Standalone relocalization worker

vibe-qc owns the localization process. The consumer needs no import of vibe-qc and the backend environment needs no installation of vibe-view. Protocol 1, worker API 1.0.0, is new in the 0.17.5 release. An existing 0.17.4 or earlier release installation does not imply that it contains this worker. Pin the implementing commit and negotiate protocol_version, worker_version and live capabilities: a reported package version alone does not prove that this worker is installed. Minimum worker version is 1.0.0, protocol version exactly 1.

Install and run

Use Python 3.11 or newer and a full vibe-qc installation, including the compiled _vibeqc_core, native libraries and bundled basis data (including Huzinaga MINI). The ordinary package dependencies suffice. No viewer, PySCF, GPU or extra Python localization dependency is needed. See installation for platform prerequisites. In a checkout containing this implementation:

./scripts/install.sh --current --extras none --venv .venv
.venv/bin/python -m vibeqc_relocalize --probe

Wire requests are one compact JSON object on one line. The checked-in JSON fixtures are indented for review, so compact them before feeding the worker:

.venv/bin/python -c 'import json,sys; print(json.dumps(json.load(sys.stdin)))' \
  < tests/data/relocalize/h2.request.json | .venv/bin/python -m vibeqc_relocalize

For a client, the exact argv is [backend_python, "-m", "vibeqc_relocalize"], and the probe argv is [backend_python, "-m", "vibeqc_relocalize", "--probe"]. The installed console script vibe-qc-relocalize accepts the same arguments. Store the absolute Python executable path globally in the consumer and launch without a shell. A backend console-script path is also usable if the consumer omits -m vibeqc_relocalize.

The lightweight vibeqc_relocalize package is deliberately outside vibeqc: python -m vibeqc.relocalize would import vibeqc.__init__ before it could report a missing native core. The supported launcher catches that failure and returns a structured capability report. A missing launcher itself is a process-launch failure, which the consumer must explain.

For source development, use an isolated venv and rebuild after native changes:

VIBEQC_REQUIRE_VENDORED=ON .venv/bin/pip install -e . --no-build-isolation

Do not run an installer that switches branches when pinning a particular commit; bootstrap prerequisites as described in the contributor setup, then use the pip command above on that checked-out commit.

Keep the backend’s native installation tree in place. The current CMake build records paths to its native dependency libraries; building a wheel does not bundle those libraries into a portable runtime. A wheel installed into another venv on the same host can use that native installation, but copying the wheel alone to another machine is not a supported deployment procedure. Install vibe-qc with its native prerequisites on the destination and probe there.

Transport and capability negotiation

One request and one terminal event per process. UTF-8 JSONL on stdin/stdout; max request 16 MiB. Write the request, newline, and close stdin. The worker does not wait for EOF after that line. Additional lines are not additional jobs; start another process. Diagnostics, Python warnings and native fd 1 output are redirected to stderr. Drain both streams concurrently. The caller owns timeout and cancellation (terminate the process, discard incomplete output). No signal or native crash can guarantee a terminal event.

Every event contains protocol, protocol_version, worker_version, id, event. Normal localization emits started (stage="validating") then exactly one result or error. A capabilities request emits only capabilities. id is an opaque string of 1 to 128 characters; it is echoed after envelope validation, otherwise null. Unknown input fields, duplicate keys and non-finite numbers are errors. UTF-16/32 input is rejected; the transport is strictly UTF-8. Numeric arrays reject boolean and string elements, including arrays mixing them with numbers; there is no boolean-to-number coercion. Do not interpret stderr as a protocol channel.

{"protocol":"vibeqc.relocalize","protocol_version":1,"id":"probe-1","operation":"capabilities"}

--probe does the same without stdin and uses null id. The report includes backend distribution version, native_core_ready, per-method ready, fresh_rhf.ready, supported dimensions/spins/coefficient types/k-point classes, required metadata and resource limits. It actually builds a Gaussian basis, computes native overlap/dipole/reference integrals, exercises all three molecular localizers with two occupied orbitals, solves a small RHF witness, and exercises the periodic complex native Fourier/projector path. Per-method failure disables that method with readiness_error. The periodic witness is a small synthetic metric problem, not an accuracy qualification of periodic SCF. native_core_ready certifies the native integral witness; use each method’s ready for its additional kernels. A functioning import alone is insufficient.

Exit codes: 0 successful result or at least one ready method on probe; 2 structured request/refusal error; 3 computational failure or no ready method. Inspect the terminal event as well as the exit code. A partial probe may return 0 with some methods unavailable; never enable a method solely from global ready. Reprobe after backend path or installation changes.

{"protocol":"vibeqc.relocalize","protocol_version":1,"worker_version":"1.0.0","id":"job-1","event":"error","error":{"code":"invalid_source","message":"supplied requires orbitals; fresh_rhf forbids them (no fallback)","field":"orbitals"}}

Stable error codes include invalid_json, invalid_request, unsupported_protocol, unsupported_operation, request_too_large, backend_unavailable, unsupported_method, unsupported_basis, incomplete_basis, unsupported_spin, unsupported_occupations, unsupported_complex, unsupported_source, invalid_source, unsupported_periodic_method, experimental_opt_in_required, unsupported_periodic_representation, unsupported_pbc, unsupported_kmesh, unsupported_complex_metric, incomplete_band_manifold, unsupported_metallic_manifold, nonorthonormal_input, resource_limit, scf_not_converged, numerical_validation_failed, computation_failed. field can be null; message text is diagnostic, not a stable API.

Supported worker methods

Method	Molecular real	Molecular complex	Periodic Gamma	Complete cyclic k mesh	Spin/occupation
ibo	Yes	No	No	No	Restricted singlet, all occupied 2
boys	Yes	No	No	No	Restricted singlet, all occupied 2
pipek-mezey	Yes	No	No	No	Restricted singlet, all occupied 2
aiccm-wannier	No	No	Real and complex, experimental	Real and complex, experimental finite-BvK only	Restricted singlet, all occupied 2

No worker route supports UHF/UKS, ROHF, spinors, noncollinear spin, ECPs, fractional occupations or metallic disentanglement. All three molecular methods describe populations and charges with MINI IAOs, so all share its all-electron and Z <= 86 limits even when their objective is Boys or Mulliken PM. These methods are different criteria, not interchangeable periodic aliases.

The periodic route requires allow_experimental: true, dimension 1, 2 or 3, periodic axes first, a full unshifted cyclic mesh with uniform weights, an isolated occupied manifold, and a time-reversal-compatible overlap. It preserves genuinely complex coefficients, including at Gamma. It does not require making each orbital real. It does not accept arbitrary infinite-crystal, shifted, irreducible or band-path samples. Gamma alone cannot stand in for an archive containing a full k mesh. Finite-torus localization is not a general Marzari-Vanderbilt/Wannier90 interpolation or disentanglement implementation.

Request contract

All lengths are bohr, primitive exponents bohr^-2, band energies hartree, atomic charges electron-charge units. Positions are Cartesian. There is no implicit unit conversion and there are no inferred occupations. source defaults to supplied; only source="fresh_rhf" runs a new RHF solve (maximum 100 SCF iterations, molecular only). fresh_rhf forbids orbitals. A bad supplied subspace is rejected; it is never orthogonalized or replaced.

The envelope requires protocol, integer protocol_version=1, string id, operation="localize", method, system, basis. Optional keys are source, orbitals, periodic, allow_experimental. Nested objects also reject unknown keys. The reviewable, executable examples are in tests/data/relocalize/.

Field	Definition
system.kind	molecular or periodic; periodic object required exactly for periodic
system.atomic_numbers	Integer list [natom], 1..118, no ghosts; 1..256 atoms
system.positions_bohr	[natom,3], finite real values
system.charge	Integer total charge per molecule or primitive cell
system.multiplicity, system.spin	Exactly 1, restricted
basis.ao_convention	Exactly qvf-gto-v1
basis.uses_ecp	Required, exactly false; caller must verify provenance
basis.name	Optional label; used to load a named basis only for fresh RHF without shells
basis.shells	Ordered contracted-shell list, required for supplied orbitals
shell center, l, pure	Zero-based atom index; integer angular momentum 0..6; boolean spherical/Cartesian
shell exponents, coefficients	Same-length nonempty primitive lists, positive exponents; QVF Appendix A.1 raw coefficients
orbitals.coefficients	Encoded array, row per occupied orbital
orbitals.occupations	[nocc] molecular; [nk,nocc] periodic, every value exactly 2

The entire occupied subspace is required: nocc=(sum(Z)-charge)/2, positive and no greater than nao. No virtual coefficient rows are accepted. Molecular coefficient shape is [nocc,nao]; periodic shape is [nk,nocc,nao]. Gamma still has a leading nk=1 axis. There are at most 512 AOs (and 128 total AOs in a periodic torus), 512 shells and 128 primitives per shell.

Encoded arrays are objects {"encoding":"real","data":[...]} or {"encoding":"complex_split_last_axis","data":[...]}. Complex encoding adds a final axis of length 2 containing [real,imag], as in QVF Bloch members. No complex-to-real cast occurs. Molecular requests reject the complex encoding even when every imaginary component is zero; the consumer may explicitly choose real encoding only if it has proved the data are real.

Exact AO convention

Shell list order is AO block order. Within a spherical shell, use libint STANDARD real solid harmonics m=-l,...,+l; a p shell is y,z,x. Cartesian order is descending lx, then descending ly, with lz=l-lx-ly. Per-shell pure is authoritative, including mixed spherical/Cartesian bases.

For every primitive the worker multiplies archived raw coefficient c by N=(2 alpha/pi)^(3/4) (4 alpha)^(l/2) / sqrt((2l-1)!!), then constructs the native basis with pre-normalized coefficients. It applies no additional contraction normalization, spherical permutation, or Cartesian component correction. This exactly reverses output.formats.qvf._basis_shell_payload. The shell center is the corresponding system atom position. Diffuse, Cartesian, custom and mixed bases keep their archived coefficients; a basis name alone cannot establish their identity. Very ill-conditioned AO metrics are refused (smallest eigenvalue must exceed both 1e-14 and 1e-10 times the largest). Input C^H S C must agree with identity to Frobenius error < 1e-7.

Periodic data

The periodic object requires all of:

Field	Definition
representation	finite_bvk; an assertion of the source Hamiltonian/metric representation, not a conversion request
lattice_bohr	[3,3], primitive lattice vectors in columns, invertible including inactive embedding axes
dimension, pbc	1..3; [true,false,false], [true,true,false] or [true,true,true]
mesh	Three positive integers; inactive axes equal 1; product nk
kpoints_fractional	[nk,3], fractional reciprocal coordinates in [0,1), lexicographic ix/nx,iy/ny,iz/nz order, z fastest
weights	[nk], each exactly 1/nk within 1e-12
bloch_convention	exp(+2pi*i*k.R); lattice translation phase, no extra atom-position phase
overlap	Encoded [nk,nao,nao] Hermitian positive-definite S(k), in the identical AO order/normalization and phase convention as C(k)
orbital_energies_hartree	[nk,nband] sorted reference energies, nocc < nband <= nao; must include at least the first virtual band

The indirect reference gap must exceed 1e-6 hartree. Energies certify the declared source occupied manifold; the worker does not rebuild the Fock operator to authenticate them. It likewise trusts the caller’s basis and finite-BvK provenance. Orthonormality alone cannot authenticate AO ordering or the Hamiltonian. S(-k)=conj(S(k)) is required within 1e-10, including a real Gamma metric. The existing native transform additionally refuses imaginary residue in the real-space metric. Supplied C may remain genuinely complex.

No Fock, density, ERI or SCF restart object is needed for this worker route. Fock matrices would enable an additional one-particle-energy check, but are not accepted in protocol 1. The occupied projector checks do not constitute an independent total-energy calculation. For IAO-based periodic methods, matched minimal-basis S22(k), target/reference S12(k), atom maps and Gaussian/image provenance are additionally needed; those methods are not exposed here.

Result contract

event="result" carries a result object. Its coefficients always have rows as orbitals. It includes method, source, scf_performed, backend version, AO convention, spin, occupations, encoded coefficients and encoded rotation, atom populations, charges, n_centres, centre_threshold=0.1, centroids and explicit descriptor model names. There are no orbital energies for the localized mixture. citation_features names the existing feature routes in vibeqc.output.citations/database.toml (IBO, Foster-Boys, PM or Wannier); the periodic route retains its explicit approximation label. convergence="not_certified_by_kernel" is intentional: the existing Jacobi interfaces do not expose a common convergence certificate. A result certifies the stated numerical invariants, not a global localization maximum or attainment of the iteration stopping threshold.

Molecular representation="molecular_ao":

• Coefficients [nocc,nao], occupations [nocc], rotation [nocc,nocc]. Internally, AO-by-orbital matrices obey C_after=C_before @ rotation.

• atom_populations[nocc,natom] are probabilities in the MINI IAO partition; rows sum to 1. All three methods report population_model="iao-mini".

• charges[natom] are nuclear Z minus IAO electron populations, with positive values meaning electron deficiency. They sum to the system charge.

• centroids_bohr[nocc,3] are position expectations; n_centres[nocc] counts atoms with orbital population greater than 0.1.

Periodic representation="finite_torus_ao":

• Let N=prod(mesh). Coefficients are [N*nocc,N*nao], occupations [N*nocc], and rotation [N*nocc,N*nocc]. These are localized orbitals across the whole finite torus, not per-k primitive-cell orbitals.

• translations[N,3] enumerates integer cell translations in lexicographic order, z fastest. AO columns are cell-major, then the original shell/AO order; atom columns likewise repeat the primitive atoms cell-major. Their positions are r_atom + lattice_bohr @ translation. Returned orbital rows are optimizer order; do not infer one home-cell orbital per band or automatic translation equivalence from their indices.

• The canonical torus coefficients before rotation are C0[(t,mu),(r,n)] = (1/N) sum_k exp(+2pi i k.t) Ck[mu,n] exp(-2pi i k.r). The rotation acts on these columns, not directly on the stacked k rows. The torus metric uses the same Fourier transform of S(k).

• Populations [N*nocc,N*natom] and charges [N*natom] use the Lowdin finite torus partition, with population_model=charge_model="lowdin_finite_torus". They must not be labelled IAO charges. Charges sum to N*system.charge.

• centroids_bohr, spreads_bohr2 and centroid_model describe the existing projected circular AO-centre approximation. They are not exact periodic position expectations. Preserve aliasing_fraction, aliasing_detected, experimental=true, reference_gap_hartree and warnings in the overlay.

validation reports input/output orthonormality, the S-norm of the residual outside the supplied subspace, and the occupied rotation’s unitarity error, with tolerance 1e-7. The periodic input value is measured after the unitary Bloch-to-torus transform, with each original block also checked before use. Periodic density and translation-projector errors are also reported. Tests independently compare full density kernels C C^H and reconstruct the discrete Fourier transform; they do not merely re-read these reported errors.

Audit of existing vibe-qc implementations

The following code predates the worker and remains unmodified:

Implementation	What it can do with archived occupied data	Limits / additional inputs
iao.analyse_localization and localise	Molecular IBO, Foster-Boys, Mulliken PM without SCF	Real closed-shell orbitals, exact Gaussian basis, overlap/dipoles and MINI cross-overlap rebuilt natively; IBO explicitly casts to float and Boys/PM use real algebra
periodic_localise.localise_periodic_gamma	Real Gamma PM using supplied mo_coeffs and periodic overlap; Boys uses home-cell moments	PM criterion is overlap/population based; Boys and position moments are valid only for non-wrapping states. The wrapper uses real_if_close(...).real, so it is not a safe complex consumer. The new worker never calls it
periodic.ccm.localize.localise_ccm	Localization within the selected finite Gamma-CCM supercell occupied space	Delegates to the legacy Gamma wrapper; does not make primitive Gamma equivalent to general k meshes
periodic.chi.localization.localize_aiccm2026dev_b_occupied_blocks	Complex finite cyclic-mesh localization without any SCF result class, wannier or iao objective	Full C(k), S(k), lattice, mesh, AO centers/atom map; IAO additionally needs target/reference and reference overlaps on the torus. Complex unitary rotations, native Fourier and projector audits. Experimental projected-position objective
localize_aiccm2026dev_b_unrestricted_occupied	Independently rotates alpha/beta occupied spaces	Existing result-object API requires converged B-stream SCF provenance, spin blocks, overlap/Fock/energies. Not exposed by protocol 1
Native _localize_periodic_gaussian_occupied	Connected finite-image Gaussian Bloch IAO -> diabatic seed -> time-reversal-preserving IAO-PM -> Wannier chain, with supplied admitted reference, no SCF rerun	Restricted mean-field state, occupied/frozen/active/virtual masks, k data, Fock/energies/occupations, matching target/minimal Gaussian basis, cell, finite-image policy and memory/work admission. It explicitly reports hf_basis_source_authenticated=false and infinite_image_tail_certified=false. A bounded reference implementation, not a ready archive adapter

The connected native tests exercise Gamma, odd (3,1,1) and even (2,2,2) meshes and compare native IAO-PM objectives with independent AO oracles. That is real implemented multi-k functionality, but it is not support for arbitrary archived QVF states in this worker. Its IAO-PM p=4 convention is also distinct from the molecular Mulliken p=2 method named pipek-mezey in the viewer.

No native refactor or new localization algorithm is introduced here. The new periodic method selects the existing wannier block API. Its numerical model and finite-torus limits stay visible. General periodic Boys needs periodic position/link operators, usually neighboring-k overlaps M(k,b), consistent Bloch gauge and a suitable optimizer. Molecular dipoles are not a substitute. A general IAO/IBO archive adapter needs matched minimal-reference matrices or a reproducible periodic Gaussian integral/image convention, not only C(k).

QVF sufficiency and separate format proposal

This audit uses vibe-qc’s current producer python/vibeqc/output/formats/qvf.py, the vendored specification and archives under docs/_static/examples/. It changes neither the qvf repository nor any vendored schema.

• wavefunction.gto has exact ordered shells, purity, real or split-complex row-per-orbital coefficients, spin and occupations. A molecular restricted, all-electron archive with that section, authoritative charge/multiplicity, and geometry is sufficient. The worker rebuilds its metric and reference integrals without SCF. Volume-only orbitals or missing occupied rows are not sufficient. Fractional natural orbitals, ECP provenance gaps and unknown AO conventions must be disabled, not guessed.

• x_vibeqc.bloch_wavefunction carries restricted per-k complex coefficients, occupations, energies and k coordinates. The current producer can include k_weight; older archives may omit it. Its newer unrestricted restart flavor stores alpha/beta density matrices, which are not archived orbital gauges and must not be treated as supplied occupied coefficients.

• Structure JSON already has row-vector lattice data in angstrom, PBC and dimensionality. This worker expects a transposed column-vector lattice in bohr. Atomic positions likewise need conversion: divide angstrom by 0.529177210903. Do not convert shell exponents, already in bohr^-2.

• Neither generic molecular wavefunction.gto nor the current Bloch extension guarantees periodic S(k), mesh/phase/image-policy provenance, or matched minimal-reference matrices. Rebuilding a basis by name is insufficient. Even with exact shells, finite-BvK and infinite image sums may have different metrics. Do not infer finite-BvK provenance from the existence of a k mesh.

• Inspected examples: h2o-rhf/output-h2o-rhf.qvf has a molecular GTO section; mgo-route-gdf-bipole/output-mgo-rhf-sto3g-gdf-k222.qvf has eight complex Bloch blocks but lacks overlap blocks and integration weights. The two checked-in chi-ccm-b-qvf examples have no generic/Bloch occupied coefficient section suitable for this worker. A rendered Wannier volume is not sufficient data.

Proposal for the qvf repository, not implemented here: standardize an optional relocalization/restart payload (or version the existing extension) linking the exact structure and basis with immutable identities, explicit AO normalization/order, ECP/electron-count and spin/occupation semantics, Hamiltonian representation (finite_bvk, infinite-crystal, etc.), lattice orientation/units, complete mesh and shift, ordered full k points and weights, Bloch phase convention, and S(k) in lossless split-complex encoding. Preserve source band energies/gap provenance and finite-image cutoffs or boundary policy. Use explicit absent/unknown metadata, never implicit defaults.

For future IAO localization add the reference-basis identity/atom map, S12(k)/S22(k) or enough authenticated Gaussian/image metadata to rebuild them. For general Wannier/Boys add neighboring-k link overlaps and their gauge/ reciprocal-shift conventions. Optional Fock blocks support an energy-invariance check. Unrestricted orbital localization needs alpha/beta coefficient and occupation blocks; a spin-density-only restart is a separate capability. The format owner must choose the extension/version and producer migration. No mandatory QVF change is needed for the molecular restoration.

Exact remaining vibe-view changes

1. Persist an absolute backend Python path globally, independent of the viewer environment. Probe using the exact argv above, drain both pipes, check protocol/worker versions and method readiness, and surface failures.

2. Build the request from the active archive geometry and exact shell data, carrying explicit charge, multiplicity, spin, occupations and ECP status. Select the complete occupied block, preserve AO order and complex encoding, and convert structure coordinates/lattice units. Do not call a fresh RHF when coefficients are absent or rejected. Offer that as a separately named action which submits source="fresh_rhf" and marks its result as new SCF. Geometry edits invalidate the archived subspace unless compatible new orbitals exist; passing an overlap check alone does not establish provenance.

3. Replace sys.executable -m vibeview.relocalize with the configured backend argv. Use unique request IDs, one process per operation, and cancel obsolete work on file reload or geometry/basis edits. Accept only a matching terminal result for the same archive/geometry snapshot. Neither stale overlays nor a parseable but unsuccessful process exit may replace the active result.

4. Enable IBO/Boys/PM only for supported molecular real restricted cases. Keep periodic controls disabled unless the full experimental finite-BvK contract is present and the user opts in. Never relabel AICCM as periodic Boys/IBO/PM. The existing archives audited here cannot enable that periodic route.

5. Adapt result rows and occupations as supplied. Molecular overlays can use the existing renderer after renaming centroids_bohr to its internal field. Display charge/population models, fresh-SCF provenance and validation data. No localized orbital energy exists. Keep overlays separate from canonical archive data and allow clearing/reverting them.

6. A periodic overlay requires a separate finite-torus AO/atom adapter using translations, full complex coefficients and the returned shape; the current restricted primitive-cell adapter is insufficient. Display experimental status, approximate center model and aliasing flags. Do not squeeze the leading k/cell structure into molecular rows or .real.

7. Add viewer subprocess contract tests with these fixtures, including missing backend, partial readiness, malformed JSON, missing terminal event, timeout, nonzero exit, cancellation, stale IDs/geometry and population-model labels. Share fixtures or copy them with their worker/protocol version pinned.

See tests/data/relocalize/README.md for fixture provenance and numerical test commands. The worker only returns process events; it creates no job artifacts and does not modify the input archive.

Implementation verification

Initially verified in an isolated macOS arm64 Python 3.14.7 environment, with a native extension rebuilt from this checkout and no installed vibe-view:

• tests/test_relocalization_worker.py: 61 passed. This includes supplied molecular water orbitals, the existing water QVF, positive Gamma/complex finite-torus fixtures, independent projector/orthonormality checks, explicit RHF, strict rejections, UTF-8/type enforcement and broken/partial backend readiness.

• Localization/AO regression command in the fixture README: 111 passed, 1 skipped, 2 deselected. The skip needs the separately installed viewer. The two excluded tests run full periodic SCFs; the initial supplemental run was stopped before replacing it with the documented localization-focused command. No full-suite or release-gate qualification is claimed.

• tests/test_binding_sanity.py: 2 passed.

• tests/test_test_gate_lanes.py: 72 passed, after installing its required pytest-timeout test plugin in the fresh environment.

• Ruff on the worker, launcher, worker tests and fixture generator: clean. Both new Markdown documents parse with MyST without warnings. Staged privacy, prose and whitespace checks pass.

• Installed --probe and stdin capability requests report all four methods ready. python -I -m vibeqc_relocalize handles both periodic fixtures through JSONL with native diagnostics isolated from stdout.

• A normal wheel was also built with pip wheel . --no-deps --no-build-isolation, installed with its base dependencies into a fresh venv, and exercised from outside the checkout. Both module and console-script probes, all three positive fixtures and both rejection fixtures passed. Python modules and the native extension loaded from that venv’s site-packages; vibe-view was absent. This validates a separate installed environment using this host’s native libraries, not wheel portability.

Integration with post-0.17.4 main repeated the worker, localization, AO, periodic-kernel, binding and test-policy checks, adding the new IAO population suite and released-changelog tests: 330 passed, 3 skipped, 2 deselected. One unrelated policy assertion failed because upstream test_kpoints.py imports experimental CCM helpers without the module marker its checker expects. The same offender was verified directly in the upstream revision; both that file and the checker are unchanged by the worker. The three skips require optional PySCF or vibe-view, and the two excluded full periodic SCFs are the ones named above. The fresh probe still reports native, RHF and all four localization methods ready. All 191 released changelog sections match their pins.

Across the three saved positive fixtures, the largest output orthonormality error is about 1.0e-15, subspace residual 2.8e-16, and unitary error 1.2e-15 (rounded upward). The complex periodic result has an imaginary coefficient magnitude about 0.344; preservation is not achieved by dropping imaginary data. Expected finite-torus aliasing warnings remain visible in results.