Add cross-size covariance audit and research diagnostics

[LightChainr]

Purpose

Measure the implicit cross-size coupling in the historical P33 threshold-rank batches and preserve a covariance-aware diagnostic path on main.

This is research analysis infrastructure, not a general-purpose calibrated statistics library. Its outputs are suitable for comparing the historical full-covariance and diagonal diagnostics and for planning new runs. Strong paper-facing p-values or near-singular generic covariance cases can be hardened later if they become decision-critical.

Added

• reconstruction of batchwise Delta M, mean M', root-gap jackknife pseudo-values, A_M, B, and angular-normalized A_p;
• measured cross-size covariance/correlation matrices;
• full-covariance versus diagonal held-out diagnostics for the historical P33 data;
• root-doubling diagnostic outputs;
• archive validation and synthetic regression tests;
• a dedicated workflow for the covariance archive.

Current empirical takeaway

Historical P33 cross-size correlations are real but modest (maximum absolute correlation about 0.22). Using the measured covariance changes the old low-stat scores only modestly:

A_M:          5.530 full vs 5.273 diagonal
A_p:          5.552 full vs 5.293 diagonal
root doubling 3.462 full vs 3.442 diagonal

So the old radial tension was not created by ignoring a huge hidden cross-size correlation.

Scope

For the committed archive the batch design is aligned and validated. Future production should use the simpler policy in #39: domain-separate distinct N by default, or retain deliberate coupling with aligned batches when covariance reduction is useful.

Numerical hardening such as rank-aware pseudoinverses or finite-sample calibration is welcome follow-up work, but it is no longer a merge blocker for this exploratory audit.

[LightChainr]

Independent execution review completed on a029993:

• full repository suite: 59/59 passed;
• audit completed on the committed P33 10M/size, 100-batch histogram;
• missing/misaligned batches are rejected and training-to-holdout covariance is propagated into the residual score.

Measured cross-size correlations are real but moderate (roughly -0.18 to +0.26 across the retained metrics). They do not reverse the radial conclusion:

metric	diagonal held-out chi-square	full-covariance held-out chi-square
A_M	5.273 / 2	5.530 / 2
A_p	5.302 / 2	5.561 / 2

For A_p, the full-covariance training amplitude is 0.3025 +/- 0.0635; held-out N=145,170 observations are 0.6221, 0.8816. Thus the old diagonal treatment was incomplete, but covariance is not the source of the visible drift. The current 10M pilot remains underpowered/borderline and motivates the frozen high-stat test in #45.

Recommendation: merge the audit tool. Commit its generated P33 audit outputs before selecting the #39 replay policy, and keep both diagonal/full scores in the report as specified.

[LightChainr]

Follow-up after the branch was rewritten to 7d73a2f:

• rerun full suite: 60/60 passed;
• rerun P33 audit confirms root_gap_method=delete_one_jackknife_pseudovalues;
• updated A_p held-out scores are diagonal 5.29288/2, full covariance 5.55159/2 (the earlier a029 result differed only in the third decimal);
• A_M remains diagonal 5.27335/2, full 5.53002/2.

The merge recommendation remains positive. One nonblocking integrity improvement: --seed-label is currently declarative and the tool does not ingest metadata. Before using arbitrary/concatenated files, validate that all sizes share the declared RNG schema, seed, counter interval, per-batch counter ranges and samples per batch; otherwise equal batch IDs need not imply measurable cross-size coupling. The committed single-file P33 use is auditable, but the CLI should state or enforce this trust boundary.

[LightChainr]

Review: methodology is sound; add four robustness gates before interpreting the output

The main correction is correct: aligned cross-size batches must be treated jointly, nonlinear root gaps should use delete-one jackknife pseudo-values, and the held-out residual covariance must include covariance between the fitted training amplitude and held-out observations.

Before this becomes the authoritative P33/P35 score, please add or explicitly report the following.

1. Equal-batch-weight contract

covariance_of_mean() is an unweighted equal-batch estimator. _orientation_batches() checks equality between the two orientations inside each (N,batch), but it does not currently assert that all aligned batches across all sizes have the same sample count.

Either:

• assert a single common samples_per_batch across the complete aligned matrix; or
• implement a declared weighted/cluster-robust estimator.

Do not silently give unequal batches equal statistical weight.

2. Near-singular covariance handling

Common counter streams can make the cross-size covariance nearly singular. The current hand-written Gauss–Jordan inverse should not be the only path used for scientific scores.

Please emit:

• covariance eigenvalues or singular values;
• condition number/effective rank;
• score sensitivity to a prespecified eigenvalue cutoff;
• a stable Cholesky/SVD/pseudoinverse implementation where necessary.

A failed inversion or large condition number is itself a result and should remain in the report.

3. Estimated-covariance calibration

The reported quadratic form uses a covariance matrix estimated from about 100 batches. Label the resulting chi-square as a plug-in/asymptotic score. Add at least one of:

• batch bootstrap calibration of the held-out statistic;
• Hotelling/F-type finite-batch calibration where applicable;
• a sensitivity table comparing plug-in chi-square with bootstrap quantiles.

This matters most for the two-dimensional held-out test when the covariance has strong off-diagonal structure.

4. Stronger synthetic regression

The current cross-covariance test verifies that the residual off-diagonal is nonzero and the score is finite. Add a synthetic case with an analytically known answer where off-diagonal training/held-out covariance materially changes the fitted amplitude or held-out score. Assert the exact expected full-covariance and diagonal-only values.

Requested result artifact

After these gates pass, run the audit on the committed P33 histogram and commit:

results/server-20260828/P33-cross-size-covariance/

The report should compare, for both A_M and angular-normalized A_p:

• full covariance;
• diagonal-only covariance;
• covariance eigenstructure;
• plug-in and bootstrap-calibrated held-out scores;
• the original published diagonal result.

Do not overwrite the previous analysis. This audit should determine whether the apparent radial root-amplitude tension survives the actual coupling policy.

[LightChainr]

Result review: scientific conclusion is now clear; robustness requirements remain open

The committed P33 audit answers the immediate scientific question. Cross-size correlations are real but modest and mixed-sign (the largest absolute values are about 0.22). Including them does not materially change the previous low-stat radial conclusions:

A_M held-out chi2: full 5.5300 / 2; diagonal 5.2733 / 2
A_p held-out chi2: full 5.5516 / 2; diagonal 5.2929 / 2
root doubling:     full 3.4625 / 2; diagonal 3.4417 / 2

Thus the old diagonal approximation was not the source of the apparent P33 radial/root tension. The P33 data are simply underpowered/noisy for those asymptotic questions. This is an important negative audit result.

The implementation correctly uses delete-one jackknife pseudo-values for nonlinear roots and propagates training/held-out cross-covariance. The result files and workflow are useful and should be retained.

However, the four robustness gates from the earlier review are still not implemented in the current head:

1. _orientation_batches() checks equal samples only between first/second orientations inside one (N,batch), not a common batch weight across all aligned sizes. Assert one common sample count for the complete matrix or implement explicit weights.
2. Scientific scores still rely on a hand-written Gauss–Jordan inverse. Emit eigen/singular values, condition number/effective rank, and use a stable Cholesky/SVD/pseudoinverse path.
3. The chi-square values remain plug-in/asymptotic with covariance estimated from 100 batches. Add batch-bootstrap or an explicit finite-batch calibration/sensitivity table.
4. The synthetic off-diagonal test still checks only that a covariance entry is nonzero and the score is finite. Add an analytically known example asserting exact full-covariance and diagonal-only amplitudes/scores.

I therefore regard the empirical audit conclusion as valid, but not yet the general-purpose scoring implementation as fully hardened. After these four items, the PR is suitable as the authoritative covariance tool. Future production should preserve same-N orientation coupling while domain-separating distinct N by default, unless a prespecified pilot demonstrates useful parent/child covariance for the exact target statistic.

[LightChainr]

治理审查：该 PR 的 empirical archive 有价值，但当前 generic covariance/scoring path 还不应合并。阻断项如下：

1. 核心计算必须强制 equal batch weights / sample counts。 _orientation_batches 目前只检查同一 N 下 first/second 的 samples 相等，没有检查所有 N、所有 aligned batch 使用同一 sample count；随后 covariance_of_mean 却按等权 batch 处理。archive validator 虽然会拒绝不等样本数，但通用 audit API 仍可能静默产出错误 covariance/score。请在核心路径直接 fail closed，或实现并测试严格的 weighted estimator。
2. 协方差数值稳定性要进入 scorer 本身。 目前 _solve/_inverse 是通用 Gauss–Jordan，核心 scoring path 没有 SPD/condition/rank 检查；不能把这个安全门只放在事后的 archive validator。建议 Cholesky-first；若支持半正定/近奇异情况，则使用明确定义的 rank-aware pseudoinverse，并报告 effective rank / eigenvalue cutoff。
3. 有限 batch 的统计量不要无条件称作校准的 chi-square。 这里 covariance 本身来自约 100 个 batch。可以将其明确称为 covariance-weighted quadratic-form diagnostic，或加入预注册的有限样本校准（Hotelling/F、parametric/bootstrap calibration 等，取决于适用假设）。不要据此生成未经校准的 p-value。
4. 补 exact synthetic regressions。 至少加入：(a) 真正 diagonal covariance 时 full 与 diagonal score 必须逐位/容差内一致；(b) 一个有解析答案的 correlated case；(c) unequal sample-count 输入必须在 core audit 层失败；(d) near-singular covariance 的 fail-closed/rank-aware 行为。
5. 更新到当前 server head 后再重跑归档验证。 Regression-test the fresh P37 doubling result #53 已经并入 server/huawei-analysis-20260828；该 PR 当前相对 base 已 diverged。修订后请从当前 base 重放，并重新生成/校验 checksums 和 archive contract。

这些是统计基础设施的合并门槛，不是否定已记录的经验结论。现有 cross-size correlation 结果可继续作为 provenance 保留。

[LightChainr]

已由 #69 以 current-main 单提交方式迁入：covariance audit、root-doubling diagnostics、历史输出、validator 和 tests 都已在 main。旧 PR 的分叉历史不再需要继续维护；更泛化的数值 hardening 以后按实际 precision-sensitive 需求做。