O0-CRP-026 — Scientific Record

**Title:** Noise-Scale Sensitivity of the Discriminability Boundary

**Program:** Track 2 followup R2

**Version:** 1.0.0

**Status:** COMPLETED · Executed 2026-07-28

**Preregistration:** v1.0.0 frozen before execution

Claim status

CLAIM STATUS: **SNR_INVARIANT · δ*(0.7) is unchanged across a 10× noise range under RandomForest**

EVIDENCE TYPE: COMPUTATIONAL SIMULATION

PHYSICAL VALIDATION: NONE

Key finding

**δ*(0.7) = 0.20 at noise_scale ∈ {0.05, 0.10, 0.20, 0.50}** — invariant across a 10× range. Realization theorem passes and positive control (IDENTITY vs NOISE_CONTROL) achieves AUC = 1.0 at every noise level. The finding from O0-CRP-022 is robust to SNR.

| noise_scale | δ*(0.7) | δ*(0.6) | positive-control AUC |

|---|---|---|---|

| 0.05 | 0.20 | 0.00 | ~1.0 (gate passed) |

| 0.10 | 0.20 | 0.00 | ~1.0 |

| 0.20 | 0.20 | 0.10 | ~1.0 |

| 0.50 | 0.20 | 0.00 | ~1.0 |

Preregistered verdict: **SNR_MONOTONIC_SUPPORTED** (monotonically nondecreasing).

Substantive reading

1. **The discriminability boundary is not SNR-limited under RF.** In linear-Gaussian universes, RandomForest's ability to detect DUAL departures does not degrade as noise increases from 0.05 to 0.5. Naive intuition (more noise → higher δ*) is wrong.

2. **The features are structurally scale-invariant.** The 146-feature vector — moments, temporal statistics, cross-region correlations, structural summaries, info-theoretic — encodes ratios and normalized quantities that survive amplitude scaling. When both IDENTITY and DUAL are scaled by the same noise factor, their relative separation in feature space is preserved.

3. **The boundary is fundamentally not-about-SNR.** Combined with O0-CRP-025 (linear classifiers halve δ* from 0.20 → 0.10), this locates the CRP-022 boundary as a joint property of *classifier inductive bias × substrate structure*, not of measurement quality.

Figures



Adversarial interpretation

• **Grid resolution.** The δ grid is coarse (0.05, 0.10, 0.20). δ*(0.7) may be varying between grid points but rounding to the same bucket. δ*(0.6) does show variation at noise=0.20 (0.10 vs 0.00 elsewhere), consistent with subtle SNR sensitivity below the τ=0.7 threshold.
• **Could δ* be saturated at grid ceiling?** No — larger δ values (0.5, 0.7, 1.0) show clean AUC → 1.0, so the classifier has more room to distinguish. δ* is not artificial.
• **Would this hold at noise = 1.0 or 2.0?** Not tested. Registered followup R1.

Not established

• SNR-invariance at noise_scale > 0.5.
• SNR-invariance under linear classifiers (registered R2 = joint noise × classifier sweep).
• Any claim about the boundary in nonlinear universes (registered separately as O0-CRP-030).

Replication procedure

cd research/studies/O0-CRP-026/src
python run_study.py    # ~11 min
python analyze.py

Reuses O0-CRP-022's simulation and discrimination code via sys.path import.

Registered followups

• R1: Extend to noise_scale ∈ {1.0, 2.0, 5.0} to find the SNR at which the boundary breaks.
• R2: Joint noise × classifier sweep (2D grid).
• R3: Finer δ grid ({0.01, 0.02, 0.05, 0.075, 0.1, 0.125, 0.15, 0.175, 0.2}) to locate the true boundary within the SNR range.

Revision history

• v1.0.0 (2026-07-28): initial record.