fix(#108): scale-relative zero-mode separation + feat(#102): hypothesis evidence matrix

[marcohost33-maker]

Summary

Two related pieces of classifier-integrity work.

#108 — zero-mode separation is now scale-relative (CHANGES NUMERICAL RESULTS on rescaled input). The filter deciding which modes are the steady state used an absolute floor |lambda| > 1e-10, duplicated across five modules. A Liouvillian carries rate dimension, so this broke in both directions under L -> cL, and it was found by auditing the layer the #101 conformance suite does not reach:

• small c — every genuine mode falls below the floor, so D1 collapses to 0.0 (unconditionally firing the gapless F5 reach leg) and the D19 slowest-mode overlap collapses to 0.0, raising a false A11/F4 Mpemba candidate on the highest-priority rung. Measured end-to-end on an amplitude-damped qubit with rho_0 = |+><+|: A12/none NOT_EXCLUDED EXPLORATION at c = 1 became A11/F4 CANDIDATE CONFIRMATION at c = 1e-10. The issue-D19/A11 Mpemba detector false-positives on trivially symmetric initial states (README quickstart classifies as A11 CONFIRMED/PUBLICATION_GRADE) #68 non-triviality guard could not correct it — it depends on the same _slowest_mode helper.
• large c — the round-off zero mode (~eps * ||L||) rises above the floor and counts as genuine, producing a negative spectral gap (-1.4e-6 at c = 1e10), impossible for a GKSL generator by definition.

The correction is canonical and carries no free parameter — unlike the #101 F5 threshold, it needs no calibration study: numerics.scale.spectral_zero_tolerance() derives the threshold from the spectrum itself as ZERO_MODE_RTOL * max|lambda| (spectral radius: homogeneous of degree one, unitary-similarity invariant, consistent with rate_scale). At unit scale it reproduces the historical floor, so all 21 anchors and the full suite stay green byte-identically; only rescaled generators change. The legacy floor stays available as an explicit atol= opt-in on every affected function, mirroring how #99 preserved the pre-#97 steady-state tolerance.

D1 deliberately does not clamp the gap at zero: after the fix a positive Re(lambda) is no longer round-off but a genuinely unstable (non-GKSL) mode, and masking it would trade one silent failure for another.

#102 — hypothesis-wise evidence matrix (additive, report-only). ClassificationResult.hypothesis_matrix reports every hypothesis of the A1-A12 taxonomy with supporting measurements, counterevidence, missing evidence and explicit fail-closed claim floors (RESERVED/UNEVALUABLE → UNDEFINED, NOT_SUPPORTED → NOT_EXCLUDED, SUPPORTED → the verdict it would receive as winner). support_score ships as the honestly-named ordinal twin of confidence, and REACHABLE_A_CLASSES becomes the coverage denominator with A6/A7/A9 excluded from claims. The priority chain is now declarative (_ladder_spec), so decision, shadow report and matrix derive from one source.

Scope

• Bug fix (no new feature) — Absolute zero-mode tolerance EPS_GAP breaks D1/D3/D4/D16/D19/D20 under rate rescaling — false A11/F4 candidate and negative gap #108
• New diagnostic or layer — Classifier semantics: replace heuristic confidence with calibrated, hypothesis-wise evidence #102 evidence matrix (report surface, no new physics diagnostic)
• Performance / sparse-path / numerics improvement
• Docs / examples / packaging only
• CI / workflow / security
• Release / packaging / publish evidence

Verification

• pytest -q passes locally — 796 passed (669 at branch point)
• tests/test_anchors.py unchanged and green — the Absolute zero-mode tolerance EPS_GAP breaks D1/D3/D4/D16/D19/D20 under rate rescaling — false A11/F4 candidate and negative gap #108 fix is byte-identical at unit scale, which is the load-bearing claim and is asserted, not assumed
• If touching MANIFEST_SCHEMA.json: not touched — the run-manifest contract is unchanged; report fields are additive with defaults
• If new external dependency: none
• If touching .github/workflows/: not touched
• If touching claims/docs/release wording: CITATION.cff follows the repo's own 2026-08-09 convention — unreleased capability sentences go in the Pending for the next cut block, not the abstract of the cited v0.5.0 release, and Absolute zero-mode tolerance EPS_GAP breaks D1/D3/D4/D16/D19/D20 under rate rescaling — false A11/F4 candidate and negative gap #108 is flagged there as a results-changing correction rather than an addition
• Branch protection / required checks: n/a

Quality contract

• No unsupported production-ready / certified / release-complete wording
• Research disclaimer preserved
• False-pass and rework risk considered, not only green CI — tests/test_zero_mode_scale.py includes a discrimination test proving the atol opt-in genuinely restores the pre-Absolute zero-mode tolerance EPS_GAP breaks D1/D3/D4/D16/D19/D20 under rate rescaling — false A11/F4 candidate and negative gap #108 defect; without it a no-op "fix" would pass the invariance assertions

Test plan

• tests/test_zero_mode_scale.py (33 tests, c in {1e-10 ... 1e12}): tolerance homogeneity / zero-operator / fail-closed semantics; D1, D3, D4 scaling exactly with c; D19 overlap invariant; no false Mpemba candidate; D16 scaling; Petermann mode count invariant; gap never negative for a GKSL generator while a genuinely unstable mode still reports one; end-to-end diagnose() verdict invariance under t -> t/c.
• tests/test_hypothesis_matrix.py (61 tests): taxonomy coverage, SUPPORTED ⟺ ladder-fires equivalence, claim-floor truth table, partial-evidence retention, score-only-when-supported, RFC-8259 serialisation, report-only non-influence.
• Full suite 796 passed; ruff and mypy clean.

Reproducibility note

The #108 repro uses two fixed systems with no random component: an amplitude-damped qubit (H = 0, jump sigma_-) with rho_0 = |+><+|, and a Rabi-driven damped qubit (H = 0.7 sigma_x, jump sigma_-, rate 0.4). End-to-end runs use seed=1, bootstrap_B=20, t_grid = linspace(0, 5/c, 64). The #102 matrix introduces no numerical change: it is derived from the evidence dict the classifier already computes.

Linked issues

Closes #108. Refs #102 (partial: evidence matrix, rename option 1, reachability gate; the calibration/validation design stays open). Refs #101 (same defect class as #108, disjoint location — the F5 gate switch remains gated on slice C). Refs #70 (A5 no-EXCLUDED semantics reused for the claim floors).

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[marcohost33-maker]

Response to the Codex review (commit 472c4b2)

Two findings adopted, one adopted in the form the repo's own convention requires, one declined with reasoning.

✅ P2 "Avoid assigning winner-only scores to failed hypotheses" — adopted

Correct and well-spotted. _confidence answers "what grade would this class get as the winner" and keys on a subset of each firing rule, so kreiss = 11 with petermann_max = 1 failed F1 while the matrix still printed A3 at 0.85 next to that rung's own counterevidence. A score without support is not a weaker claim, it is a misleading one. support_score is now None unless the hypothesis is SUPPORTED (matching the existing RESERVED treatment), pinned by test_unsupported_hypotheses_carry_no_support_score, which asserts the invariant across the whole matrix rather than just the one example.

✅ P2 "Preserve available evidence when a rung is partially missing" — adopted

Also correct, and it cut against the matrix's own purpose: a run with a measured kreiss but no petermann_max discarded the genuine Kreiss support. Conditions whose own inputs are present are now evaluated even when a sibling is unevaluable; the rung status still degrades to UNEVALUABLE, so partial evidence never promotes a hypothesis. Pinned by test_partially_missing_rung_keeps_its_evaluable_evidence.

✅ P1 "Update citation metadata" — adopted, but in the Pending block, not the abstract

The underlying point is right and now matters more than when the review was written, because this PR also carries a results-changing correction (#108). But the change belongs in a different place than suggested: CITATION.cff carries an explicit convention added 2026-08-09 —

abstract describes the surface of the CITED release only […] Capability sentences for work that is merged but not yet released do NOT belong here; they would credit the published artifact with results it cannot produce.

Editing the abstract would credit the published, DOI-frozen v0.5.0 artifact with capabilities it cannot produce. The Pending for the next cut block is the convention-sanctioned location, and it now records the evidence matrix and flags #108 explicitly as a correction that changes numerical results, so the next release cut cannot describe it as a mere addition.

❌ P1 "Validate ensemble evidence before lifting the A11 floor" — declined, with a documentation fix

The AGENTS.md contract cited is real and is already enforced — at the API boundary, not in the report layer. liouscope.diagnose() calls reject_legacy_ensemble_confirmation(), so a bare ensemble_confirmation=True already raises fail-closed; lifting the floor requires a typed EnsembleEvidence with its digests, gate status and dual attestations.

hypothesis_evidence_matrix reads the value that classify_mechanism itself writes into the evidence dict from that already-validated argument. It introduces no new path: classify_mechanism and _apply_single_state_maxmix_floor likewise take the override as a plain argument, so a hand-built dict passed directly to any of them carries exactly the trust its caller gives it. Requiring an EnsembleEvidence object in the report function alone would make it stricter than the decision function it describes — and decoupling the two is precisely what this PR set out to prevent, since the matrix's value depends on mirroring the decision exactly.

The test the review points at documents that forwarding (floor applied without the override, suppressed with it); it does not demonstrate a bypass. What was genuinely missing was a stated trust boundary, so hypothesis_evidence_matrix's docstring now names it: the matrix reports the supplied ev, it does not re-validate it, and the typed check lives at the diagnose() boundary.

If the intent is to harden the internal boundary as well — making classify_mechanism itself accept only EnsembleEvidence — that is a worthwhile but separate, API-breaking change, and it should be its own PR against the A11 contract rather than a side effect of a reporting slice.

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[marcohost33-maker]

Response to the second Codex review (commit f424769)

Four adopted — one of them a genuine defect in my own fix — one already resolved, one declined.

✅ P1 "Preserve genuine slow modes below the relative cutoff" — adopted; this was a real regression

Correct, and the most valuable finding in either review. My first cut used tol = 1e-10 * max|lambda|, which silently imposes a fixed dynamic-range ceiling of 1e10 — and a wide separation of physical rates is not an artefact but the defining feature of the metastable (A5) systems this library exists to study. Reproduced exactly as described:

slow rate	true gap	reported (before)
1e-2	5.0e-03	5.0e-03 ✓
1e-6	5.0e-07	5.0e-07 ✓
1e-10	5.0e-11	5.0e-01 ✗
1e-12	5.0e-13	5.0e-01 ✗

Adopting the suggested basis: the threshold is now a multiple of the eigensolver backward error, ZERO_MODE_EPS_FACTOR * eps * max|lambda|. A computed eigenvalue is uncertain to order eps·‖L‖, so that — not a fixed ratio — is the scale on which "indistinguishable from zero" is decided.

The factor is calibrated by measurement rather than chosen: across amplitude damping, Rabi-driven damping, dephasing, a strongly non-normal near-defective generator and a 64-dim 3-qubit chain, each at c ∈ {1, 1e6, 1e12}, the numerical zero mode never exceeded 1.94 · eps · max|lambda|. The default keeps ~500× headroom above that while resolving genuine modes further down than even the pre-#108 absolute floor did at unit scale. Pinned by test_genuine_slow_modes_survive_the_zero_mode_filter, test_slow_mode_survival_is_also_unit_invariant (separation and rescaling must compose, not conflict) and test_threshold_sits_far_above_measured_round_off, which asserts the calibration claim rather than trusting it.

✅ P1 "Prevent the rate-rescaling test from overflowing the fitter" — already fixed, and by the route you preferred

This was the CI failure, diagnosed independently before the review arrived; the review's analysis matches exactly. Of the two options offered I took stabilise the fit, since the test scaling is legitimate physics (a slow generator in small rate units genuinely produces a long grid) and inf/nan residuals give least-squares no gradient to step back from — the real failure mode is silent non-convergence on valid input, not merely a promoted warning.

M0–M3b now clip the exponent at 345, not at the ~709 where np.exp itself overflows: M3a multiplies by the polynomial prefactor (A + B t), so a clip at 709 converts an exp overflow into a multiply overflow one line later. A test pins that the clip is bit-identical in the well-conditioned regime, so no ordinary fit moves.

✅ P2 "Align F5's required keys with its defaulted predicate" — adopted

Correct: _f5_reach reads ev.get("gap", 0.0), so declaring gap required made the matrix report UNEVALUABLE for evidence the ladder fires on. _Condition now separates keys the predicate indexes (required → UNEVALUABLE) from keys it reads with a documented default (optional → surfaced in a new missing_optional column, still decided).

One refinement the review's framing surfaced: the same key is required for one rung and optional for another (gap_to_gns_ratio is indexed by F3 but defaulted by F5), which a single mixed missing list could not express — hence the split column rather than a reclassification. A parametrised test now pins matrix/ladder agreement under every single-key omission, and encodes the deliberate asymmetry: the matrix is the robust reporter, the ladder raises rather than deciding from a value nobody measured, and both refusing to rule is agreement.

✅ P2 "Validate the spectrum before honoring the absolute override" — adopted

Correct and a genuine fail-closed hole: liouvillian_gap([0, nan], atol=1e-10) silently returned 0.0. Validation now runs before the override. A compatibility switch may restore the old threshold; it must not restore the old silent acceptance of corrupted solver output.

✅ P2 "Qualify the mechanism-verdict invariance claim" — adopted

Right, and exactly the kind of overclaim this repo's conventions exist to prevent. My wording asserted general verdict invariance while A10/F5 still gates on rate-dimensioned henrici_eta > 1.0. Both CHANGELOG.md and CITATION.cff now scope the claim to zero-mode-induced verdict changes and name the remaining #101 limitation explicitly.

❌ P1 "Use absolute imports for the new scale helper" — declined

AGENTS.md does say "absolute from liouscope, no .. traversal", but the entire package is written the other way: from .._consts import, from .._types import, from ..numerics.linalg import appear in essentially every module, including the files being edited here. Following the suggestion would make the five new import lines the only absolute ones in the package and leave each touched file internally inconsistent.

This is a real divergence between the stated convention and the codebase, but it is repo-wide and predates this PR, so the fix is a single mechanical sweep with its own review — not five inconsistent lines smuggled in on a numerics PR. Worth its own issue if the convention is the side that should win.

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---

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[marcohost33-maker]

Response to the third Codex review (commit 9bc909f)

All five adopted. Two were genuine defects introduced by the previous commit — both reproduced before fixing.

✅ P1 "Match zero-mode epsilon to the eigensolver dtype"

Correct. The threshold is deliberately a multiple of the eigensolver backward error, but eps was hard-coded to float64 — so for a single-precision spectrum (round-off ~1e-7 relative) the threshold sat about nine decades below that solver's own noise, and the numerical steady-state eigenvalue survived as physical. That is exactly the negative-gap failure the function exists to prevent, reintroduced through the back door.

eps now comes from the real dtype underlying the spectrum (complex64 → float32), with a float64 fallback for integer/object input. Pinned by test_tolerance_tracks_the_spectrum_dtype (asserts the ratio equals eps32/eps64 rather than just "larger") and test_single_precision_zero_mode_is_still_filtered for the end-to-end consequence.

Worth noting for the record: on this machine np.linalg.eigvals promotes a complex64 input to double internally, so the defect did not reproduce through that particular entry point. The finding is right regardless — spectral_zero_tolerance is public and takes a spectrum from any source, and correctness must not rest on one solver's promotion behaviour.

✅ P2 "Preserve the true decaying tail when clipping exponentials"

Correct, and the more damaging of the two. Measured:

exponent	true	with symmetric clip
−300	5.148e-131	5.148e-131 ✓
−400	1.915e-174	1.474e-150 ✗
−700	9.860e-305	1.474e-150 ✗

A factor of 1e24 at −400, past 1e150 by −700 — an artificial constant tail on every model, distorting residuals, fitted offsets and AICc on high-dynamic-range trajectories. I had traded an overflow for a silent bias, which is the worse of the two.

The cap is now one-sided, as suggested. Underflow needs no guard: it is exact in the limit and NumPy's default error state ignores it (verified — np.exp(-800) only raises under an explicit errstate(all="raise"), which the suite does not set). Pinned by test_clip_does_not_truncate_representable_decay (exact equality at −300/−400/−700/−745) and test_extreme_decay_underflows_to_zero_without_warning.

✅ P2 "Make the A12 fallback unevaluable when a rung is unknown"

Correct, and it is the same epistemics the rest of the matrix already applies: not any_fired does not establish "no mechanism applies" when a rung could not be evaluated — the missing value could have made it fire. Calling A12 SUPPORTED there claims more than the run measured.

A12 is now UNEVALUABLE (floor UNDEFINED, no score) whenever any rung is unevaluable and none fired. A fired rung still refutes A12 outright, which the second new test pins so the fix does not overshoot into "unknown whenever anything is missing".

✅ P2 "Derive the new alias from legacy confidence"

Correct — the alias contract broke precisely on the path it exists to serve. __post_init__ now fills an omitted support_score from confidence; an explicitly supplied value is left untouched (both directions pinned).

✅ P2 "Correct the stated unit-scale compatibility"

Correct, and this one I should have caught when switching to the backward-error basis: 1e3 · eps64 ≈ 2.22e-13 is not the historical 1e-10, so modes in that band are now classified as genuine without any rescaling — "only rescaled generators change" was false.

Both CHANGELOG.md and the constant's rationale now state the actual change. The direction is the intended improvement (it is what rescues metastable slow modes), and no anchor system carries a mode in that band — which is why the reference behaviour is unchanged, rather than the claim that nothing outside rescaling moved.

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[marcohost33-maker]

Response to the fifth Codex review (commit 1038f7e)

Adopted — and it caught a defect that I introduced by acting on an earlier review finding I had been unable to reproduce. Worth recording plainly, because the sequence is the lesson.

✅ P1 "Preserve resolvable single-precision slow modes" — adopted, by reverting the dtype branch

Reproduced exactly as described:

storage dtype	reported gap (true: 5e-5)
complex128	5.000000e-05 ✓
complex64	5.000000e-01 ✗

The cause is the dtype-derived epsilon added in round 3. Measured, NumPy/SciPy solve eigenproblems in double regardless of input dtype: a complex64 generator returns a complex64 array whose numerical zero mode sits at ~1.5e-19 — double-level, not single-level. The storage dtype says nothing about the precision the backward error was actually incurred in, so keying the threshold to it inflated the cutoff to ~1.2e-4 relative and discarded modes four decades above the solver's real noise floor — corrupting precisely the metastable case the widened tolerance existed to protect.

On the round-3 finding that motivated it

The claim there was that a complex64 Rabi-damped generator scaled by 1e-3 reports a gap near -1.7e-11 instead of 2e-4. Measured on this branch:

complex128: eig dtype=complex128  min|lambda|=1.2065e-19  gap=2.000000e-04
complex64 : eig dtype=complex64   min|lambda|=1.4626e-19  gap=2.000000e-04

It does not reproduce, in either dtype. I said as much at the time — "the defect did not reproduce through that particular entry point" — and changed the code anyway, on the reasoning that the correction was cheap and defensive. That was the mistake: a cheap change to a numerical threshold is not free, and this one traded a hypothetical failure for a measured one. The rule I should have followed is the repo's own: no change to a numerical contract without a reproduction.

The genuine single-precision case (an external or GPU solver) is real but indistinguishable from a downcast double result by inspection, so it belongs to the caller through the existing rtol argument, and is now documented there rather than guessed at from array metadata.

Tests pin the measured behaviour in both directions: the tolerance is independent of storage dtype, a downcast metastable spectrum keeps its slow branch, and the round-off mode is still excluded so no negative gap returns.

Also in this push

The previous commit's mypy failure (redundant-expr on the NaN guard) reached CI because I piped mypy through tail, which masks the exit status — the command chain reported success and pushed. Fixed, and gate exit codes are now checked directly rather than through a pipe.

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[marcohost33-maker]

Correction to my fifth-round comment + response to the sixth review (commit b4ddca4)

⚠️ Correction of my own claim

In the fifth-round response I wrote: "NumPy/SciPy solve eigenproblems in double regardless of the input dtype." That statement is half wrong, and the wrong half is the half this library uses. Measured on a generic 40×40 matrix whose entries are not exactly representable in float32 (so single-precision round-off is forced to show):

solver, complex64 input	max|Δλ| vs. double solve
numpy.linalg.eigvals	3.3e-07 — consistent with input-casting error only; numpy.linalg._commonType computes in cdouble always and casts the result back
scipy.linalg.eig	1.0e-05 — ~30× more: scipy dispatches by dtype and genuinely runs single-precision cgeev (SciPy LAPACK docs)

LiouScope's dense eigen/Schur paths all go through scipy, and eig_nonhermitian even documents "Always uses LAPACK zgeev" — a contract the code did not enforce. My round-3 measurement (zero mode at 1.5e-19 for a complex64 Liouvillian) was an artifact of exactly-representable matrix entries, not evidence of double computation; I drew a general conclusion from a special case, twice.

The root fix, superseding both dtype rounds

All dense eigen/Schur boundaries (eig_nonhermitian, the Mpemba layer, Petermann/Henrici, D24) now promote to complex128 before solving, making the documented zgeev contract true. Every backward-error tolerance in this PR is calibrated against the double solve — now the double solve is guaranteed, so the threshold model is valid by construction rather than by luck of the input dtype. Representation error already present in caller-supplied single-precision data is the caller's data quality and is neither masked nor "corrected" (the standard backward-error stance).

✅ Sixth review — all four adopted

1. Stale CHANGELOG claim — correct, and embarrassing in a useful way: the round-3 sentence "eps taken from the spectrum's own dtype" survived my round-5 revert, so the changelog described the exact mechanism the code no longer had. Now documents the fixed double-precision epsilon and the external-solver limitation.
2. Expose rtol — adopted on liouvillian_gap / oscillating_mode_gap / spectral_spread / lep_proximity. Pinned with the reviewer's own example: a displaced stationary mode at 1e-7·max|λ| from an external single-precision solver yields -1e-7 under the double-calibrated default and the correct 0.2 with rtol = 1e3·(eps32/eps64) — scale-relative, no absolute floor.
3. Factor multiplication overflow — adopted: an amplitude probe like 1e200 made the product inf before _bounded ever saw it, and 0·inf yields NaN. Models now evaluate under a suppressed overflow errstate and _bounded maps non-finite intermediates to the saturation bound; both encode "absurdly far from the data", which is exactly what the optimiser needs to hear.
4. Immutable taxonomy mappings — adopted: RESERVED_A_CLASSES.pop("A6") could silently desynchronise the taxonomy from the import-time coverage guard, which compares against the precomputed REACHABLE_A_CLASSES tuple. All four exported taxonomy mappings are now MappingProxyType, pinned by a mutation test.

Full suite 849 passed; ruff and mypy clean.

Sources: SciPy low-level LAPACK docs, numpy.linalg.eig, numpy linalg/_linalg.py _commonType ("always double or cdouble", verified against the installed source).

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[marcohost33-maker]

Thirteenth review round: all three findings reproduced first, then adopted in d4f9004.

One zero-mode scale (P1, numerics/linalg.py) — Confirmed exactly as described: on 4×4 trace-preserving constructions with ||L||₂/max|λ| ≥ ~1e3, the certified-resolved stationary residual sits above the radius-based spectral_zero_tolerance and survived the downstream filter (20/20 reproductions at skew ≤ 1e-3; D1 ≈ 1e-12 and occasionally negative against a true gap of 1). Fix: new shared helper operator_zero_tolerance (pinned equal to the certificate bound by test); every consumer that holds the operator now filters with it — spectral layer (D1/D3/D4, has_complex_pairs), Mpemba layer (_certified_decomposition carries the bound), petermann_factors (which was returning four eigenmodes where three exist), and D24. Genuine slow modes inside the coarser band are not silently swallowed — the #113 ambiguity split floors them as resolved=False. The radius default stays for spectrum-only call sites; caller atol still wins. A deterministic mismatch fixture is frozen as exact float64 literals with a guard-skip should a future LAPACK resolve it below the radius tolerance.

Certify the D24 eigensolve (P2, _zhou.py) — Reproduced: gap = 7.28e-6 raw vs 1.074e-5 certified on the stiff fixture. The recomputation is now routed through certified_eig with the certificate bound as filter; an applicable-but-unresolved certificate returns an unconverged record (inf bounds, NaN gap/K), honouring caller-supplied values exactly like the existing no-nonzero-modes branch.

Conclusive refutation beats UNEVALUABLE (P2, classification.py) — Adopted with the suggested rule verbatim: UNEVALUABLE only when no evaluated condition is false and missing evidence could still flip the rung to supported. kreiss = 1 with petermann_max missing now reads NOT_SUPPORTED with the counterevidence recorded and the absent key kept in missing for the audit trail; when every partially collected rung is conclusively refuted, the A12 fallback is SUPPORTED — matching the ladder's deterministic A12, restoring the matrix/decision equivalence. The NaN-encoding-equivalence test now pins the genuinely open case via gns_certified = 1.

Full suite 929 passed (+9 new pins), anchors byte-identical, ruff and mypy clean. CHANGELOG, the CITATION.cff pending block and the taxonomy docs are updated.

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[marcohost33-maker]

Fourteenth review round: both findings reproduced first, then adopted in 467ed8f.

Certify the Petermann eigendecomposition (P1, nonnormality.py) — Reproduced exactly: on the stiff #112 fixture the raw zgeev path reported 16 "non-zero" modes with petermann_max ≈ 622.69, while the certified route (dgeev-real) returns the physical 15 modes with ≈ 2.0 — and indeed no cutoff can restore an eigenvalue that is absent from the raw spectrum. petermann_factors now consumes certified_eig. On an applicable-but-unresolved certificate both returned arrays are the NaN unavailable sentinel (with a RuntimeWarning), so petermann_max becomes NaN and the F1 rung reads UNEVALUABLE — deliberately not the empty-array default K_max = 1.0, which would assert perfect normality from a spectrum the solver demonstrably could not resolve.

Radius fallback when the certificate is inapplicable (P2, spectral.py + _zhou.py) — Reproduced with your construction (diag(-1,-2,-3,-4) plus a 1e16 off-diagonal): certificate.bound ≈ 2.2e3 exceeds the whole spectrum, D24 reported gap 0.0 / unconverged, and D1 through the layer (with a supplied steady state) likewise 0.0 for a true gap of 1. Every round-13 call site — spectral layer (D1/D3/D4, has_complex_pairs), Mpemba layer, D9, and D24 — now uses the certificate bound only when certificate.applicable and falls back to the radius-based #108 tolerance otherwise.

Full suite 933 passed (+4 new pins: certified Petermann count/K on the stiff fixture, NaN withholding on the unresolved fixture, and the radius fallback for D1 and D24), anchors byte-identical, ruff and mypy clean. CHANGELOG and the CITATION.cff pending block are updated.

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[marcohost33-maker]

Fifteenth review round: both findings reproduced by scan (4000 random stiff four-level networks each), then adopted in ebdd30b.

Validate eigenvectors before certifying (P1, numerics/linalg.py) — Confirmed: valid stiff classical networks reach certified=True, resolved=True while the slow mode's left eigenvector has residual up to 3.1e-4 against a bound of 3.2e-7 (right vectors fine). The gate is per mode and relative — r_j ≤ max(VECTOR_RESIDUAL_REL_MAX · |λ_j|, bound) with the larger of the unit-normalised left/right residuals — because r/|λ| is the first-order relative error scale of anything computed from the pair, and a single operator-scale cutoff does not separate the measured populations (healthy zgeev over 301 generators ≤ 2.1e-10; legitimate dgeev-real repairs 1.2e-2…6.5e-2; corrupt decompositions 2.2e-1…2.9e1). The boundary at 1e-1 is calibrated and documented at the constant; the extreme repair at spectral spread ~4e11 carrying a 79% slow-mode error deliberately fails closed. A vector-failed candidate continues the ladder; when no route passes, certified=False with the offending residual reported, and D19/D9/D24 withhold. certified_eigvals is deliberately untouched — the eigenvalues of such a decomposition remain usable for D1/D3/D4, and a new test pins exactly that division.

Continue past ambiguous repair candidates (P2, both ladders) — Confirmed on 3 scan hits: zgeev certified with one ambiguous mode at 3.5e-7…1.6e-6 while dgeev-real returns a machine-zero stationary mode (7.3e-17…1.3e-14) with none. Both ladders now accept only ambiguity-free candidates; the best ambiguous candidate (fewest ambiguous modes, ties by ladder order) is returned fail-closed only when every route stays ambiguous. The healthy path is unchanged and still lazy (pinned by the existing Schur-counter test), and certified_eig follows the same rule.

Full suite 936 passed (+3 new pins), anchors byte-identical, ruff and mypy clean. CHANGELOG and the CITATION.cff pending block are updated.

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[marcohost33-maker]

Sixteenth review round: all four findings reproduced first, then adopted in e26df05.

Grid-relative Prony fallback (P2, fitting/prony.py) — Reproduced exactly: on a valid non-uniform grid spanning t = 1e7, the absolute (beta, omega) = (1, 1) fallback made the M3b fit "converge" (success=True) onto the seed itself — [A, beta, omega] ≈ [0.006, 1, 1] for true values 5e-8 / 2e-6. Fallback rates are now 5.0 / t_span and the success-path positivity floors 5e-6 / t_span, both reproducing the historical values exactly at the canonical t_span = 5 (the ALPHA_SEED_FLOOR_FRAC / M3A_SLOPE_SEED_FRAC convention). The measured non-uniform scenario is now pinned unit-invariant across c ∈ [1e-6, 1e6] end to end.

Eigenvalue certificate for the gap-only D24 path (P2, _zhou.py) — Reproduced: with petermann_factor=2.0 supplied, the fixture's eigenvalue certificate resolves a usable gap of 3.32e-6 while only the round-15 eigenvector gate fails, yet D24 returned an unconverged NaN record. The certificate now matches what is consumed: certified_eigvals when only the gap is recomputed, the stricter certified_eig when the Petermann factor is (that path stays fail-closed, pinned).

Decouple D11 from the D9 vector gate (P2, nonnormality.py) — Reproduced with a ladder-Hamiltonian variant of the bad-vector network: the certified spectrum carries a length-3 imaginary-part progression, D9 is withheld, and D11 reported the fabricated default 1. D11's input is now recomputed from the certified spectrum (it consumes only eigenvalues); when the eigenvalues themselves are unresolved, bohr_ap_length is NaN — the field is now float-typed with NaN as the documented unavailable sentinel.

Builder atol release note (P2, CHANGELOG.md) — Correct: the opt-in exists on the standalone is_hermitian predicate only. The #109 entry now says so explicitly and notes that the builders' relative gate cannot be bypassed, instead of advertising an unavailable builder argument.

Full suite 942 passed (+6 new pins), anchors byte-identical, ruff and mypy clean. CHANGELOG and the CITATION.cff pending block are updated.

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[chatgpt-codex-connector]

Do not treat every sub-split decay mode as zero

Fresh evidence after the certificate fixes is a valid weak-dissipation qubit with H=diag(0,1) and amplitude-damping/dephasing rates 1e-15 and 1e-14: SciPy returns the exact spectrum [0, -1e-15, -2.05e-14±i], but the global-norm split is 6.66e-15, so this condition declares the genuine -1e-15 population mode an unambiguous zero mode. The certificate therefore reports resolved=True, its bound filters that mode, and D1 becomes 2.05e-14 instead of the true 1e-15, propagating a wrong gap to downstream diagnostics. Determine zero-mode membership from nullspace/stationary residual evidence rather than assuming every eigenvalue below a global eps*||L|| split is machine zero.

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[marcohost33-maker]

Zutreffend, auf dem aktuellen Stand reproduziert — und nicht behoben. Ich lasse den Thread deshalb offen und sage, was stattdessen geschehen ist.

Nachgefahren auf pr107-fix (PR #121, Stand f194c97), also auf dem neuesten Zweig, nicht nur hier:

H = diag(0, 1),  Amplitudendaempfung 1e-15,  Dephasierung 1e-14

SciPy-Spektrum      [-5.5e-15-1j, -5.5e-15+1j, -1.0e-15+0j, 0+0j]
certified_eigvals    solver=zgeev  applicable=True  certified=True  resolved=True
Zertifikat-bound     2.220446049250313e-13
|Eigenwerte|         [0, 1e-15, 1, 1]

Die echte Populationsmode bei 1e-15 liegt unter der Schranke 2.22e-13 und wird gefiltert. Genau wie beschrieben.

Warum ich es nicht in diesem PR repariere. Der Befund ist eine Instanz der bereits erfassten Decke aus #113: die spektrale Spreizung ist hier 1e15, über der dort dokumentierten Grenze von ~4.5e12. Ihr Vorschlag ist aber schärfer als das, was in #113 stand, und ich habe ihn dort eingetragen (#113, Kommentar von heute) statt ihn in einem Thread verschwinden zu lassen:

Determine zero-mode membership from nullspace/stationary residual evidence rather than assuming every eigenvalue below a global eps*||L|| split is machine zero.

Das ist der Wechsel von einer Betrags-Frage zu einer Struktur-Frage. |λ| < eps·‖L‖ misst den Eigenwert gegen eine globale Norm, die hier vom Hamilton-Anteil gesetzt wird — mit der langsamen Mode hat sie nichts zu tun. Das Nullraum-Residuum ‖L v‖/‖v‖ fragt direkt, ob der Vektor stationär ist. Das ist eine Änderung am Zertifikat-Begriff, nicht ein Wächter-Nachzug, und gehört nicht in einen PR mit diesem Zuschnitt.

Ein Punkt, den Ihr Beispiel beiträgt und der in #113 fehlte: es braucht keinen exotisch steifen Generator, um in die Decke zu laufen. Es genügt, dass der Hamilton-Anteil die Norm dominiert, während alle dissipativen Raten klein sind — eine physikalisch gewöhnliche Lage. Die Decke ist erreichbarer, als die Formulierung „above ~4.5e12 spread" vermuten liess.

In #113 steht jetzt auch die Auflage für die Umsetzung: die Diskriminierung muss an genau diesem Paar belegt werden — diese 1e-15-Mode muss überleben, eine echte Maschinen-Null muss weiterhin gefiltert werden. Ein Kriterium, das beide durchlässt, wäre keine Verbesserung, sondern das Abschalten des Filters.

[marcohost33-maker]

You are right, and this is now fixed on the follow-up branch.

Zero-mode membership is no longer decided by the global eps * ||L|| split. certified_nonzero_modes (src/liouscope/numerics/linalg.py:303) computes the a posteriori backward-error bound from the residuals actually attained -- max(||Lx - lam_hat x||, ||L^H y - conj(lam_hat) y||) / |y^H x| -- and any mode whose magnitude exceeds margin * bound is certified as genuinely non-stationary. refine_zero_band (linalg.py:412) then removes those certified modes from the band:

nonzero = certified_nonzero_modes(L_c, eigenvalues, magnitudes <= bound, ...)
in_band = (magnitudes <= bound) & ~nonzero

The move is deliberately one-directional -- it can only take a mode OUT of the zero set, never put one in -- so it cannot manufacture a false resolved verdict.

Your exact counterexample is pinned as a regression test: tests/test_issue118_residual_findings.py::test_slow_mode_below_the_norm_scaled_band_survives_as_the_gap builds H = diag(0, 1) with rates [1e-15, 1e-14] and asserts layer.gap == approx(1e-15), i.e. the genuine population mode, not the 2.05e-14 the old split reported. A positive control sits next to it (test_healthy_generator_keeps_its_untouched_certificate) so the refinement is proven inert where there is nothing to rescue.

Discrimination: reverting that & ~nonzero to the bare magnitudes <= bound turns the test red; restoring it turns it green. The rescue is load-bearing, not decorative.

Evidence for this reply: full suite 995 passed (exit 0) on pr107-fix @ 9581f39, and a mutation run over all four fixes below in which every one discriminates (take the fix out -> the named test goes red; restore -> green; 4/4, none blind). The mutation harness verifies restoration by hash, so no mutated source survives the run.

[marcohost33-maker]

This finding is correct on this branch. Measured at 4a8ae9c: zero_mode_count=2 - the tolerance eps*||L|| swallows the genuine 1e-15 mode.

It is closed in the follow-up PR #121, which contains this branch in full: src/liouscope/numerics/linalg.py:455 (_certified_non_stationary_modes) and :531 (refine_zero_band) decide zero-mode membership from the a-posteriori backward-error bound over the residuals actually achieved, instead of from eps*||L||. At 123bd57 the same setup yields zero_mode_count=1 and D1 = 1e-15.

Deliberately left unresolved here: the fix lives on the successor branch, not on this one. Back-porting it would mean cherry-picking f3b73b4 together with its second axis and tests into a branch the successor already replaces - divergent history for no gain. Whether to close this PR as superseded is a product decision, not a technical one, and is with the maintainer.

---

Verified locally on the pushed branch: ruff and mypy clean, tests/test_anchors.py 21 passed. Reverse-mutation runs are recorded in an evidence ledger with one run_id per run; a run that dies by error rather than on an assertion is not counted as proof. CI on GitHub not measured here.

[marcohost33-maker]

Review-Threads durchgesehen (2026-08-18): 38 von 54 aufgelöst, 16 bleiben

Der PR war durch required_conversation_resolution blockiert — bei 52 offenen
Threads, von denen keiner einzige eine Antwort trug. 16 Review-Runden hatten
Code geändert, aber nie auf die Befunde geantwortet.

Aufgelöst, jeweils mit Begründung im Thread:

• 7 P1-Befunde am aktuellen Stand — vier davon nachweislich behoben (Zero-Mode-
  Epsilon, Eigenvektor-Residuen-Gate, Zertifikat-Skala im Filter, A11-Boden über
  validierte EnsembleEvidence), zwei Fehlalarme gegen repo-eigene Konventionen
  (Import-Regel seit Import convention: AGENTS.md requires absolute imports, the package uses relative traversal throughout #110 umgedreht; CITATION.cff folgt der „Pending for the next
  cut"-Konvention), einer nach Zero-mode conditioning: is the structural certificate enough for stiff non-normal generators? #117 übertragen.
• 28 veraltete Befunde — je mit den Commits, die die Datei seither geändert
  haben, und einem geprüften Beleg am aktuellen Stand.
• 1 CodeQL-Fehlalarm (REACHABLE_A_CLASSES ist über einen Import lasttragend).

Nicht aufgelöst: 16 Befunde am aktuellen Stand → #118. Jeder davon ist eine
inhaltliche Entscheidung (NaN-Semantik in Pflicht-Evidenz, Beschränkung negativer
Zerfallsraten, mehrdeutige Reparatur-Routen), keine Nachpflege. Sie im Stapel zu
schliessen hiesse, sie zu raten.

Bewertung: Der PR ist nicht merge-reif, und das liegt nicht an der Formalie.
Mit +5541/−175 über 16 Runden ist er zu gross geworden, um in einem Zug beurteilt
zu werden — ein Zuschnitt entlang der 16 Punkte wäre der geradere Weg als eine
17. Runde. #115 hängt daran und kann erst danach.

Grundlinie lokal geprüft: 942 Tests grün (.venv, 4 min).

[marcohost33-maker]

Zuschnitt liegt bereit — zwei Zweige statt einer 17. Runde

Wie im Kommentar oben angekündigt ist dieser PR zugeschnitten. Die Naht liegt
dort, wo sie schon im Titel steht: #108 (Zero-Mode-Skala) gegen #102
(Evidenz-Matrix).

Teil	Zweig	Inhalt	lokal
A	split/a-zero-mode-zertifikat	Nullmode-Zertifikat, skalenrelative Trennung, Hermitizität, Diagnostik darauf (#108/#109/#112/#113) + AGENTS.md (#110)	855 Tests grün
B	split/b-hypothesen-matrix	Hypothesenweise Evidenz-Matrix (#102), baut auf A	942 Tests grün

Der Vollständigkeitsbeleg: git diff split/b-hypothesen-matrix <dieser Zweig>
ist leer. Beide Teile zusammen ergeben exakt den Stand dieses PRs — nichts
ist unterwegs verlorengegangen, nichts hinzugekommen. Und 942 ist dieselbe
Testzahl wie hier.

Was der Schnitt gekostet hat: genau einen Test von 856.
test_unresolved_certificate_floors_the_verdict_to_undefined prüft die Wirkung
des Zertifikats auf den Verdikt und braucht dafür die Klassifikations-Schicht.
Er ist in Teil A nicht gelöscht, sondern an seiner Stelle mit Begründung
vermerkt, und in Teil B wieder scharf.

Was der Schnitt gezeigt hat: die Schichtgrenze verläuft anders, als der
PR-Titel vermuten lässt. _types.py und _consts.py tragen Felder für beide
Themen, und die Fundament-Tests laufen durch die Diagnostik — ein Zuschnitt
allein entlang numerics/ scheitert mit 23 roten Tests. Das ist kein
Nebenbefund, sondern der Grund, warum dieser PR so gross werden konnte.

Die Pull Requests sind bewusst noch nicht eröffnet. Eine PR-Eröffnung gegen
main startet hier fünf Workflows über fünf Python-Versionen, und der
Budget-Freeze steht. Die Zweige sind gepusht und lokal geprüft; der Klick
gehört Marco.

Dieser PR sollte geschlossen werden, sobald die beiden Teile offen sind — die
38 hier aufgelösten Threads und ihre Begründungen bleiben im Verlauf erhalten.
Die 16 offenen Sachfragen stehen in #118 und wandern nicht mit.

#115 hängt an Teil B, nicht mehr an diesem PR: es ändert das
Relaxations-Fenster und braucht die _safe_exp/_bounded-Wächter aus dem
Zuschnitt.

[marcohost33-maker]

Review-Fäden nachgezählt: 16 offen → 3

Die 16 offenen Review-Fäden dieses Pull Requests wurden gegen den heutigen Kopf des
Zweigs (4a8ae9c09e2d682d9da0ad69b8390e6f9adf92f5) durchgesehen. 13 davon treffen
dort nicht mehr zu und sind aufgelöst worden — sie waren offen geblieben, weil
niemand sie geschlossen hatte, nicht weil sie unbeantwortet waren.

Die vollständige Zuordnung Befund → Fundstelle steht in Issue #118.

Zwölf sind im Code beantwortet, jeweils mit Datei und Zeile belegt. Bei einem
weiteren trägt die Prämisse nicht: der Befund begründet sich mit
„Because ClassificationResult is not keyword-only" — die Klasse ist
kw_only=True (_types.py:277), und war es bereits vor dem Befund. Die
beschriebene Verschiebung der Konstruktor-Argumente kann daher nicht eintreten.

Was offen bleibt

Befund	Stand am Kopf
Constrain decay rates instead of flattening negative probes	fitting/models.py:53 — der einseitige Exponenten-Deckel steht unverändert, und die produktiven Aufrufe fitten weiterhin ohne Schranken
Do not treat every sub-split decay mode as zero	numerics/linalg.py:342 und :531 — die Zugehörigkeit wird weiterhin rein über den globalen Betragsschnitt entschieden
Disclose that the certificate changes verdicts	CHANGELOG.md:215 nennt das Feld „report-only", während classify_mechanism es auswertet und ein unaufgelöstes Zertifikat auf UNDEFINED zwingt

Zwei davon sind numerisch, eines ist eine Textkorrektur.

Methodischer Vorbehalt

Die dreizehn sind durch Lesen des Codes am genannten Stand belegt, nicht durch
erneutes Ausführen der jeweiligen Reproduktionen. Vier wurden zusätzlich unabhängig
an der Quelle nachgeprüft (_consts.py:126, fitting/models.py:211-219,
fitting/gls.py:82-88, _types.py:277); zur Kontrolle wurde derselbe Weg auf einen
der noch offenen Punkte angewandt, der erwartungsgemäss nicht als erledigt
erschien. Für die beiden Invarianz-Befunde zu den Startwerten ist belegt, dass die
verlangte gitter-relative Skalierung im Code steht — der numerische Nachweis über das
behauptete Intervall steht aus.

Wer einen der aufgelösten Fäden anders sieht, kann ihn jederzeit wieder öffnen.

[marcohost33-maker]

Antwort auf "Do not treat every sub-split decay mode as zero"

Ihr Gegenbeispiel läuft auf dem Nachfolgezweig (pr107-fix, PR #121) korrekt durch — wir haben es wörtlich nachgefahren, nicht nur die Änderung gelesen.

H = diag(0,1), Raten 1e-15 / 1e-14, zero_tolerance = 5e-16: die echte Populationsmode bei 1e-15 überlebt, D1 = 1.0000e-15 statt zuvor 2.05e-14.

Der Grund ist, dass die Zugehörigkeit zur Null-Mode nicht mehr über den globalen eps*||L||-Split entschieden wird: certified_nonzero_modes zertifiziert Moden aus dem a-posteriori-Rückwärtsfehler, und refine_zero_band nimmt sie aus dem Band heraus — src/liouscope/numerics/linalg.py:478, in_band = (magnitudes <= bound) & ~nonzero.

Rücknahme-Probe: entfernt man & ~nonzero, wird test_slow_mode_below_the_norm_scaled_band_survives_as_the_gap rot; wiederhergestellt grün (protokolliert, Stand d7086ca).

Der Thread hängt an diesem PR, der Code dazu liegt in PR #121 — dort ist er Teil der Sammelantwort.

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[marcohost33-maker]

Status 2026-09-07 — do not merge this separately; it is strictly contained in two other PRs

Measured, not inferred (git merge-base --is-ancestor, git rev-list --left-right --count):

#107 head 4a8ae9c is an ancestor of  #121 head bac5fe0d   -> true
#107 head 4a8ae9c is an ancestor of  #127 head e0a6479    -> true
commits unique to #107 vs #121 head                       -> 0

Zero commits are unique to this PR. Everything here is already inside #121 and inside #127. Merging it on its own would not add a line of code; it would only decide which SHA main records.

Current state: mergeStateStatus = DIRTY, mergeable = CONFLICTING against main. The green rollup this PR is known for — 20 check-runs, 0 non-success at 4a8ae9c — is real and still there, but it describes a tree that is 39 commits behind pr107-fix.

Closes #108 is correctly set and verified via closingIssuesReferences. That band is the reason the merge method matters:

#107's head SHA must remain reachable from main for GitHub to close this PR and fire Closes #108. A merge commit does that. A squash or a rebase rewrites the SHA, and then #107 stays open as a zombie with #108 still open behind it — even though every line of it landed.

What Marco has to decide

Merging #121 with a merge commit retires this PR and #108 automatically, because 4a8ae9c becomes reachable. That is the cheapest path and it needs no work here. Resolving the conflicts on this branch would be effort spent on a tree that is superseded.

Read-only measurement. No push, no merge, no rebase, nothing resolved.