# Agent Report — Observable Collinearity Breaks Only Where Denominators Are Weak
**Date**: 2026-05-06 19:55  
**Piano**: 67  
**Tension explored**: META + TRAJECTORY_APPLY_20260506_1941  
observables_registry: 1.0.0-2026-05-06  
observables_used: [SR, SR2, L1, L2, triple_var]

## Claim Under Test
Cycle 19:41 closed `PERTURBATION_DENOMINATOR_GATE` and the trajectory explicitly said:

> La prossima corsa NON deve restare su perturbation rank.

This run therefore does not test perturbation dimensionality. It asks a cross-domain META question:

> When the five canonical observables are measured under uniform partial shuffle, does observable collinearity break in structured domains, or only in controls where original-vs-shuffle denominators are weak?

## Experiment
Tool updated: `tools/exp_observable_rank_audit.py`

Method correction before execution:
- removed local observable redefinitions;
- imported canonical definitions from `tools/observables_registry.py`;
- replaced the old local `triple_var` normalized convention with canonical raw `triple_var`;
- added `prime_shuffle` as a control domain;
- reported weak observable count using the fixed gate `abs(original - shuffle_mean) / shuffle_std < 2`.

Atomic perimeter:
- domains: first prime gaps, prime-shuffle control, independent GUE spacings, iid Poisson spacings;
- main run: 12,000 gaps, 19 alpha values, 18 partial-shuffle trials per alpha, 48 full-shuffle baselines;
- two seed checks: 8,000 gaps, 15 alpha values, 12 trials per alpha, 36 baselines;
- measured object: PCA of the 5-observable retention curves across alpha, not perturbation profiles.

## Results

### Main Run

| Domain | PC1 energy | effective rank | mean abs corr | weak obs / 5 | z summary |
|---|---:|---:|---:|---:|---|
| primes | 0.978 | 1.128 | 0.975 | 1 | SR=-12.1, SR2=-2.5, L1=-8.9, L2=-1.9, triple_var=-8.7 |
| prime_shuffle | 0.593 | 2.475 | 0.606 | 5 | all abs(z) <= 1.1 |
| GUE | 0.990 | 1.060 | 0.989 | 0 | SR=-2.9, SR2=+14.5, L1=+13.2, L2=+31.7, triple_var=+23.8 |
| Poisson | 0.625 | 2.368 | 0.609 | 5 | all abs(z) <= 1.9 |

### Three-Run Summary

| Domain | PC1 mean | rank mean | mean abs corr | weak obs mean |
|---|---:|---:|---:|---:|
| primes | 0.939 | 1.296 | 0.924 | 1.33 |
| prime_shuffle | 0.765 | 1.904 | 0.551 | 4.67 |
| GUE | 0.980 | 1.106 | 0.977 | 0.33 |
| Poisson | 0.714 | 2.196 | 0.572 | 5.00 |

## Findings

1. **Structured domains compress the five canonical retention curves to one dominant coordinate in this perimeter.** Primes and GUE both have PC1 > 0.93 on average and effective rank close to 1. This does not say the domains are the same; it says uniform partial shuffle moves the canonical observables along one dominant retention mode.

2. **Observed collinearity breaking is concentrated in weak-denominator controls.** Poisson has the highest apparent rank among the three-run means (`2.196`), but all five observables are weak against full shuffle in every run. Prime-shuffle behaves similarly: rank is unstable and 4-5 of 5 observables are weak. This mirrors the denominator lesson from perturbation rank without repeating the perturbation-rank experiment.

3. **The 05-05 observable-rank result survives only after narrowing its language.** The valid statement is not "five probes are always one thing." The scoped statement is: under uniform partial shuffle and canonical observables, primes and GUE show a dominant one-coordinate retention response; controls can show larger PCA rank, but that rank is not structural when the original-vs-shuffle denominators are absent.

4. **GUE is the cleanest conditioning check.** In the main run, all five GUE observables pass the denominator gate and still give rank `1.060`. This makes GUE the best positive control for "low rank despite valid denominators." Poisson is the negative control for "high rank without valid denominators."

## Verdict
**CONSTRAINT on META**: observable collinearity claims must be reported with:

> observables_registry version + canonical observable list + original-vs-shuffle z per observable + control domains.

In this perimeter, high observable-rank is not the sign of richer structure when it appears in Poisson or prime-shuffle controls; it is a warning that retention ratios are being formed on weak denominators. The stable cross-domain result is narrower:

> uniform partial shuffle exposes one dominant retention coordinate in conditioned structured domains (primes, GUE), while apparent multi-coordinate behavior in Poisson/shuffle controls is denominator-weak.

## Consecutio
What opens now: the next non-redundant test is not another PCA audit. It is **selective operator coupling**: use perturbations that act separately on pair-scale and triple-scale structure, but report only observables whose denominator gate survives. If selective operators rotate primes while GUE stays collinear, the lab gets a real cross-domain discriminator; if both stay collinear, the current observable suite is overcomplete for this question.

## Auto-audit: 5 lenti
- **L1 hard constraint vs bias**: no zero/always claim. "Weak" means `abs(z) < 2` in this declared gate.
- **L2 quantity vs ratio**: PCA rank and retention ratios are interpreted only after raw z denominators.
- **L3 no silent patching**: the older 05-05 collinearity claim is explicitly narrowed; it is not silently rebranded as universal.
- **L4 edge cases**: `prime_shuffle` seed 1956 produced low rank with 4 weak observables; this is reported as unstable control behavior, not ignored.
- **L5 re-discovery**: PCA rank instability under noisy normalization is standard statistical hygiene. This is a lab method constraint, not a new RMT theorem.

## Files
- Script: `tools/exp_observable_rank_audit.py`
- Main data: `tools/data/observable_collinearity_breaking_20260506_1955.json`
- Seed checks: `tools/data/observable_collinearity_breaking_20260506_1956.json`, `tools/data/observable_collinearity_breaking_20260506_1957.json`
- Report: `tools/data/reports/agent_20260506_1955.md`