Separate spectral geometry from temporal order with controlled references

[GoGoKo699]

Scientific question

Which parts of multi-metric entanglement agreement reflect instantaneous spectral geometry, and which depend on temporal ordering?

Completed study

The full study was run locally and independently in the pinned hosted environment. The committed summary and draw archive come from the hosted run (CPython 3.11.15, NumPy 2.4.6), not from copying local outcome tables.

• 96 trajectories / 5,856 observations; original integer recording grids and fixed missing-value masks.
• 999 realizations for each primary joint, fixed-endpoint, and within-window chronology shuffle, plus late-window sensitivity.
• 199 realizations of each of four explicitly defined (dimension, lambda_max)-matched spectrum laws: capped gamma weights of three shapes and an extremizer-segment mixture. These are not Haar or uniform capped-simplex samples.
• Stable-extraction regeneration of all 656 n=10 observations.
• Independent analytical permutation expectations and all 16,200 within-run pairs of the five selected complete-spectrum runs.

Findings and limits

The 90.26% level common mode is invariant to chronology shuffling. Matched static references give larger common modes, 97.50% to 97.89%, so high PC1 alone is not a dynamical signature. Observed chronological paths are much smoother and show more local raw-metric competition than reordered references. Increment PC1 is lower than unrestricted shuffled references, and native-grid distance agreement is not uniformly chronology-enhanced across sizes. Majorization constrains pairs regardless of order.

These are conditional finite-design reference comparisons, not population confidence intervals, proof of chaos, a universal classifier, or a new topological invariant. The original lambda_max(t) path is retained by the static references. The work is exploratory, not externally preregistered, and is clearly identified as later repository evidence rather than a result from the 2024 article.

Repository changes and preservation

13 changed files: 6 additions, 7 replacements, no deleted files. Adds the control implementation, runner, tests, explanatory document, machine-readable summary, and compact draw archive, with navigation and Makefile integration.

Released data, old result archives, committed public figures, numerical claim snapshots, licences, environment locks, VERSION and v1.0.0 are unchanged. Temporary transfer files and workflow are absent from this clean commit and its ancestry.

Verification

• Local suite: 203 tests passed.
• Full pinned hosted computation and candidate validation passed in run 34042335680.
• Exact source-content checks against the locally tested candidate passed.
• Existing public-figure numerical comparison, paper corrections, release-evidence checks and repository validation passed.

The ordinary repository-qa workflow must also pass on this clean PR before merging. Automated checks are not external journal peer review.

[GoGoKo699]

Post-merge verification completed

Merged main commit: 88d8e420ee292359cb5fb6c10869534c9e59cb03 (tree 4a6bccb9d6b541eac739effa9d9369505d457a01). The separate main workflow 34042917821 completed successfully, including the pinned environment, context/figure regeneration, numeric figure-source comparison, all 203 tests, repository validation, and existing release-evidence checks. The clean PR workflow 34042771717 also passed before merging.

The full 999-permutation / four 199-realization control study was independently recomputed in the pinned environment in 34042335680, which produced the committed summary and draw archive. The ordinary QA workflow checks implementation and archived consistency; it does not repeat that full production computation.

The update changes 13 files (6 additions, 7 replacements, no deletions). The 23 original data/public-figure files were verified unchanged. v1.0.0 remains at 90baf8c8124123a98ef1a654e14ca5ec83eae609. No new release was created, and the temporary transfer branch was removed; no transfer workflow or payload appears in the merged source or its ancestry.

Interpretation: high level PC1 describes instantaneous agreement, not chronology. The matched static references give still larger PC1 values; chronological sequences are smoother and encounter more local metric competition than the specified reordered references. Neither a universal chaos diagnostic nor a formal topological invariant follows. All reference ranges and tail fractions remain conditional on the declared finite design and surrogate laws.