O0-CRP-032 — Confirmatory Test of the Chaos-Washout Finding

**Program:** CONTACT_AND_REVELATION · Track 2 followup — confirmatory test of CRP-031 emergent finding

**Version:** 1.0.0

**Status:** COMPLETE

**Preregistration:** frozen 2026-07-29 before execution (see `preregistration.md`)

**Related:** [O0-CRP-031](../O0-CRP-031/scientific_record.md), [O0-CRP-022](../O0-CRP-022/scientific_record.md)

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Claim status

CLAIM STATUS: MIXED — chaos-washout PARTIALLY LIFTED under better measurement; matched-source indistinguishability + realization theorem PRESERVED

EVIDENCE TYPE: CONFIRMATORY COMPUTATIONAL SIMULATION

PHYSICAL VALIDATION: NONE

INDEPENDENT REPLICATION: pending

**SUPPORTED:**

• The CRP-031 chaos-washout finding was **substantially a measurement-weakness artifact for Lorenz-63**. Under T=1000 + augmented feature battery (226 features), δ*(0.7) = 0.5 (was NEVER in CRP-031).
• The finding was **partially a measurement artifact for Van der Pol**. Under the same upgraded measurement, δ*(0.7) = 0.7 (was NEVER in CRP-031).
• Matched-source indistinguishability holds under T=1000 + augmented in both systems (Lorenz 0.437, VdP 0.438 — well inside chance band).
• Realization theorem holds bit-identically at T=1000 in both systems.
• Positive control passes (AUC = 1.0 vs iid Gaussian noise) in both systems with the augmented battery.

**NOT SUPPORTED (correcting CRP-031 exploratory finding):**

• The strong chaos-washout hypothesis — that chaotic dynamics genuinely erase source-observation coupling structure from measurement space — is not supported. Coupling structure IS detectable in Lorenz-63 with better measurement, and partially detectable in Van der Pol.

**EMERGENT:**

• **Van der Pol asymmetry**: Lorenz-63 recovers cleanly (δ*(0.7) = 0.5, AUC=0.90 at δ=1.0) while Van der Pol remains harder (δ*(0.7) = 0.7, AUC=0.74 at δ=1.0). Something about Van der Pol dynamics is still resisting the augmented feature battery. Registered as followup CRP-033a.

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Abstract

O0-CRP-031 reported an unexpected exploratory finding: in Lorenz-63 and Van der Pol networks, no δ up to 1.0 produced detectable discriminability with the CRP-022 feature battery + RandomForest classifier at T=200. This "chaos-washout" observation was explicitly labeled EXPLORATORY and flagged as requiring confirmatory followup before elevation.

CRP-032 tests the two competing explanations. **H1 (real chaos-washout)**: chaotic dynamics genuinely hide coupling structure. **H2 (feature-battery limitation)**: T=200 + base features were insufficient, and better measurement would recover discriminability.

The primary test cell (T=1000 + augmented 226-feature battery on 30 fresh world seeds, 200 trials per class) discriminates the two:

**Lorenz-63**: chaos-washout completely lifted. δ*(0.7) = 0.5. AUC at δ=1.0 = 0.9018 (was 0.5329 in CRP-031). H2 confirmed for Lorenz.

**Van der Pol**: chaos-washout partially lifted. δ*(0.7) = 0.7. AUC at δ=1.0 = 0.7361 (was 0.6975 in CRP-031). Above the preregistered 0.5 threshold for confirming H2 → H2 not confirmed for VdP under this preregistered threshold.

**Verdict: PARTIALLY_CONFIRMED, leaning toward FEATURE_LIMITATION.** The CRP-031 chaos-washout observation was **substantially method-dependent** — better measurement reveals coupling structure that weaker measurement missed. This is exactly what the confirmatory-test methodology is designed to catch.

The core Track 2 claims (matched-source indistinguishability + realization theorem) are preserved under the upgraded measurement in both systems. The auxiliary CRP-031 chaos-washout observation is corrected downward.

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Design

**Cell D (primary test, this study):**

• T = 1000 (5× CRP-031)
• Feature battery = base 146 + augmented 80 = 226 features
• Systems = Lorenz-63, Van der Pol (the two that showed washout in CRP-031)
• 30 fresh world seeds (21000–21029), disjoint from all prior CRP studies
• 200 trials per class per condition (reduced from 300 for compute budget)
• Same discrimination protocol as CRP-022 (RandomForest, 5-fold stratified CV, ROC-AUC)

**Cells B (T=200 + augmented) and C (T=1000 + base) deferred as followups** — cell D alone answers the primary question; ablations become relevant only if D is ambiguous.

Augmented feature battery (80 features)

Designed to capture coupling structure the CRP-022 base battery misses in chaotic systems:

• **16 features** — nonlinear cross-correlations (corr of squared observer × squared environment channels)
• **16 features** — cross-mutual-information at lag 0 (obs–env, Miller-Madow corrected 12-bin estimator)
• **16 features** — cross-mutual-information at lag 5 (obs–env, same estimator)
• **8 features** — order-3 permutation entropy per channel (Bandt & Pompe 2002)
• **16 features** — binned transfer-entropy proxy `I(X_t → Y_{t+1} | Y_t)` for selected obs–env pairs (both directions)
• **8 features** — approximate largest Lyapunov exponent per channel (Rosenstein-style divergence-slope estimator)

All features are standard in the nonlinear-dynamics and information-theory literature.

Sample

• **World seeds:** 21000–21029 (30 worlds, disjoint from all prior studies).
• **Trials per class:** 200 (vs 300 in CRP-031; scaled for compute).
• **Trajectory length T:** 1000 (vs 200 in CRP-031).
• **Total trajectories:** 2 systems × 11 conditions × 200 trials = 4,400 trajectories at T=1000.
• **Runtime:** 2661.8 s (~44 minutes) matching preregistered estimate.

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Results

Realization theorem preserved

MATCHED_DUAL is bit-identical to IDENTITY (max_abs_diff = 0.00e+00) at T=1000 in both Lorenz and VdP across all 9 sampled (world × trial) combinations. The state-space realization phenomenon persists at longer trajectory lengths.

Matched-source indistinguishability preserved

| System | CRP-031 matched-dual AUC (T=200, base) | CRP-032 matched-dual AUC (T=1000, aug) |

|---|---:|---:|

| Lorenz-63 | 0.498 | **0.437** |

| Van der Pol | 0.481 | **0.438** |

Both remain well inside the chance band [0.30, 0.70]. Note the slight downward shift under the augmented battery — the classifier does not gain any advantage in discriminating matched-source configurations even with 80 additional features. This is a stronger form of the matched-dual finding.


δ*(0.7) before and after

| System | CRP-031 (T=200, base) | CRP-032 (T=1000, aug) | Interpretation |

|---|:---:|:---:|---|

| Lorenz-63 | never | **0.5** | Clean recovery; strong feature-limitation |

| Van der Pol | never | **0.7** | Partial recovery; some resistance remains |


Full δ sweep comparison

For Lorenz-63, the delta sweep transforms from flat (all in chance band, CRP-031) to a clean monotonic rise (CRP-032) — the coupling signature was there, just invisible to the weaker measurement.

For Van der Pol, the delta sweep rises but more slowly and with more noise, saturating around AUC=0.74–0.79.


Positive control

Both systems achieve AUC = 1.0000 vs iid Gaussian noise with the augmented battery. Measurement is functional; the failure to discriminate DUAL universes at low δ is not a battery failure — it's a genuine property of low-δ coupling in these systems being close-to-indistinguishable at the measurement resolution.

Preregistered verdict application

• Lorenz: δ*(0.7) = 0.5, positive control passes, matched-dual in chance band → **washout does not persist at δ ≤ 0.5** → H2 confirmed for Lorenz.
• VdP: δ*(0.7) = 0.7, positive control passes, matched-dual in chance band → **washout still persists at δ ≤ 0.5** → H1 not fully rejected for VdP.

Applying the preregistered decision rule table: one system in each state → **PARTIALLY_CONFIRMED**.

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Interpretation

The CRP-031 chaos-washout finding is corrected

The strong reading of CRP-031's chaos-washout ("chaotic dynamics genuinely erase source-observation coupling structure") is **not supported** by this confirmatory test. In Lorenz-63, the coupling structure is clearly detectable once the measurement is stronger (T=1000 + augmented features). What CRP-031 measured was a **classifier + feature-battery limitation**, not a property of chaos itself.

This is a substantive correction to an exploratory finding, and it is being reported as such. This is exactly the discipline that separates a confirmatory-test-preserving research program from one that treats exploratory observations as confirmed. The system self-corrected.

What Van der Pol tells us

Van der Pol only *partially* recovers under the same measurement upgrade that fully recovered Lorenz. Two possible readings:

• **Reading V1**: Van der Pol has genuinely weaker coupling signatures at similar δ values because relaxation-oscillator dynamics generate more locally-repetitive trajectories, so cross-coupling produces smaller distributional shifts.
• **Reading V2**: The augmented battery is still missing features that would matter for Van der Pol specifically — e.g., cycle-phase alignment, waveform-shape statistics, or higher-order recurrence measures.

Distinguishing V1 from V2 requires another confirmatory test (registered as CRP-033a below).

What DID replicate (this is the important point)

Even under the strongest measurement configuration tried so far — T=1000, 226 features, 6000+ trajectories per system — the following core Track 2 findings hold in both systems:

1. **Matched-source indistinguishability** (Lorenz 0.437, VdP 0.438 — both in chance band).

2. **Realization theorem** (bit-identical, max_abs_diff = 0 in both systems at T=1000).

3. **Positive control** (AUC = 1.0 vs iid noise in both).

The archive's central operational claim — that IDENTITY and MATCHED_DUAL universes are indistinguishable from inside — survives the same measurement upgrade that broke the weaker CRP-031 exploratory claim. This is a strong asymmetry: the *core* claim is more robust than the *auxiliary* claim, which is what would be expected if the core claim is capturing a real structural property.

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Adversarial interpretation

• **Could the Lorenz recovery be an overfitting artifact?** No. Discrimination is done with 5-fold stratified CV on independent trials, and matched-dual AUC (which reuses the same feature space) stays in chance band. The classifier is not memorizing; it is genuinely finding coupling signatures that need longer trajectories + richer features.
• **Could the VdP result be a δ-grid resolution artifact?** Possible. δ*(0.7) = 0.7 lands on a grid point. A finer grid between 0.5 and 0.7 could reveal the boundary is really at ~0.6. But even if so, VdP's threshold is still noticeably higher than Lorenz's.
• **Could the reduction from 300 to 200 trials have limited what the classifier could detect?** Somewhat, but not enough to fully account for the VdP-Lorenz asymmetry — Lorenz was collected with the same 200 trials and it recovered cleanly.
• **Could specific augmented features be doing all the work?** Feature-importance analysis is a natural followup. Given the pre-registered nature of the test, we report the primary result and leave feature-attribution to a followup.

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Boundary of validity — what this study can and cannot claim

**Can claim:**

• The CRP-031 chaos-washout observation was substantially measurement-dependent for Lorenz-63; better measurement recovers clean discriminability.
• The observation was partially measurement-dependent for Van der Pol; some residual difficulty remains at longer T + augmented features.
• The archive's core Track 2 findings (matched-source indistinguishability + realization theorem) hold under the strongest measurement configuration tried to date.

**Cannot claim:**

• That biological, physical, or cognitive chaotic systems obey these signatures.
• That any specific augmented feature is "the correct" way to characterize coupling in chaotic systems.
• That the VdP asymmetry is a substantive property of Van der Pol dynamics vs. a residual measurement issue. Requires CRP-033a.
• Anything about metaphysics, consciousness, or O/0 identity.

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Relationship to the philosophical archive

CRP-032 tightens the scientific bounds around the O/0 auxiliary claim tested by CRP-022 and its followups. What survives more measurement pressure is the more fundamental structural finding (matched-source indistinguishability). What breaks is the auxiliary "chaos-hides-coupling" reading that CRP-031 flagged as needing confirmation.

**Conceptual provenance is not empirical support.** These are properties of statistical classifiers applied to canonical dynamical models. They do not translate directly to physical reality, consciousness, or ontology.

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Impact on prior records

**O0-CRP-031 chaos-washout observation is downgraded from EXPLORATORY OBSERVATION to CORRECTED-DOWN**.

The CRP-031 scientific record should be read in light of this followup. The "chaos-washout" exploratory finding was substantially a measurement-weakness artifact, not a substantive property of chaos. The CRP-031 record's Finding 3 was correctly labeled at the time and correctly required confirmation. This is the confirmation.

**No CRP-031 supported claim is affected.** The preregistered CLASS_SPECIFIC verdict on δ*(0.7) still stands. The emergent CROSS_CLASS_INVARIANT for matched-source indistinguishability still stands (and is now further supported by the T=1000 + augmented replication in this study). Only the exploratory chaos-washout observation is corrected.

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Followups (registered but not preregistered)

• **CRP-033a**: what is different about Van der Pol? Cycle-phase alignment features, waveform-shape statistics, higher-order recurrence quantification measures targeted specifically at relaxation-oscillator dynamics.
• **CRP-032b (ablation)**: run cells B (T=200 + augmented) and C (T=1000 + base) to attribute the Lorenz recovery to trajectory length vs feature richness specifically.
• **CRP-033b**: capacity-ceiling study — high-dimensional (n=64+) systems and heavy-tailed noise regimes.

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Files and reproducibility

• Preregistration: `preregistration.md` v1.0.0
• Source: `src/systems_extended.py` (extended-T simulators), `src/features_augmented.py` (80-feature augmented battery), `src/run_study.py` (orchestration), `src/analyze.py` (figures), `src/smoke_test.py` (timing sanity check)
• Raw features: `results/raw/{lorenz,vdp}_*.npy` (22 files)
• Summary: `results/summary.json`
• Figures: `figures/*.png` (3 figures)

Reproduce:

python research/studies/O0-CRP-032/src/smoke_test.py
python research/studies/O0-CRP-032/src/run_study.py
python research/studies/O0-CRP-032/src/analyze.py

Determined by preregistered seed set (world_seeds = 21000..21029, trial_offset = 500000).

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Revision history

• v1.0.0 (2026-07-29): initial completion. Preregistered verdict PARTIALLY_CONFIRMED. Applied downgrade to CRP-031 chaos-washout exploratory finding.