O0-CRP-027 — Scientific Record

**Title:** Fresh-World Replication of O0-CRP-022

**Program:** Track 2 followup R4

**Version:** 1.0.0

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

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

Claim status

CLAIM STATUS: **APPROXIMATELY_REPLICATED · δ* shifts one grid step (0.20 → 0.10)**

EVIDENCE TYPE: COMPUTATIONAL SIMULATION, direct replication with fresh seeds

PHYSICAL VALIDATION: NONE

Key finding

On 30 independent fresh worlds (seeds 15000-15029, trial_offset=200_000), δ*(0.7) = **0.10** — one grid step below the O0-CRP-022 value of 0.20. Positive control AUC = 1.000, realization theorem PASS. The finding is *close* to the original but does not reproduce the specific value.

| Metric | O0-CRP-022 (original) | O0-CRP-027 (replication) |

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

| world seeds | 13000-13029 | 15000-15029 |

| δ*(0.7) | 0.20 | **0.10** |

| δ*(0.6) | 0.10 | 0.00 |

| matched-dual AUC | 0.376 ± 0.044 | 0.386 ± 0.067 |

| noise-control AUC | 1.000 | 1.000 |

| AUC at δ=0.10 | 0.643 | 0.701 |

| AUC at δ=0.20 | 0.896 | 0.912 |

Preregistered verdict: **APPROXIMATELY_REPLICATED**.

Substantive reading

1. **The boundary is close but not exactly 0.20.** The AUC at δ=0.10 is 0.701 (just above the 0.7 threshold) in this replication, vs 0.643 (just below) in the original. This is threshold-crossing sampling variance, not two different phenomena.

2. **The "true" δ* is likely in the range [0.10, 0.15].** Three lines of evidence now converge on this:

• CRP-025: linear classifiers get δ*(0.7) = 0.10
• CRP-026: RF at multiple noise scales stays at 0.20 (this study's original seed set)
• CRP-027: RF on fresh seeds gets 0.10

The finer δ grid (registered R3 in CRP-026) should pin this down.

3. **The CRP-022 value of 0.20 was on the pessimistic edge of sampling variance.** In this replication and at all classifiers in CRP-025 except MLP and grad_boost, δ*(0.7) is ≤ 0.20. The 0.20 finding was correct as reported (the CRP-022 sample crossed the threshold at 0.20), but the true asymptotic boundary is likely smaller.

Figures



Adversarial interpretation

• **Sampling variance.** With 30 worlds × 300 trials, the confidence band on δ* is naturally at the resolution of the δ grid. A one-step shift is exactly what we'd expect from independent samples.
• **Different world distribution.** Seeds 13000-13029 and 15000-15029 draw different specific system matrices from the prior; the seed distributions are identical but the specific matrices differ. This is what independent replication is *for* — it separates seed-specific artifacts from substrate-level truth.
• **Not a null result.** Positive control passes, matched-dual AUC ≈ 0.39 (near chance), and the sweep monotonically ascends to AUC → 1.0 as δ → 1.0. The classifier is behaving normally.

Not established

• Exact value of δ*(0.7). A finer grid is needed (registered followup).
• Whether the shift toward 0.10 would continue if we sampled a third seed set.
• Anything about nonlinear universes (O0-CRP-030, registered).

Retrospective correction to O0-CRP-022

The O0-CRP-022 scientific record reported δ*(0.7) = 0.20 as a substrate property. That value is *specific to seeds 13000-13029*. On seeds 15000-15029, the boundary sits at 0.10. Both are within one δ-grid step of each other and both are near the τ=0.7 threshold, so this is threshold sampling variance, not a contradiction. But the CRP-022 record should be read as "at least 0.20" rather than "exactly 0.20."

Replication procedure

cd research/studies/O0-CRP-027/src
python run_study.py    # ~170s
python analyze.py

Registered followups

• R1: A third independent seed set (seeds 17000-17029) at fine δ grid to statistically converge on the boundary value.
• R2: Bootstrap CI on δ* via resampling worlds.

Revision history

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