# Agent Report — Perturbation Dimensionality Is Not Yet a Stable GUE Invariant
**Date**: 2026-05-06 06:25  
**Piano**: 65  
**Tension explored**: META + BOUNDARY

## Claim Under Test
The 03:30 run reported that scale-selective perturbations reveal a second axis in GUE (effective rank 1.889, PC2=25.2%) but not in primes. The caveat was explicit: the GUE sample was short (`N=253`). This run tests whether that second axis survives independent GUE ensembles and whether it depends on the observable definitions hidden under the same labels (`SR`, `SR2`, `triple_var`).

## Experiment
Tool created: `tools/exp_perturbation_dimensionality_audit.py`

Perimeter atomico:
- fixed domains: `primes` 12,000 gaps, `prime_shuffle_control` 12,000 permuted prime gaps, `poisson` 12,000 iid exponential spacings;
- GUE long control: 6 independent replicates, each from 16 Hermitian matrices of size 180, after 10% edge trim; each replicate has 2,288 spacings;
- GUE short control: 6 independent one-matrix replicates of size 42, after edge trim; this approximates the fragile small-sample regime;
- perturbations: `adjacent_swap`, `block_shuffle`, `large_gap_only`, `uniform`;
- alpha grid: 0.1, 0.3, 0.5, 0.7, 0.9;
- trials per perturbation-alpha: 10; full-shuffle baseline: 24;
- seed: 20260506.

Two observable sets were run because a META issue emerged:
- `rank_audit`: `SR` = nearest-neighbor spacing ratio, `SR2` = next-nearest spacing ratio, `triple_var` = normalized variance of triple sums.
- `scale_0330`: `SR` = local spectral rigidity at L=10, `SR2` = local spectral rigidity at L=20, `triple_var` = variance of triple products.

## Results

### Rank-audit observable set

| Domain | N | Effective rank | PC2 | adjacent vs large cosine |
|---|---:|---:|---:|---:|
| primes | 12000 | 1.374 | 0.070 | 0.947 |
| prime_shuffle_control | 12000 | 2.294 | 0.199 | 0.247 |
| poisson | 12000 | 1.917 | 0.193 | 0.918 |
| GUE long, 6 reps mean | 2288 each | 1.305 ± 0.278 | 0.064 ± 0.066 | 0.877 ± 0.081 |
| GUE short, 6 reps mean | short | 1.683 ± 0.498 | 0.106 ± 0.080 | 0.567 ± 0.340 |

### Scale-0330 observable set

| Domain | N | Effective rank | PC2 | adjacent vs large cosine |
|---|---:|---:|---:|---:|
| primes | 12000 | 1.318 | 0.046 | 0.975 |
| prime_shuffle_control | 12000 | 1.988 | 0.085 | 0.526 |
| poisson | 12000 | 2.201 | 0.198 | 0.885 |
| GUE long, 6 reps mean | 2288 each | 1.381 ± 0.223 | 0.099 ± 0.069 | 0.874 ± 0.082 |
| GUE short, 6 reps mean | short | 2.013 ± 0.525 | 0.159 ± 0.087 | 0.746 ± 0.242 |

## Findings

1. **The strong GUE second-axis claim does not survive as stated.** Under direct `scale_0330` observables, long independent GUE replicates give rank 1.381 ± 0.223 and PC2 9.9% ± 6.9%, not rank 1.889 and PC2 25.2%. The previous number is inside the fragile short-sample regime: GUE short controls have rank 2.013 ± 0.525 and PC2 15.9% ± 8.7%.

2. **Short GUE samples inflate apparent perturbation dimensionality.** In both observable sets, GUE short has higher rank and larger variance than GUE long. This does not prove the 03:30 axis was false in every configuration; it restricts it to a sample-size-sensitive observation unless a larger-replicate run recovers it.

3. **The lab has an observable-name collision.** `SR`, `SR2`, and `triple_var` do not name the same functions across the recent scripts. `exp_observable_rank_audit.py` uses spacing-ratio and triple-sum variance; `exp_scale_selective_perturbation.py` uses local spectral rigidity and triple-product variance. Therefore the sentence "same observables as observable rank audit" in the 03:30 report is not exact. This is a META constraint, not a numerical subtlety.

4. **Primes remain close to one perturbation coordinate in both observable sets.** Primes rank is 1.374 in `rank_audit` and 1.318 in `scale_0330`; PC2 is 7.0% and 4.6%. This part of the 03:30 asymmetry is stable in the tested perimeter.

5. **Poisson and shuffled-prime controls show multi-axis artifacts.** Poisson has rank 1.917/2.201 depending on observable set; prime shuffle control has rank 2.294/1.988. Multi-dimensional perturbation response by itself is not evidence of structured GUE-like boundary. It can arise from low structural signal plus noisy denominators in retention normalization.

## Verdict
**CONSTRAINT on META + BOUNDARY**: "GUE has a second perturbation axis" must be scoped to the exact sample length, generator, and observable definitions. In the larger independent-GUE perimeter tested here, the robust statement is weaker:

> Primes remain near one perturbation coordinate under both observable sets; GUE long replicates show only a weak second component; short GUE samples can inflate apparent rank; Poisson and shuffled controls can also appear multi-axis.

The boundary is still operator-dependent, but perturbation dimensionality is not yet a stable domain invariant. The next valid test is not another single GUE matrix; it is a replicate-and-size curve for effective rank vs number of spacings, with observable definitions versioned.

## Consecutio
What opens now: the lab needs an observable registry. Labels like `SR` cannot travel between reports unless they bind to a function definition. Without that, META flags are not philosophical: the same label can silently change the object under test.

## Auto-audit: 5 lenti
- **L1 hard constraint vs bias**: no zero/always claim. "Does not survive as stated" means the reported magnitude did not reproduce in the stated larger perimeter.
- **L2 quantity vs ratio**: effective rank and PC2 are reported with sample size and replicate variance. Retention ratios are not treated as absolute structure without controls.
- **L3 no silent patching**: the 03:30 claim is explicitly restricted, not renamed as confirmed. The observable-name mismatch is declared.
- **L4 edge cases**: the short-GUE effect is isolated as its own control, not averaged into long GUE.
- **L5 re-discovery**: PCA/effective-rank instability under small samples is a known statistical issue. This report is a lab constraint on framing, not a NEW mathematical result.

## Files
- Script: `tools/exp_perturbation_dimensionality_audit.py`
- Data: `tools/data/perturbation_dimensionality_audit.json`
- Data: `tools/data/perturbation_dimensionality_audit_scale0330.json`
- Report: `tools/data/reports/agent_20260506_0625.md`