases it. The local/DLPNO real-torus route still keeps the full pair cache because its inverse finite-group cderi transform requires all pairs simultaneously.
D51	Release χ-CCM RI temporaries immediately after their last mathematical use.	The AO-space pair cache is cleared as soon as the real-torus cderi tensor has been formed, and the canonical MP2 Lov dictionary is cleared after the native energy contraction. This changes only object lifetimes, not tensor definitions or contraction order.
D52	Partition χ-CCM local-correlation occupied-pair orbits in a native finite-group kernel.	The mathematical object is still the breadth-first closure of unordered occupied pairs under the supplied translation and optional point-group permutations. The implementation no longer builds that closure with Python sets on production paths; it returns representatives, offsets, and flattened members from a private native kernel while retaining the Python closure as the test oracle.
D53	Stream the real-torus complete-domain MP2 audit contraction in native OpenMP code.	Local-PNO exact-limit corrections need the full-domain MP2 energy on the real finite torus, but they do not need the full (ijab) tensor to be resident. The native kernel contracts (L_{Pia}L_{Pjb}) and (L_{Pib}L_{Pja}) directly inside the denominator loop and keeps the old tensor expression as a regression oracle.
D54	Build finite-translation occupied-index permutations in the private native χ-CCM kernel layer.	The permutations still represent simultaneous cyclic translations of all localized occupied orbitals, ordered by the same lexicographic finite-torus cell convention. Moving the table generator out of Python removes another setup loop before the native occupied-pair orbit closure, without changing the local-correlation approximation level.
D55	Move the finite-character inverse Bloch transform for residue blocks to native OpenMP code.	The transform (M(R)=\sum_k w_k\exp(-2\pi i k\cdot R)M(k)) defines density and property residue blocks throughout χ-CCM diagnostics. The native kernel streams over requested residues and matrix elements directly, preserving arbitrary normalized k weights and retaining the former einsum as a regression formula.
D56	Expose χ-CCM analytic-gradient status as a B-owned fail-closed API.	Γ-CCM now has an analytic gradient for its separately constructed union-and-weight energy, but χ-CCM production numbers declare the finite-character Hamiltonian with coulomb_kernel="3d-periodic-g0" and exchange_q0="bvk-ewald". A B force must differentiate that Hamiltonian, including the exchange seam, character AO/Pulay adjoint, and RI/RIJCOSX response where applicable. The public B gradient entry point records the convention and raises instead of substituting a Γ-CCM gradient; run_periodic_job also rejects B geometry optimizations and Hessians.
D57	Expose the 3-D Ewald nuclear-repulsion gradient as a χ-CCM-B component helper, not as a total force.	compute_aiccm2026dev_b_ewald_nuclear_gradient(system, result) validates the result’s finite-torus convention and returns only (\partial E_{nn}^{Ewald}/\partial R_A) for 3-D 3d-periodic-g0 / bvk-ewald B records. The helper gives the gradient derivation a parity-tested first term while compute_aiccm2026dev_b_gradient remains fail-closed until electron-nuclear, Pulay, exchange-seam, RI/RIJCOSX, and response terms are assembled.
D58	Expose the fixed-density 3-D Ewald electron-nuclear gradient as a χ-CCM-B component helper.	compute_aiccm2026dev_b_ewald_electron_nuclear_gradient(system, basis, result, density, lattice_options=...) validates the same finite-torus convention and differentiates only (\sum_g \mathrm{Tr}[D(g)V_{ne}^{Ewald}(g)]) for a caller-supplied real-torus density and lattice cutoff. Requiring explicit density and lattice options prevents silently mixing cutoffs or relaxed-density assumptions; the total force remains fail-closed until the SCF Pulay/adjoint, exchange seam, RI/RIJCOSX metric response, and post-HF response are assembled.
D59	Bundle the fixed-density 3-D Ewald electrostatic gradient components without exposing a total force.	compute_aiccm2026dev_b_ewald_electrostatic_gradient_components(...) returns the nuclear, electron-nuclear, and fixed-density sum arrays while recording the Ewald alpha, nuclear cutoff, reciprocal cutoff, and finite-torus convention used. This makes the next derivation tests compare one electrostatic object against finite differences, but still avoids claiming an SCF force because Pulay/adjoint, exchange seam, RI/RIJCOSX response, and relaxed-density terms are absent.
D60	Expose χ-CCM-B SCF density folding for fixed-density gradient components.	compute_aiccm2026dev_b_scf_density_lattice(system, basis, result, lattice_options=...) inverse-Bloch folds the result’s converged k-density onto the exact LatticeMatrixSet.cells requested by the lattice-sum options, with a fail-closed imaginary-residue guard. This removes ad hoc caller-side density reconstruction for the Ewald component helpers, but it is still not SCF force assembly because energy-weighted Pulay, exchange seam, RI/RIJCOSX response, and relaxed-density terms are absent.
D61	Expose the SCF-density 3-D Ewald electrostatic component bundle without exposing a force.	compute_aiccm2026dev_b_scf_ewald_electrostatic_gradient_components(system, basis, result, lattice_options=...) first inverse-Bloch folds the stored B SCF k-density onto the requested lattice-cell list, then reuses the fixed-density Ewald electrostatic bundle. This gives derivation tests a convention-checked Hellmann-Feynman electrostatic object for the stored density, but still excludes energy-weighted Pulay/adjoint, the BvK exchange seam, RI/RIJCOSX response, and post-HF response terms.
D62	Expose matching fixed-density 3-D Ewald electrostatic energy bundles for component finite-difference audits.	compute_aiccm2026dev_b_ewald_electrostatic_energy_components(...) and its SCF-density wrapper evaluate only E_nn^Ewald + sum_g Tr[D(g) V_ne^Ewald(g)] with the same alpha, nuclear cutoff, reciprocal cutoff, and finite-torus convention as the gradient component bundle. This removes duplicated caller-side V_ne scalar assembly from derivation tests, but it still is not a total SCF force or response energy because Pulay/adjoint, exchange seam, RI/RIJCOSX response, and relaxed-density terms remain absent.
D63	Require exact lattice-cell and AO-space support for explicit fixed-density Ewald electrostatic audits.	The explicit compute_aiccm2026dev_b_ewald_electron_nuclear_gradient(...), compute_aiccm2026dev_b_ewald_electrostatic_energy_components(...), and compute_aiccm2026dev_b_ewald_electrostatic_gradient_components(...) helpers now fail closed unless the caller-supplied density LatticeMatrixSet.cells exactly matches the cell list implied by lattice_options, the density header carries the same AO dimension as the operator template, and there is one block of the expected AO shape for every cell. This prevents comparing a scalar audit energy that ignores extra density cells with a derivative helper that would otherwise differentiate over them, and catches malformed component-test densities before lower-level contractions. The SCF-density wrappers already construct the matching cell list and AO space internally.
D64	Validate unrestricted SCF-density spin metadata before folding stored density blocks.	compute_aiccm2026dev_b_scf_density_lattice(...) now rejects UHF/UKS records whose effective electron count and multiplicity do not define non-negative integer alpha/beta occupations. Even when explicit alpha/beta density blocks are already present, folding them under impossible spin labels would corrupt component-gradient audits and downstream convention records.
D65	Validate restricted SCF-density electron metadata before folding stored density blocks.	compute_aiccm2026dev_b_scf_density_lattice(...) now rejects RHF/RKS-style records unless the result is labelled by singlet multiplicity and a non-negative even effective electron count. Explicit closed-shell density blocks no longer bypass the metadata check, so Ewald component audits cannot proceed with an impossible spin-paired density label.
D66	Validate stored SCF k-density AO dimensions before real-torus folding.	compute_aiccm2026dev_b_scf_density_lattice(...) now checks every stored k-density block against the active AO basis dimension before the inverse Bloch transform. A malformed result wrapper or stale density cache therefore fails at the B density-extraction boundary instead of reaching lower-level lattice setters or producing component-gradient audits in the wrong AO space.
D67	Stream the finite-cutoff multi-k Ewald Hartree J output-cell contraction used by BIPOLE comparisons.	compute_j_ewald_3d_ft_k_density_to_cells(...) now batches output cells when evaluating the AO-pair Fourier transform for the G != 0, zero-mode-dropped Hartree J reference, with the automatic cell batch sized from the active G slice. The contraction is exact on the selected finite G set and the dense all-cell path remains its regression oracle, but the selected kinetic-energy cutoff is a numerical partial sum rather than a proof of reciprocal-tail convergence.
D68	Emit optional χ-CCM-B Wannier-centre overlays as a QVF vendor section.	run_periodic_job(..., jk_method="aiccm2026dev-b", output_qvf=True, qvf_wannier_centers=True) now localizes the complete occupied finite-torus space with the B-owned Wannier gauge and writes x_ccm.wannier_centers in Angstrom and Angstrom-squared units for vibe-view. The density and orbital visual objects remain precomputed torus-periodic grids over the full BvK cell, and the overlay is opt-in so routine SCF output does not acquire extra localization work.
D69	Fold stored RI/RIJCOSX k-density blocks when emitting χ-CCM-B periodic QVF grids.	Four-center B results can expose real-space lattice density aliases directly, but RI and RIJCOSX store the converged finite-character density per k point. The QVF path now inverse-Bloch folds those k-density blocks onto the cyclic residues before expanding the BvK supercell density grid, so multi-cell 3D RI/RIJCOSX B archives carry the same torus-spanning periodic-grid contract as four-center B archives.
D70	Regression-test vibe-view’s χ-CCM-B QVF periodic contract on 3D controls.	The QVF writer tests now include a 3D vacuum-padded H-chain RI control and a compact 3D periodic H2-pair RI control with qvf_wannier_centers=True. Both assert structure.pbc, Angstrom row-vector BvK lattice fields, torus-spanning density grids, electron-count integration, orbital volume grids, and x_ccm.wannier_centers. This is a visualization/output contract gate only; it does not change the finite Hamiltonian or re-enable lower-dimensional RI/GDF routes.
D71	Cover unrestricted χ-CCM-B QVF output with spin-summed density and alpha/beta Wannier overlays.	The UHF/RI H3 doublet regression validates the upstream odd-electron periodic-output multiplicity normalization against the B route: the archive keeps the declared 3D finite-torus convention, writes a torus-spanning alpha-plus-beta density grid, and emits two alpha plus one beta x_ccm.wannier_centers entries. This is still a QVF/output contract; unrestricted crystalline orbital grids are not claimed until a spin-resolved periodic orbital-grid writer is added.
D72	Adopt the shared lower-dimensional neutral-RI/GDF fail-closed guard for χ-CCM-B RI and RIJCOSX.	The upstream 2026-07-10 audit showed that the lower-dimensional neutral-RI mesh is not merely a different gauge: by pinning every vacuum-axis reciprocal component to zero, it removes transverse Coulomb structure and produces vacuum-padding artifacts. χ-CCM-B therefore now fails closed for 1D/2D RI and RIJCOSX just as it already did for 1D/2D four-center, until O1 supplies one shared wire/slab Hamiltonian with matched electron-electron, electron-nuclear, nuclear, and exchange-seam terms. Fleet and paper route generators must keep every lower-dimensional row as explicit unsupported coverage rather than submitting it as a runnable calculation.
D73	Historically fail closed for every proposed Γ/χ energy delta unless both records carry one complete paired producer and numerical-input contract (superseded by D89’s empty approach map).	Route names and the exchange-q=0 label identify an intended pairing but do not prove the same numerical realization or construction. A reportable control value requires finite converged energies, the same clean full source SHA, native-core SHA256, versioned successful host probe, canonical input SHA256, 3D boundary/kernel, two-electron operator, auxiliary basis, RSGDF method/cutoff, linear-dependence threshold, and auxiliary phase convention. Contract v1 is RSGDF-only because it does not fingerprint MDF’s active cutoff. Conflicting payload aliases or missing/mismatched fields leave the control undefined, including raw JSON. The historical map excluded pure-PBE RI, the research WSSC aiccm-rijcosx, and all four-center A direct-torus versus B BIPOLE pairs because identical discretized operators had not been established. This prevents stale-build and common-mode backend defects from being mislabelled as approach or construction evidence. D89 further establishes that even a complete neutral-torus control contract would not by itself define a Γ-CCM/χ-CCM approach delta.
D74	Supersede v1 with the aiccm2026-gamma-chi/v2 comparator acceptance schema and historically retain B rhf-ri versus A aiccm-hf-direct as an SCF-representation candidate (superseded by D89).	The previously mapped A RI and RIJCOSX routes call the same multi-k GDF SCF drivers as B, so their agreement is common-path regression evidence rather than a Γ/χ representation delta. Contract v2 requires each producer to embed comparison_input, validates its exact shape and consistency with the result/contract, requires its canonical hash to equal comparison_contract.input_sha256, and records ao_linear_dependence_threshold=1e-7 separately from auxiliary_metric_linear_dependence_threshold=1e-9. It also reconciles requested and reported SCF smearing and accepts only smearing_temperature=0.0 Ha, preventing a finite-temperature state from being labelled as a representation delta. This removes v1’s ambiguous single threshold and makes the hashed input inspectable. The direct-torus A solver independently assembles and minimizes the Γ-supercell SCF representation but intentionally reuses the common per-q RSGDF fit and one-electron primitives, so it tests neutral-torus representation assembly rather than independently validating the RI builder or the union-and-weight Γ-CCM approach. It remains unreportable until both runners emit v2 with matched build and the composite producer-process provenance required by D77. A curation sidecar cannot retroactively attest the inputs, binary, probe, payload, or producer process that produced an existing energy. D89 supersedes this row’s former terminology and any approach-equivalence premise; its numerical or implementation decision remains historical context.
D75	Make the two historical benchmark producers’ attestations symmetric before revising or emitting the numerical-input schema.	Both benchmark producers now derive the source commit and cleanliness from the checkout providing imported vibeqc, record the same host/package/core identities, and bind the exact embedded pre-run numerical-probe attestation to a canonical digest. Generated B jobs use the same run.sh probe path through an explicit --b selector; the wrapper creates each attestation in an atomic private temporary directory, so an opt-out cannot inherit an old pass or collide with another job. Probe caching is allowed only for a clean tracked source and is keyed by source, core, host, package version, probe version, and the executing probe-script SHA256; changing the probe implementation therefore invalidates old passes. Cheap producer imports and API-shape checks still run before every cache hit. The comparator recomputes the attestation digest and requires these producer fields to agree, but the control remains undefined because no producer emits v2 numerical input. Emission is deferred until the common Bloch pair-density phase is separated from the different auxiliary factor gauges (canonical auxiliary-AO frame and compact eigenmodes). Every character must retain all primitive-cell AO directions for the current control; if projected spaces are admitted later, compare Fourier-related retained-space projectors rather than ranks alone. This changes evidence provenance only. It neither assigns a shared finite Hamiltonian to the Γ-CCM and χ-CCM constructions nor makes the control a cross-approach comparison.
D76	Serialize the resolved 3D direct electronic and nuclear lattice cutoffs in every χ-CCM-B four-center benchmark record.	The shared BIPOLE fix in 6fed8620 makes direct RHF/UHF/UKS callers apply the same neutral-cell policy already used by RKS and run_periodic_job: with the 3D Ewald J split active, the nuclear real-space cutoff cannot exceed the electronic J/K cutoff. The default pair therefore resolves from 15/25 bohr to 15/15 bohr. run_case_b.py now records the post-driver values as direct_lattice_cutoffs; RI and RIJCOSX records use null because those are not direct BIPOLE two-electron cutoffs. Pre-6fed8620 3D four-center records, including the June 21 H2 RHF/PBE0 smoke values, are revision-bound and must be rerun before quotation. The 15/15 pair records coherent physical density and nuclear support; it does not attest the larger internal ket-image traversal required by D82. This is numerical support within the declared BvK-Ewald Hamiltonian, not evidence about equality or difference between the Γ-CCM and χ-CCM constructions.
D77	Replace D75’s pre-run-only producer evidence with a composite producer-process attestation.	The cached aiccm-host-probe/v2 preflight remains required for a trusted dispatch, but each A and B producer now validates it against its own current clean source, host, package, native-core path SHA256, and probe implementation. In the producer process it binds a canonical SHA256 manifest of the copied benchmark payload, records linked native-library versions, and always runs a cheap shifted-mesh native-versus-Python AO-pair Fourier-transform canary. If the core-path SHA256 changed after preflight, the producer reruns the full v2 API, cutoff, and LiH direct-versus-GDF host checks in process; the cheap canary alone cannot recover a changed core. Immediately before serializing the result it re-reads the producer identity, library versions, and payload and requires exact stability. The core SHA256 identifies bytes currently at the imported module’s filesystem path, not bytes already mapped into memory, so the same-process numerical checks attest loaded behavior without overclaiming a cryptographic loaded-image identity. The comparator independently validates every nested shape, canonical digest, check version, and tolerance, then compares A and B by their current producer identities rather than requiring identical preflight history or identical stream-specific payload digests. D75 remains the history of the preflight cache and phase/AO-space blocks, but its pre-run-only evidence mechanics are superseded. Existing rows are not retroactively upgraded by curation or sidecars. D89 supersedes this row’s former terminology and any approach-equivalence premise; its numerical or implementation decision remains historical context.
D78	Build each Bloch RSGDF factor on the physical shifted reciprocal sphere `0 <	G+q
D79	Expose the fixed-density kinetic scalar and AO-centre derivative as a separate 3D χ-CCM-B gradient component.	compute_aiccm2026dev_b_fixed_density_kinetic_energy(...) evaluates sum_g Tr[D(g) T(g)] for a caller-supplied real-torus density, and compute_aiccm2026dev_b_fixed_density_kinetic_gradient(...) evaluates its analytic AO-centre derivative at the same fixed density. Both require the density cell indices, Cartesian translations, and AO blocks to match the caller’s lattice_options exactly, and the derivative is checked against central differences of the matching scalar on displaced bases. No SCF wrapper is exposed because current SCF results do not retain an attested resolved one-electron lattice cutoff from which the identical operator support can be reconstructed. This is one independently checkable derivative component, not a total force: the energy-weighted Pulay/adjoint, BvK exchange-q=0 seam, RI/RIJCOSX response, and post-HF response terms remain open and the total-gradient API remains fail-closed. D89 supersedes this row’s former terminology and any approach-equivalence premise; its numerical or implementation decision remains historical context.
D80	Expose a fixed energy-weighted overlap Lagrangian scalar and AO-centre derivative as a separate 3D χ-CCM-B gradient component.	compute_aiccm2026dev_b_fixed_energy_weighted_overlap_lagrangian(...) evaluates -sum_g,mu,nu W_mu,nu(g) S_mu,nu(g) for a caller-supplied real-torus energy-weighted density, and compute_aiccm2026dev_b_fixed_energy_weighted_overlap_gradient(...) evaluates its analytic AO-centre derivative with the numerical W(g) blocks and lattice held fixed. The scalar is a Lagrangian constraint companion, not a separately additive energy. Both helpers require exact cell indices, Cartesian translations, AO dimension, and block shapes, and the derivative is checked against central differences of the matching scalar using a time-reversal-consistent odd-character conjugate pair whose real-space blocks are individually nonsymmetric. No SCF wrapper is exposed: constructing the stationary B-owned energy-weighted density requires backend, spin, occupation, gauge, and support provenance, while the BvK seam or screened-exchange derivative remains a separate explicit term. The total-gradient API remains fail-closed. D89 supersedes this row’s former terminology and any approach-equivalence premise; its numerical or implementation decision remains historical context.
D81	Partly superseded by D88. Bind every χ-CCM-B gradient component audit and SCF-density fold to the recorded finite torus before adding another derivative term.	The mesh, boundary, descriptor-agreement, and complete-character-net requirements remain valid. Its historical row-vector premise and A_BvK = diag(N) A_system formula were wrong because PeriodicSystem.lattice stores vectors as columns; D88 replaces that binding with A_BvK = A_system diag(N). The other provenance limits remain: atoms, basis identity, resolved operator cutoffs, and the origin of caller-supplied D or W are unattested; stresses and cell derivatives are outside the contract; total gradients still fail closed.
D82	Treat two-electron numerical-support convergence as a separate reportability requirement for active 3D χ-CCM-B backends.	The MgO split audit in 51e3b250 proves that the four-center BIPOLE short-range ket-image traversal needs a smeared-kernel internal pad even when the physical 15/15-bohr density/nuclear supports are coherent. M4a established the explicit absolute-radius oracle; M4b added the separation-aware QQR bound and all pair-resolved padded compositions; M5 makes sr_image_precision=1e-6 the default for every erfc SR build, derives cutoff_bohr + bipole_sr_image_extent(...), enables range screening, and forwards the policy through all four drivers and unrestricted spin recursion. Historical unpadded four-center records are therefore revision-bound. A reportable producer must record the resolved precision or absolute radius rather than infer support from the physical cutoff alone. Restricted semilocal four-center RKS remains on the exact-FT Hartree default in this merge, so its dense-core reciprocal-tail warning and converged reciprocal-tail requirement remain; retiring that default in favor of repaired SR+LR is a separate decision. HSE’s dedicated screened \(K_{\mathrm{erfc}}\) traversal is owned by a separate workstream and is not attested by M5. RI and RIJCOSX do not traverse BIPOLE and retain their distinct default-RSGDF-KE=200 high-G fitting limitation from 2355f52e and tests/test_rsgdf_dense_mesh_tail.py. These are numerical realization defects, not new gauges, Coulomb kernels, or Γ/χ theory differences.
D83	Record whether the declared exchange-q=0 convention is active in the actual operator.	exchange_q0="bvk-ewald" names the finite-torus family convention, while the new exchange_q0_applicability records active only when the actual operator has a nonzero full-range exact-exchange arm. RHF, UHF, and supported global hybrids such as PBE0 are active; pure functionals and HSE06 are inactive. HSE06 instead carries finite short-range K_erfc exchange with no singular q=0 seam. The value is derived from the shared periodic exchange assembly, not a functional-name table. This prevents a convention label from outrunning the operator without inventing another theory or Coulomb kernel.
D84	Render an absent Γ/χ comparison as not-defined, never as a blank beside an ok χ record.	D89 retains the explicit gamma_ccm_chi_ccm_approach_comparison_status="not-defined" field and empties the approach route map. The table and CSV no longer expose an unavailable Γ route, Γ energy, or χ-minus-Γ field. A separate real_gamma_control_status and explicitly named character-minus-real-Gamma value describe the neutral-torus Fourier control when its complete contract passes. The χ calculation status remains separate and is not a comparison verdict; the comparator defines no pass threshold.
D85	Bind the future stationary χ-CCM energy-weighted density to the final variational Fock, occupied space, and complete numerical realization before assembling D80 into a Pulay term.	For each character and spin, construct Lambda = C_occ^H F_var C_occ from the rebuilt physical, unmixed, unshifted final Fock and define restricted W=2 C_occ Lambda C_occ^H or unrestricted W=sum_sigma C_occ,sigma Lambda_sigma C_occ,sigma^H. This is covariant under occupied rotations and avoids relying on possibly stale stored canonical eigenvalues. Version 1 remains zero-temperature and integer-occupation only. The binding must attest the structure, basis/AO order, finite torus, retained-space projectors, density/orbital/occupation/Fock/W digests, resolved one- and two-electron support, exchange assembly, XC grid where applicable, and backend variational closure. The active BvK seam and screened exchange enter F_var and therefore W, but their explicit fixed-density nuclear-coordinate derivatives remain separate terms. Each approach binds its own stationary state to a construction-specific contract. Within one specified block-circulant Hamiltonian, character and real-Gamma forms may be mapped by the finite Fourier transform; that internal representation map does not identify the Γ-CCM and χ-CCM constructions. Total gradients remain fail-closed.
D86	Define the existing χ-CCM-B Fock-mixing diagnostic as the executed effective previous-Fock weight, while scf_options.fock_mixing remains the requested input.	Four-center RKS/UKS can resolve requested fock_mixing=0.0 to an executed 0.30 when DIIS is disabled. The earlier B diagnostic copied the request and therefore understated the accelerator that the shared driver actually used. AICCM2026DevBDiagnostics.fock_mixing and fleet convergence_diagnostics.fock_mixing now carry the executed value; the input record remains unchanged. This corrects provenance only and changes neither the SCF algorithm, energy, nor finite Hamiltonian. Pre-D86 DIIS-off four-center KS records remain useful but are not convergence-fingerprint-complete. Comparator v2 remains unchanged and incomplete. D89 supersedes this row’s former terminology and any approach-equivalence premise; its numerical or implementation decision remains historical context.
D87	Give every χ-CCM-B direct SCF runner one explicit Fock-mixing override rule, and fail closed where the selected route cannot execute the resolved request without changing operators.	A non-None fock_mixing= keyword overrides options.fock_mixing; otherwise the options value is used. The resolved request is validated in [0, 1) without rewriting the caller’s options.fock_mixing and is forwarded through all four four_center BIPOLE drivers, including both phases of unrestricted spin schedules, and multi-cell fitted RHF/RKS paths. Three-dimensional Gamma-only RI RHF accepts resolved zero but rejects nonzero: the shared dispatcher could execute mixing there only by substituting its legacy molecular-limit GDF exchange for the declared pair-resolved exxdiv="ewald" operator. The other one-cell fitted restrictions remain unchanged. RI and RIJCOSX UHF/UKS still have no previous-Fock mixing loop, so a nonzero resolved request raises NotImplementedError rather than being accepted and ignored; zero remains valid. The result and AICCM2026DevBDiagnostics.fock_mixing continue to record the executed backend-resolved value under D86, so a requested zero can still execute as 0.30 for DIIS-off four-center KS. On supported execution routes this repairs input plumbing and changes which existing convergence accelerator a caller selects, not the finite Hamiltonian or backend mixing formula. The Gamma explicit-zero correction deliberately restores the declared operator instead of preserving the old route-selection bug. The closed-shell fleet uses the options field and is unchanged. Successful pre-D87 direct calls with differing keyword/options values, plus fitted RI/RIJCOSX UHF/UKS calls with a nonzero options-only request, are not request-fingerprint-complete. Pre-D87 Gamma-only RI RHF calls where either input source was nonzero, including an explicit-zero keyword over nonzero options, followed the legacy operator and are not χ-CCM-B results. The common D72 guard now precedes all backend-specific Gamma and mixing guards, closing the 1D one-cell RI-RHF escape; any value from that route is invalid and unreportable. The lower-dimensional absolute-energy fail-close and analytic-total-gradient fail-close remain in force. D89 supersedes this row’s former terminology and any approach-equivalence premise; its numerical or implementation decision remains historical context.
D88	Repair χ-CCM-B lattice algebra and shared periodic fingerprints to the authoritative column-vector convention.	PeriodicSystem.lattice stores direct-lattice vectors as columns, so R_n = A_system n and A_BvK = A_system diag(N); successful B fleet payloads record primitive_lattice_bohr, and new B convention records serialize lattice_vector_convention="columns". This supersedes the false row-lattice premises in D17 and D81 across B torus, localization, symmetry, post-HF, reciprocal-vector, Madelung, probe-charge, and fleet-geometry helpers. The Madelung, probe-charge, and fleet helpers are shared, so the quarantine is not χ-only. For A=[[7,.4,.2],[.3,8,.5],[.1,.6,9]] bohr and N=(2,3,1), the corrected positive code convention gives xi_M=0.138352993811598; the pre-D88 fitted helper gave 0.143621616230995, while the pre-D88 four-center probe gave 0.138913224426180. The fitted error would overbind a two-electron RHF seam by 5.268622 mHa/cell. All affected pre-D88 Γ-CCM and χ-CCM records must be rerun under the fingerprint rule because no missing lattice-semantics field is inferred or retrofitted. A symmetric lattice that commutes with diag(mesh) is numerically outside this defect class, but its old record is not newly attested. The shared builders for graphene, mgo-slab, ice-ih, co2-dryice, and sio2-quartz require fresh Γ and χ fingerprints. Ordinary pre-D88 periodic GDF exact-exchange and BIPOLE J/K records for affected lattice/mesh combinations also require audit and rerun because they traverse the shared helpers. The theory article already uses the column convention correctly: this is a code and fingerprint repair, not a Coulomb-kernel, signed-Madelung, or theory change. The 1D/2D χ-CCM-B absolute-energy and analytic-total-gradient fail-closed policies remain in force. D89 supersedes this row’s former terminology and any approach-equivalence premise; its numerical or implementation decision remains historical context.
D89	Supersede the premise that Γ-CCM and χ-CCM are merely representation labels or are globally unitarily equivalent by name; empty the reportable Γ/χ approach-comparison map.	Γ-CCM and χ-CCM are distinct CCM approaches. Γ-CCM uses the union-and-weight/Wigner–Seitz integral-weighting construction; χ-CCM uses the finite-translation-group character construction. They are compared at a declared common exchange-q=0 convention. Their distinction is not a choice of Coulomb kernels, and equality for a specified operator/route is evidence to establish, not a naming premise. The current aiccm-hf-direct versus B rhf-ri pair is only a neutral-torus Γ-supercell/character representation control and is not evidence for the union-and-weight Γ-CCM approach, so no route is currently mapped to a reportable Γ/χ approach delta. This does not disturb the exact finite Fourier equivalence between character and real-Gamma representations of the same χ-defined finite Hamiltonian. B convention records use ccm_approach="chi-ccm", ccm_construction="finite-translation-group-character", and evaluation_representation="gamma-centred-character-mesh"; no Γ-CCM identity is assigned to the real-Gamma control. The bare gamma selector belongs to Γ-CCM; neutral fitted-torus controls use the explicit neutral-bloch/gdf and real-gamma names. Pre-D89 records are not numerically retracted solely for lacking these fields, but cannot support construction-comparison claims. D89 supersedes the terminology and approach-equivalence clauses in D73–D88 where present and in related prose while leaving their numerical, provenance, fail-closed, and implementation decisions in force.
D90	Classify each route by an explicitly bound construction, not by namespace ownership, evaluation representation, or inherited solver ancestry.	A-line ownership, real-Gamma evaluation, and reuse of an existing post-HF solver do not confer union-and-weight Γ-CCM identity. The mixed-boundary implementation in lowd_four_center.py and lowd_scf.py therefore remains an A-line wire construction/control until its complete Hamiltonian is derived from and gated against the union-and-weight/Wigner–Seitz map. Neutral-only UCCSD and DLPNO routes remain neutral fitted-torus controls unless their complete Hamiltonian and reference contracts are separately bound to an approach; solver ancestry cannot fill that gap. This classification changes no equations, APIs, numerical results, or route availability. Every 1D/2D χ-CCM-B SCF backend remains fail-closed, and no A-line wire result may be substituted for B.

Acceptance supersession: D74 records the historical v2 scaffold, D78 supersedes its emission condition, D89 empties the approach route map, and D90 prevents namespace, representation, or solver ancestry from filling that map. aiccm2026-gamma-chi/v2 must not be emitted unchanged. Even a complete neutral-torus representation-control contract would not by itself establish a Γ-CCM/χ-CCM approach delta. The q=0 support/order is byte-preserved. Pre-D78 exact-GDF-K RHF/UHF and hybrid RI, neutral-torus fold, and RI post-HF/full-pair records built nonzero-q RSGDF factors and are revision-bound. Semilocal RI and RIJCOSX SCF use only q=0 RSGDF factors for J and are numerically unaffected by D78.

Source disagreements recorded

• The 2014 paper’s numerical convergence is evidence, not a proof of a variational energy. The independent formulation supplies the missing finite Hamiltonian and constrained variational statement.

• The historical two-, three-, and four-centre pair-product boundary factors are not adopted. aiccm2026dev-b weights translation equivalence classes, not arbitrary centre pairs.

• A converged, plausible energy is not accepted if the density is non-idempotent, the electron count is wrong, the Fock is non-Hermitian, or the finite-mesh/supercell identity fails.

• A long-range correction added only to the final scalar energy is insufficient. Its functional derivative must be present in the SCF Fock.

• The deMon2k two-center claim that the reference center is arbitrary requires equality of the two weighted representative sums, not only symmetry of the underlying free-space integral. Its explicitly symmetrized three-center Eq. (20), however, already addresses the simplest AO-pair interchange.

Open questions and queued work

ID	Question / work	Current position
O1	One common long-range convention for 1D chains and 2D slabs.	χ-CCM-B now fails closed for all 1D/2D SCF backends. Four-center is blocked because its direct-truncated lower-dimensional BIPOLE gauge is not the neutral finite-torus Hamiltonian and over-binds chain benchmarks by a Madelung-scale constant. RI and RIJCOSX are blocked because the shared lower-dimensional neutral-RI/GDF mesh collapses transverse reciprocal components to (G_\perp=0), producing a sheet-like non-Coulomb kernel and vacuum-padding artifacts. A future shared mixed-boundary kernel must derive the 1D/2D Green function, self-potential, electron-nuclear and nuclear terms, and exchange q=0 seam together before any lower-dimensional B absolute energy can be reported.
O2	Global-minimum and stability analysis.	RHF SCF gives a stationary determinant in the constrained space. Add orbital-Hessian/stability checks before production status.
O3	Finite-size convergence law for exact exchange.	Measure rather than assume monotonicity; fit insulating test ladders by geometry and basis.
O4	Open-shell production validation.	UHF/UKS now run through 3D four-center and 3D RI/RIJCOSX; 3D UMP2/UCCSD(T)/PNO pilots use the exact χ-CCM transform. Add external periodic open-shell references, stability analysis, and larger spin-contaminated controls.
O5	KS-DFT production validation.	Closed-shell RKS now runs through 3D direct, RI, and RIJCOSX backends. Multi-k GDF/RKS now Bloch-folds the lattice XC matrix from the full real-space density. The 2026-06-28 c-diamond and si-diamond STO-3G/PBE/RI local re-runs and the 2026-06-30 OpenBLAS-pinned Twin re-runs converged with the default accelerator after this fix. The 2026-07-01 Twin LiH/MgO/NaCl STO-3G/PBE/RIJCOSX runs also converged on the 2 x 2 x 2 B net; because pure PBE has zero exact-exchange weight, this primarily validates RIJCOSX route plumbing rather than COSX exchange physics. A separate STO-3G/PBE0/RI block converged for the same three systems, but it does not exercise COSX. PBE0/RIJCOSX validation remains open; when attempted, LiH/STO-3G should be treated only as route smoke because it is the known ultra-diffuse short-range-envelope warning case. Since 87bd4ee3, 3D B four-center RKS/UKS evaluates HSE06 with its screened 0.25 K_erfc(omega=0.11) exchange and no full-range seam, while B RI and RIJCOSX fail closed for every range-separated functional because their fitted/COSX exchange path is full-range only. PBE and PBE0 are unchanged. Four-center PBE, PBE0, and HSE06 are algebraically active but are not absolute-validation routes before D82’s internal-domain and reciprocal-tail requirements are met. M4a can pad the base corrected-gauge traversal but does not pad HSE’s dedicated screened \(K_{\mathrm{erfc}}\) build, so HSE still needs a separate screened-exchange domain fix. Grid convergence, nonlocal functionals, forces, broader fleet confirmation, matched all-electron basis/reference comparisons, lower-dimensional mixed-boundary support, and the historical DFT weighting comparison remain open.
O6	Coupled cluster and local correlation.	Restricted and unrestricted real-torus PNO MP2/CCSD/(T) routes are implemented in 3D, including full-domain exact-limit oracles. The finite-torus setup transforms and canonical RI-MP2 energy contraction now use native OpenMP kernels, but the correlated CC solvers still evaluate all pairs/triples with full contractions. Translation-representative amplitude propagation, minimum-image screening/local fitting, relaxed correlated densities, and external periodic CC benchmarks remain open.
O7	ECP benchmark validation.	Basic effective-charge neutrality is now checked before χ-CCM SCF and recorded in diagnostics. Remaining work is numerical validation on ECP-bearing periodic benchmarks, including post-HF reference consistency and output citation/provenance audits for each ECP basis family.
O8	3D ionic benchmark ladder.	LiH, MgO, and NaCl have Twin STO-3G RKS/PBE/RI, RKS/PBE0/RI, and RKS/PBE/RIJCOSX records on the 2 x 2 x 2 B net with the declared 3d-periodic-g0 / bvk-ewald convention. They do not yet have RKS/PBE0/RIJCOSX records. Diamond has the earlier RKS/PBE/RI confirmation, while Al2O3 remains the missing member of that common PBE/RI four-crystal ladder. The records remain convergence and route-plumbing evidence, but D82 holds their dense-core default-KE absolute energies until a high-G truncation contract is recorded; PBE0/RI rows are additionally revision-bound by D78. The BIPOLE finding does not traverse these GDF rows, but quantitative four-center rows still require an attested M4a extent or M4b, and Al2O3 must not be launched as a reportable RSGDF-200 absolute-energy point. The 2026-07-08 curated A-stream neutral-GDF c-diamond aiccm-ri control value is not reproducible on verified current main (about 24.5 mHa/atom shift) and must not be used for a Γ/χ delta. Verified 2026-07-10 reruns strongly support the shifted-mesh mirror bug as the explanation for that exact-exchange row: mirror-insensitive aiccm-hf-direct lands on the post-fix RI value within 5e-5 Ha/atom and pure PBE is unchanged to 3e-13 Ha/atom. The attribution remains an inference because the old row lacks build attestation and was not rerun on old and fixed cores with an otherwise identical setup. The reruns predate embedded self-attestation, and a later route audit established that A RI and RIJCOSX call the same multi-k drivers as B, so they cannot supply an independent approach delta. Under D89 the reportable Γ/χ approach map is empty. B rhf-ri versus A aiccm-hf-direct is only a neutral-torus representation control, not union-and-weight Γ-CCM evidence; it shares the per-q RSGDF fit and one-electron primitives and therefore does not independently validate those common components. Composite producer-process attestation is now symmetric, but no existing pair is upgraded by that change, no existing pair satisfies the numerical-input contract, and neither runner emits it. Revise the phase/factor-frame and AO retained-space semantics retained from D75, then emit and rerun the neutral-torus representation control under D77 from one clean current producer identity and one embedded canonical 3D input. The reportable approach map remains empty until a separate route binds the union-and-weight Γ-CCM construction. Matched all-electron basis/reference conventions, full mesh convergence data, and hybrid COSX production validation with periodic-adapted bases remain open.
O9	H4 four-centre versus RI discrepancy.	At the two-cell, 40-bohr-vacuum H4 geometry, corrected-gauge four-centre RHF is -2.1870080428 Ha/cell while RI is -2.1648043358 Ha/cell, a -22.204 mHa difference. The compact H2 two-cell control agrees across all three backends within 44 microhartree. Treat the H4 difference as unresolved truncation/cell-embedding behaviour, not as evidence that either number is the dense-limit oracle.
O10	Exact periodic IAO cross overlap.	The current IAO target/reference overlap is evaluated in the explicit supercell and omits cross-boundary images. Periodize it before using IAO translations to reduce correlated pairs.
O11	Space-group integral acceleration.	Derive backend-specific general-k sewing matrices, real-solid-harmonic shell actions, quartet stabilizers, and petite-list scatter. Enable only after symmetry-on/off Fock and energy parity. Layer and rod groups and little-group irrep labels are also open.
O12	3D diamond-family RKS/PBE/RI convergence.	The queue reported non-convergence after 120 iterations for c-diamond and si-diamond at a 2 x 2 x 2 B net with STO-3G, def2-svp-jk auxiliary basis, and RSGDF KE 200, while the RHF-RI counterparts converged. After the multi-k RKS XC assembly fix, local 2026-06-28 re-runs of the same default PBE/RI inputs converged without damping, level shift, or accelerator-policy changes: c-diamond in 4 iterations and si-diamond in 6. Fresh Twin queue attempts on 2026-06-30 first exposed a broken system-MKL linkage and did not reach SCF. After an OpenBLAS-pinned Twin rebuild at main @ 8d1e985, compute smoke 2da593b58815 resolved libopenblas.so.0 without MKL, and the default 12-core confirmations passed: c-diamond job 25e7051cd427 converged in 4 iterations with E = -75.168945009903 Ha/cell, final dE = -3.88e-10 Ha, and final gradient norm 2.45e-08; si-diamond job 0d4bbdf01d81 converged in 6 iterations with E = -575.614688770867 Ha/cell, final dE = -9.78e-12 Ha, and final gradient norm 4.46e-09. The original SCF evidence is therefore classified as the fixed XC folding bug; no accelerator-policy change is indicated. These rows confirm convergence behavior, not absolute-energy accuracy at RSGDF KE 200; D82 requires a separate high-G truncation audit before quotation.
O13	F1 1D four-center over-binding on benchmark chains.	The lower-dimensional four-center route now fails closed, so no new 1D/2D four-center benchmark should be accepted. The archived h-chain value (E_\mathrm{RHF}^{4c}=-1.3841759702) Ha/cell at extension (8\times1\times1) remains the reproduced failure motivating the guard. Five curated pre-D72 H-chain, LiH-chain, and polyethylene B four-center records now carry retracted=true in qc-input-library; their numbers remain only as defect evidence. A later A-line mixed-boundary wire-quadrature g_max fix does not change this χ-CCM-B policy and does not acquire Γ-CCM identity by namespace or real-Gamma evaluation. The B lower-dimensional finite Hamiltonian is not proved identical at the declared convention. Re-enable only after deriving a neutral wire/slab Green function and passing dense reciprocal/GDF anchors.
O14	χ-CCM analytic gradients.	Derive and gate the derivative of the declared finite-character Hamiltonian before exposing forces. The 3-D Ewald nuclear-repulsion and fixed-density electron-nuclear components are parity-tested as standalone helpers, explicit fixed-density electrostatic energy and gradient bundles have exact density/operator cell-list matching, and B-owned SCF density folding feeds SCF-density electrostatic bundles. The fixed-density kinetic scalar and AO-centre derivative are parity-tested on explicit caller-declared support, without an SCF wrapper until the resolved one-electron cutoff is attested. The fixed energy-weighted overlap Lagrangian scalar and AO-centre derivative now prove the sign and Frobenius orientation of the native overlap skeleton on the same exact-support contract, but they do not construct the stationary SCF energy-weighted density or complete a Pulay/adjoint. Required open pieces still include B-owned energy-weighted density construction and variational assembly, the BvK exchange-q=0 seam or screened-exchange kernel derivative, RI/RIJCOSX three-center and metric derivatives, XC terms where applicable, and post-HF relaxed-density or amplitude-response terms. The total-gradient API reports this status and fails closed.

O8’s “then emit” means define and emit the superseding acceptance contract; it does not authorize emission of the incomplete v2 scaffold.

Current measured evidence

The committed benchmark was run on the alternating H4/STO-3G chain with a 40-bohr transverse simulation lattice. For cyclic lengths 1, 2, and 4, the new energy per cell was respectively -2.0733777009, -2.1648043358, and -2.1719609271 Ha. A direct call to the full Gamma-centred character mesh was identical to all printed digits at every length. The historical union12 CCM gave -2.1615967328, -2.1618792916, and -2.1707034746 Ha/cell. The separately developed symmetric aiccm2026dev-a weighting gave the same displayed sequence in this 1D case. This is useful comparison evidence, not a correctness proof. New-route wall times in the archived current-main run were 22.58, 20.61, and 97.23 seconds; the four-cell jump reflects all-k-pair exact-exchange fitting.

That H4 ladder used the ri backend. The backend-crossing smoke benchmark uses H2/STO-3G in an 8 x 12 x 12 bohr cell at a (2,1,1) cyclic mesh. RHF energies are -1.1213506456 (four_center), -1.1213722182 (ri), and -1.1213943367 Ha/cell (rijcosx). PBE0 energies are -1.1554208287, -1.1554589526, and -1.1554644822 Ha/cell in the same order. These are actual runs from 2026-06-21; the maximum spread is 43.7 microhartree for RHF and 43.7 microhartree for PBE0. They establish executable cross-backend consistency on this compact control, not a universal error bound. The direct four-center entries predate the shared 3D neutral-cell cutoff clamp in 6fed8620; the six-value table is therefore revision-bound and must be rerun before quotation, with direct_lattice_cutoffs retained in the new record.

The pre-guard 1D/2D route matrix on H2/STO-3G at a (2,1,1) cyclic mesh is no longer accepted as a valid three-backend comparison. The archived 1D RHF energies were -1.5341898653, -2.2845855922, and -2.2846076938 Ha/cell for four-center, RI, and RIJCOSX, respectively; the 2D values were -3.4506478026, -5.2158679833, and -5.2158905993 Ha/cell. Those large gaps are the evidence behind O1, D37, and D72: the four-center column used the direct-truncated lower-dimensional gauge, while the RI/RIJCOSX columns used the now-blocked transverse-collapsed neutral-RI/GDF kernel. Current main blocks all 1D/2D χ-CCM-B SCF backends until a shared neutral wire/slab Coulomb convention is implemented.

The first 3D canonical RI-MP2 control uses an H2/STO-3G cell of 20 x 20 x 6 bohr and the (1,1,2) character mesh. B gives HF, correlation, and total energies of -1.1182352381008094, -0.0130227001540294, and -1.1312579382548390 Ha per cell. The out-of-process PySCF 2.13.1 KRHF/KMP2 reference gives -1.1182352386944080, -0.0130226999202183, and -1.1312579386146264 Ha per cell. The corresponding absolute differences are below 0.6 nanohartree. The archived record is docs/manuscripts/aiccm_comparison/data/h2_mp2_2026-06-21.json.

The exact inverse transform was tested by running the existing local solvers on the real finite torus. H2/STO-3G at the same (1,1,2) mesh gives a no-truncation local-MP2 correlation energy identical to canonical χ-CCM RI-MP2 within 7e-18 Ha per cell. A LiH/STO-3G cell of 20 x 20 x 7 bohr at the same mesh gives canonical finite-torus DF-CCSD and (T) totals of -0.0302475329439885 and -0.0000934031163267 Ha. The no-truncation local solver differs by 6.9e-12 and 1.4e-12 Ha, respectively. The nonzero-triples record and inverse-transform residuals are archived in docs/manuscripts/aiccm_comparison/data/lih_dlpno_ccsdt_2026-06-21.json. This is an internal finite-Hamiltonian oracle, not an external infinite-crystal CCSD(T) result.

The first unrestricted transform control is a neutral Li doublet in a 15 x 15 x 15 bohr cell with STO-3G and extension (1,1,1), run on 2026-06-22. RI-UHF is -7.32670108299121 Ha/cell, UMP2 correlation is -0.000243259672659 Ha/cell, and full-domain UCCSD correlation is -0.000257809105931 Ha/cell. The triples correction is numerically zero for this three-electron minimal-basis control. The transformed RI factor has a 2.31e-16 maximum imaginary residual and a 7.11e-15 permutation residual. Independent alpha/beta localization changes the density by 4.3e-34, and the zero-threshold localized UCCSD(T) total agrees with the canonical gauge within 5e-14 Ha. These values establish the finite-torus unrestricted transform and PNO exact limit only; a one-cell Li array is not a converged crystal benchmark.

The 2026-06-24 four-center low-dimensional guard uses H2/STO-3G with a 1.4 bohr bond, a 15 bohr repeat along the periodic direction, and 40 bohr transverse padding. The molecular RHF anchor is -1.1167143251 Ha. Current aiccm2026dev-b four-center RHF gives -1.1167140350, -1.1167140379, and -1.1167140379 Ha/cell at extensions (1,1,1), (2,1,1), and (4,1,1). The nuclear component is larger than the isolated molecule because direct low-dimensional image point charges are present, but the total energy cancels the neutral image terms to below 0.3 microhartree per cell. This supersedes the untracked 2026-06-22 benchmark note that reported a stale over-binding snapshot.