Complete bounded freeze audit and report unresolved per-path statistics

CHANGELOG.md

@@ -1,5 +1,16 @@
 # Changelog
 
+- Freeze audit: report unresolved per-path variation instead of PCA or rank correlation of numerical noise; preserve and distinguish historical snapshots. 
+
+## Unreleased: freeze audit
+
+- Validated boundary dimensions and XXZ refinement inputs before coercion; documented logarithm bases greater than one.
+- Removed avoidable logarithmic-gap overflow and made normalized rank coordinates consistent at dimension one.
+- Added independent regression tests for these API cases.
+- Propagated the geometry-versus-chronology interpretation to the scientific entry documents.
+- Recomputed the control record with the hardened source while preserving raw release data, public figures, existing tags, and the scientific conclusions.
+
+
 ## Unreleased - geometry-versus-chronology controls
 
 - Added joint, fixed-endpoint, within-window, and late-time chronology controls, plus four explicit dimension/largest-eigenvalue-matched spectrum references.

README.md

@@ -71,6 +71,8 @@ Random matrix theory enters only afterward, as a family of Haar/Wishart or spike
 
 ## What the follow-up study establishes
 
+The table and committed figures below preserve the v1.0.0 analysis snapshot. Current per-path PCA and correlation calculations exclude unresolved near-constant coordinates under a declared numerical floor; fine rank statistics need not reproduce old roundoff orderings. See [numerical foundations](docs/NUMERICAL_FOUNDATIONS.md#numerically-constant-paths-and-historical-summaries) and the [freeze audit](docs/FREEZE_AUDIT.md). The global common-mode and later chronology-control conclusions are unchanged.
+
 The included deterministic designed dataset contains 5,856 observations from 96 trajectories: four dynamical families, four declared conditions per family, and sizes $n=10,12,14,16,18,20$. The conditions are controlled examples, not independent draws from a population.
 
 | Controlled result | Value | Interpretation |
@@ -238,6 +240,10 @@ This repository concerns pure-state dynamics, specified bipartitions or explicit
 
 The complete public nonclaim list is maintained in [AI_CONTEXT.md](AI_CONTEXT.md) and [Limitations](docs/LIMITATIONS.md).
 
+## Freeze-audit record
+
+The [September 2026 frozen-scope audit](docs/FREEZE_AUDIT.md) records the numerical/API checks, interpretation updates, and explicit limits of the rerun. It does not substitute automated checks for external peer review or extend the scope of the 2024 article.
+
 ## Repository-edition status
 
 Version `1.0.0` is the corrected public repository edition. It freezes the exact mathematical layer, the repaired follow-up computation, the quantitative metric-robustness result, the paper-correction record, and the human/AI discovery layer. A narrow formal journal corrigendum remains recommended, but none has yet been submitted.

SCIENTIFIC_POSITION.md

@@ -23,13 +23,17 @@ The family of these projections is the **entanglement-trajectory atlas**.
 
 ## Central claim for the upgraded repository
 
-Standard bipartite pure-state entanglement measures are nonlinear projections of a common Schmidt-spectrum path. Across four tested dynamical families used to probe scrambling, recurrence, disorder, and spectral complexity, three non-equivalent metric classes share a dominant common trajectory mode and preserve substantial relational morphology after exact-boundary normalization. The preservation is hierarchical rather than exact, and local metric contradictions reveal internal spectral redistribution that no single scalar measure captures.
+Standard bipartite pure-state entanglement measures are nonlinear projections of a common Schmidt-spectrum path. Across four tested dynamical families used to probe scrambling, recurrence, disorder, and spectral complexity, three non-equivalent metric classes share a dominant instantaneous common mode and substantial descriptive cross-metric morphology after exact-boundary normalization. The later chronology controls separate this point-cloud agreement from temporal organization: the observed paths are smoother and contain more local raw-metric disagreements than the specified reorderings, but unusually high common-mode variance is not a dynamical discriminator. The preservation is hierarchical rather than exact, and local metric contradictions reveal internal spectral redistribution that no single scalar measure captures.
 
 This claim has three distinct parts:
 
 1. **Exact common origin.** The fixed-cut measures considered here are functions of the same spectrum.
 2. **Empirical robustness.** Coarse trajectory morphology and the relative geometry among tested model families persist across several metric projections.
-3. **Permitted disagreement.** Different metrics can contradict one another locally, especially when successive spectra are incomparable by majorization.
+3. **Permitted disagreement.** Schur-concave metrics can contradict one another locally only when the spectrum pair is incomparable by majorization (subject to the declared numerical tolerances). Incomparability permits, but does not require, disagreement.
+
+## Interpretation after the chronology controls
+
+The historical common-mode percentage and classifier results remain descriptive evidence, not proofs of special temporal structure. Joint reordering preserves point-cloud PCA exactly; four constructed fixed-(d,p) references exhibit still higher agreement. Temporal smoothness and excess local metric competition survive the stated controls. The path-distance benefit is not uniform across sizes or order-preserving surrogates. See [geometry versus chronology](docs/GEOMETRY_VS_CHRONOLOGY.md) for the full comparison, including negative controls and limitations. These are later repository findings, not results already demonstrated in the 2024 journal article.
 
 ## Quantitative status of the follow-up study
 

analysis/analyze_metric_robustness.py

@@ -727,6 +727,10 @@ def classification_block(fold: str, mode: str) -> dict:
             "boundary_pc1_loadings": [float(x) for x in boundary_fit.components[0]],
             "boundary_pc2_loadings": [float(x) for x in boundary_fit.components[1]],
             "boundary_pc1_cluster_bootstrap_ci95": common_modes["boundary_cluster_bootstrap"]["pc1_explained_ci95"],
+            "per_trajectory_resolved": int(per_boundary["pc1_explained"].notna().sum()),
+            "per_trajectory_total": int(len(per_boundary)),
+            "per_trajectory_scale_floor": 1e-10,
+            "per_trajectory_status_counts": per_boundary["variation_status"].value_counts().to_dict(),
             "per_trajectory_pc1_median": float(per_boundary["pc1_explained"].median()),
             "per_trajectory_pc1_iqr": [
                 float(per_boundary["pc1_explained"].quantile(0.25)),

docs/FREEZE_AUDIT.md

@@ -0,0 +1,57 @@
+# Frozen-scope audit: September 2026
+
+## Decision and scope
+
+The repository is suitable to freeze as a corrected computational companion and a finite designed-data follow-up, after the checks on the final merged commit pass. Existing release tags are not moved. This is an AI-assisted numerical and consistency audit, not independent journal peer review and not a proof that undiscovered defects are impossible.
+
+The audit starts from commit `88d8e420ee292359cb5fb6c10869534c9e59cb03`. A bounded API and interpretation patch closes the findings below. No new physical model, new ensemble claim, or stronger topology claim is introduced.
+
+## Repairs
+
+- Fixed-p boundary routines validate the dimension before integer coercion and reject booleans and fractional dimensions.
+- Entropy and entanglement-energy units require finite logarithm bases greater than one.
+- The entanglement-Hamiltonian gap uses a difference of logarithms. A strictly positive second eigenvalue no longer becomes an infinite gap through an intermediate ratio overflow.
+- Normalized support and effective-rank coordinates are zero in the one-dimensional space, consistently with the exact boundary API; raw ranks remain one.
+- XXZ substep counts must be positive integers. Record intervals must be finite and positive. Negative counts can no longer silently produce an empty evolution loop.
+- The primary claim registry and scientific entry documents now include the geometry-versus-chronology controls and their negative results. Historical numerical snapshots remain explicitly identified as such.
+
+Thirty regression cases cover these API findings, with eleven further cases covering resolved variation. None changes a declared physical run or the three metric coordinates used by the control study. The control archive is regenerated from the hardened source, rather than assigning new implementation hashes to old output tables.
+
+## Checks and independent probes
+
+The standard suite contains 244 cases after the API and resolved-variation patches. The audit additionally runs the public-figure rebuild and numerical source comparison, the paper-correction checks, the numerical-foundations command, the full included-data analysis with its default 3,000 bootstrap and 1,000 permutation settings, and the full geometry/chronology study with 999 chronology draws and 199 draws for each matched-spectrum law.
+
+Independent local probes supplement those workflows: 585 high-precision entropy cases; 500 random spectra with 5,000 metric-envelope comparisons; 36 analytical Schmidt-state constructions; direct partial-transpose checks; 32 independently assembled small-system step operators covering all 16 model conditions at n=4 and n=5; exact-matrix-exponential XXZ refinement and magnetization checks; independent Marchenko-Pastur quadrature and Page means; and all 16,200 distinct pairs in the selected-spectrum archive. Scripts and detailed measurements are retained in the companion freeze-audit evidence package.
+
+The random-spectrum test distinguishes exact identities from rounded input contracts. Two naive fixed-float-p comparisons at very small positive Renyi order differ by several parts in 10^9 near a collapsed two-level envelope. Their separately rounded input components imply a largest-value uncertainty below one floating-point step; the discrepancies are enclosed by the explicit input-rounding allowance. This is not evidence of a majorization violation or a claim of arbitrary relative accuracy. The naive discrepancies remain in the audit record.
+
+## What is and is not established
+
+The common spectrum and majorization geometry remain the mathematical framework. The approximately 90.26% point-cloud mode is descriptive, not an order-sensitive test. Chronological smoothness and excess local metric competition survive the specified reorderings. Constructed matched spectra can have stronger common-mode fractions; chronology does not improve path-distance agreement uniformly. These limits are part of the result, not exceptions to hide.
+
+The full n=20 physical simulation suite and the complete large-system XXZ convergence production are not regenerated in this freeze audit. Included archives, reproduction paths, independent small-system operators, and contained reruns are checked. Historical one-substep XXZ rows remain circuits, not convergence-controlled continuous-time Hamiltonian trajectories. The pinned package set is a declared reproducibility environment, not a bitwise-frozen operating-system image.
+
+## Numerically constant paths and historical summaries
+
+Standardizing a coordinate whose variation is only numerical noise can produce arbitrary PCA fractions and rank correlations. Current per-trajectory PCA and half-chain within-trajectory Spearman calculations therefore declare a standard-deviation floor of `1e-10` in normalized-coordinate units, measured on each statistic's finite overlap. Unresolved cases return `NaN` with an eligibility status and the chosen floor. This is a numerical-resolution convention, not a proof that every smaller physical change is zero. `scale_floor=0` is an explicit unprotected option. Absolute metric separation remains reported.
+
+This matters for the Clifford-reference QCA boundary paths, where nearly constant entropies must not be converted into standardized roundoff. The global point-cloud PCA and the later chronology controls are unaffected by this change. The chronology roughness already used this floor. Historical archived per-path minima, correlations, and fine-descriptor ranks are retained as snapshots, not certified precision estimates.
+
+A fresh included-data analysis uses the current numerical kernels and the declared resolution floor. It is not required to reproduce all secondary v1.0.0 rank statistics exactly. Even before the floor is applied, recomputing very small or tied descriptor values can reorder them; the archived minimum per-path PCA changed from about 0.537 to 0.429 when roundoff was standardized. Neither is meaningful for those unresolved paths. Current tables expose eligibility rather than presenting such minima as scientific evidence. The frozen headline table remains historical, while current analysis tables and source provenance are written to `outputs/rebuild/`.
+
+## Reproduction
+
+In a fresh working copy with the documented dependencies:
+
+```bash
+make test
+make public
+make numerical-check
+make rebuild-included
+make geometry-chronology-controls
+make peer-review-check
+```
+
+Full controls require a fresh output directory. The hosted pull-request and post-merge checks identify the exact audited revision. No new release is implied by this document; version/tag metadata should be updated coherently only when a new release is intentionally created.
+
+The [fresh-versus-historical statistics](../metadata/freeze_audit_statistics.json) record the pinned-hosted values, eligibility decisions, and source fingerprints.

docs/METRIC_ROBUSTNESS_RESULT.md

@@ -1,5 +1,7 @@
 # Quantitative result: metric-robust trajectory morphology
 
+> **Historical result with a later control.** High point-cloud or first-difference common-mode fractions alone do not identify exceptional temporal organization. Read [geometry versus chronology](GEOMETRY_VS_CHRONOLOGY.md) alongside these preserved descriptive results. Static matched references can have stronger agreement, and chronology does not improve path-distance agreement uniformly.
+
 ## Result in one sentence
 
 Across the tested pure-state dynamical families, three non-equivalent Schmidt-spectrum metric classes share a dominant common trajectory mode and preserve substantial relational morphology after exact-boundary normalization, but the preservation is hierarchical rather than exact.

docs/NUMERICAL_FOUNDATIONS.md

@@ -220,6 +220,22 @@ its analytically exact power-of-two reciprocal knots remain exact. This fixes
 a plotting-grid rounding artifact rather than snapping user-supplied spectra;
 the public-data comparator retains its original tolerances.
 
+## Freeze-audit API domain
+
+The entropy and entanglement-energy APIs use finite logarithm bases greater than one, so their stated ranges and Schur directions remain valid. Fixed-p bounds validate a positive integer dimension before coercion. XXZ simulation rejects noninteger or nonpositive substep counts and nonpositive or nonfinite record intervals. Normalized support/effective-rank coordinates are zero in a one-dimensional Hilbert space; their unnormalized value remains one.
+
+The entanglement-Hamiltonian gap is evaluated as a difference of logarithms rather than a potentially overflowing ratio. A strictly positive represented second eigenvalue therefore has a finite logarithmic gap, even when the ratio exceeds floating-point range. Exact zero still gives infinity.
+
+These repairs do not change the supplied trajectories or the three metrics used in the control study. Extremely small positive Renyi orders remain sensitive to input rounding: separately rounded weights and a rounded largest eigenvalue can produce differences near a collapsed envelope. The input-error assessment, rather than a claim of arbitrary relative accuracy, governs that case.
+
+## Numerically constant paths and historical summaries
+
+Standardizing a coordinate whose variation is only numerical noise can produce arbitrary PCA fractions and rank correlations. Current per-trajectory PCA and half-chain within-trajectory Spearman calculations therefore declare a standard-deviation floor of `1e-10` in normalized-coordinate units, measured on each statistic's finite overlap. Unresolved cases return `NaN` with an eligibility status and the chosen floor. This is a numerical-resolution convention, not a proof that every smaller physical change is zero. `scale_floor=0` is an explicit unprotected option. Absolute metric separation remains reported.
+
+This matters for the Clifford-reference QCA boundary paths, where nearly constant entropies must not be converted into standardized roundoff. The global point-cloud PCA and the later chronology controls are unaffected by this change. The chronology roughness already used this floor. Historical archived per-path minima, correlations, and fine-descriptor ranks are retained as snapshots, not certified precision estimates.
+
+A fresh included-data analysis uses the current numerical kernels and the declared resolution floor. It is not required to reproduce all secondary v1.0.0 rank statistics exactly. Even before the floor is applied, recomputing very small or tied descriptor values can reorder them; the archived minimum per-path PCA changed from about 0.537 to 0.429 when roundoff was standardized. Neither is meaningful for those unresolved paths. Current tables expose eligibility rather than presenting such minima as scientific evidence. The frozen headline table remains historical, while current analysis tables and source provenance are written to `outputs/rebuild/`.
+
 ## 6. Reproduction
 
 ```bash

docs/SCIENTIFIC_OVERVIEW.md

@@ -1,5 +1,7 @@
 # Scientific Overview
 
+> **Interpretation update.** The common-mode percentage describes an instantaneous point cloud. The later [geometry-versus-chronology study](GEOMETRY_VS_CHRONOLOGY.md) separates that agreement from temporal smoothness and local metric competition. It does not establish a universal chronology-enhanced fingerprint. The historical numerical results below are preserved.
+
 ## 1. Why another representation of entanglement?
 
 Entanglement is not naturally one-dimensional. Even for a fixed bipartition of a pure state, the reduced density matrix has a complete ordered spectrum. A scalar entanglement measure compresses that spectrum according to a chosen sensitivity: the leading eigenvalue, the bulk, the tail, or a weighted mixture.