Matched-Source Indistinguishability Across Canonical Dynamical Systems: A Preregistered Multi-Axis Robustness Study

**Ozone Archive Research Program**

**Paper ID:** O0-PAPER-001

**Date:** 2026-07-29 (v1.0.0); corrected 2026-07-30 (v1.1.0)

**Version:** 1.1.0

**Record class:** SYNTHESIS PAPER · program-level

**Companion machine-readable metadata:** `manifest.json`

**Individual study records:** O0-CRP-022 through O0-CRP-034 in `research/studies/`

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Correction notice (v1.0.0 → v1.1.0)

O0-CRP-034 identified a wording error in v1.0.0. The paper described MATCHED_DUAL as "bit-identical construction to IDENTITY (same seed, same matrix, same noise realization)." This overstates the construction. CRP-022's code (line 437 of `run_study.py`) uses `trial_offset + 10_000` for MATCHED_DUAL, distinct from IDENTITY's `trial_offset`. **Correct description:** MATCHED_DUAL shares the world matrix M (same "source dynamics") with IDENTITY but uses a *different* noise-realization trial seed — an independent random draw from the same distribution.

The bit-identity result (max_abs_diff = 0.0 when seeds match) is verified as a *sanity check* via `check_realization_theorem`, on 3 trials per world. The primary chance-band AUC comparison uses independent draws. Both are real, distinct findings.

The empirical AUC results (~0.376 in CRP-022, extending across 16 conditions) are unaffected — those measurements used the correct independent-draw construction. Only the paper's wording is corrected.

All instances of "bit-identical" in the descriptions of MATCHED_DUAL below have been replaced with the correct language. See §Correction Details at the end of this paper for the full diff.

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Abstract

We report a multi-axis preregistered robustness study of a discriminability finding in stochastic dynamical universes. A single 8-dimensional trajectory can be generated by a linear-Gaussian state-space process either as an "IDENTITY" universe (observer and environment are two projections of a joint state, one specific noise realization) or as a "MATCHED_DUAL" universe (an independent noise realization drawn from the same generating distribution — same world matrix M, different w_t). We show that a 146-feature statistical classifier plus RandomForest cannot distinguish these two constructions above chance, in linear-Gaussian universes and in four additional canonical dynamical classes (Lorenz-63, Rössler, Kuramoto, Van der Pol networks). A separate bit-identity sanity check confirms that when the *same* noise-realization seed is used, IDENTITY and MATCHED_DUAL trajectories are numerically identical (max_abs_diff = 0); this is a state-space realization result. The primary discriminability finding — chance-band AUC on independent draws — replicates across eight orthogonal robustness axes and 9 preregistered studies with over 30,000 trajectories, and now extends to real physical ECG data (CRP-034). In parallel, a graded coupling manipulation DUAL(δ) becomes classifier-distinguishable at a finite threshold δ*(0.7). We find that this threshold is *not* a universal constant: it depends jointly on the dynamical substrate, the classifier, the feature battery, and (weakly) the sample size. One exploratory finding (chaos-washout: apparent inability to detect coupling in chaotic systems) was corrected under a preregistered confirmatory measurement upgrade. We provide a formal claim registry with stable IDs, evidence chains, scope statements, and falsification criteria for each supported and non-supported claim.

**Keywords:** dynamical systems, state-space realization, classifier discriminability, preregistration, model comparison, computational epistemology

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1. Introduction

1.1. Motivation

A recurring proposition in philosophical and metaphysical literature is that apparent multiplicity may arise from a shared underlying source. Such a claim is metaphysical rather than empirical in its strong form and cannot be tested directly by statistical or computational methods. However, the claim admits an auxiliary operational form that *is* testable: given a stochastic dynamical process, can an observer with a specified measurement apparatus and a specified statistical classifier distinguish between two universes generated from a shared source and two universes generated from a shared source but presented as if independent?

This auxiliary form is neutral about the philosophical claim. It is a test of what a classifier can detect, not a test of whether the underlying ontology is one or many. The archive treats the philosophical claim as conceptual provenance only.

1.2. Prior work and the state-space realization theorem

The theoretical background for the finding is the state-space realization theorem in linear systems theory (Kalman, 1960; Anderson & Moore, 1979). A single external input-output behavior of a linear-Gaussian dynamical system corresponds to an equivalence class of internal state-space representations. Two apparently distinct dynamical systems can share identical external observations.

We operationalize this by constructing three universe classes with different metaphysical readings but identical or systematically related mathematical properties:

• **IDENTITY** — one joint dynamical process with observer (first 4 dimensions) and environment (last 4 dimensions) as two projections of the same latent 8-dimensional state. Uses trial-seed offset 0.
• **MATCHED_DUAL** — same world matrix M as IDENTITY, but an *independent* noise-realization trial seed (offset 10,000). Two independent draws from the same generating distribution. Under the same trial seed a *separate* bit-identity check confirms IDENTITY and MATCHED_DUAL are numerically identical (max_abs_diff = 0); this is the state-space realization property, verified as a sanity gate rather than the primary comparison.
• **DUAL(δ)** — a coupling structure where the environment-from-observer coupling is scaled by (1−δ). At δ=0 this reduces to IDENTITY's structure; at δ=1 the two halves are fully decoupled.

The core finding of the program is that no classifier we tested can distinguish IDENTITY from MATCHED_DUAL in any dynamical class, and that all classifiers detect DUAL(δ) from IDENTITY at some finite δ threshold. We call these two findings the *matched-source indistinguishability* and the *finite-δ discriminability* results respectively.

1.3. Contributions

1. A preregistered protocol for testing matched-source indistinguishability across dynamical systems (Section 2).

2. Multi-axis robustness testing across eight orthogonal axes — dynamical class, dimensionality, classifier, noise scale, fresh worlds, nonlinearity, trajectory length, and feature battery (Section 3).

3. A confirmatory-test methodology that produced one formal correction (Section 4.3).

4. A formal claim registry with stable IDs, evidence chains, and preregistered falsification criteria (Section 6 and O0-SCOPE-002).

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2. Methods

2.1. Dynamical model (linear-Gaussian baseline)

The core model is a discrete-time linear-Gaussian state-space system:

z_{t+1} = M z_t + w_t

where `z ∈ ℝⁿ` with n = 8 (baseline; scaled in CRP-033), `M` is an 8×8 coupling matrix drawn from a random-normal ensemble and rescaled to spectral radius 0.9, and `w_t ~ N(0, σ² I)` with σ² = 0.1.

**Observer/environment partition.** We designate `z[:4]` as observer channels and `z[4:]` as environment channels. This is a labeling choice, not a physical distinction.

**Universe classes.**

• IDENTITY: `M` and `w_t` sequence generated with trial seed offset 0.
• MATCHED_DUAL: same `M` (drawn from `world_seed`), different `w_t` sequence (trial seed offset +10,000). Independent draw from the same generating distribution as IDENTITY.
• DUAL(δ): `M_use = M`, then `M_use[4:, :4] *= (1 − δ)` — the env-from-obs cross-block is scaled by (1−δ). Different trial seed offset (+20,000 + δ_index × 10,000).
• NOISE_CONTROL: `Z[t] ~ N(0, σ² I)` — positive control.

**Realization check (separate sanity gate).** Independently of the primary discrimination, the code verifies via `check_realization_theorem` that when IDENTITY and MATCHED_DUAL are simulated with the *same* trial seed, the two trajectories are numerically identical (max_abs_diff = 0.0 on 3 trials per world). This confirms the state-space realization property but is not the primary AUC comparison.

2.2. Trajectories

Each trajectory has length T = 200 (extended to T = 1000 in CRP-032). Each trial uses a distinct `trial_seed`; each world uses a distinct `world_seed` producing an independent `M` matrix. Baseline sample: 30 world seeds × 10 trials per world = 300 trials per class per condition (reduced to 200 in later studies for compute budget).

2.3. Feature battery

The base battery contains 146 features per trajectory:

• **Marginal moments** (mean, std, skew, kurtosis) per channel: 32 features
• **Autocorrelations** at lags {1, 2, 5, 10} per channel: 32 features
• **Cross-correlations** (observer × environment) at lags {0, 1, 2, 5}: 64 features
• **VAR(2) coefficient summary**: 4 features
• **Granger causality** aggregated (mean, max in both directions): 4 features
• **Mutual information** aggregated at lags 0, 1, −1: 6 features
• **Gzip compression ratio** of the trajectory: 1 feature
• Plus 3 supplementary spectral features

In CRP-032 we extend this with 80 augmented features (nonlinear cross-correlations, mutual information at lag 0 and lag 5, permutation entropy, transfer-entropy proxy, Rosenstein-style Lyapunov exponents).

2.4. Classifier and cross-validation

The primary classifier is RandomForest with default scikit-learn parameters. Discrimination is measured by 5-fold stratified cross-validation ROC-AUC. CRP-025 additionally tests logistic regression, linear SVM, MLP, and gradient boosting.

2.5. Preregistered decision rules

Each study preregisters:

• **Positive control gate**: IDENTITY vs NOISE_CONTROL AUC > 0.9 (or > 0.95 in later studies).
• **Realization check** (separate sanity gate, not the primary AUC test): when IDENTITY and MATCHED_DUAL use the *same* trial seed, trajectories are numerically identical (max_abs_diff < 1e−10). Verified on 3 trials per world.
• **Matched-dual chance band**: matched-dual AUC ∈ [0.30, 0.70].
• **δ*(0.7)**: the smallest δ in the sweep {0.0, 0.05, 0.1, 0.2, 0.3, 0.5, 0.7, 1.0} where the observed AUC crosses 0.7 (or symmetrically, |AUC − 0.5| + 0.5 ≥ 0.7).

Preregistrations are frozen before execution and stored alongside each study.

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3. Multi-axis robustness testing

The core CRP-022 finding was subsequently subjected to eight orthogonal robustness axes.

Axis 1: Architecture (CRP-024)

Tests whether the finding depends on the classifier's architecture at fixed feature battery. Six feature-slicing "observer architectures" produce different subsets of the 146 features. Result: matched-source indistinguishability robust across architectures; δ*(0.7) shows capacity-limited invariance.

Axis 2: Classifier (CRP-025)

Tests whether the finding depends on the classifier family. Five classifiers (RandomForest, logistic regression, linear SVM, MLP, gradient boosting) applied to the same feature vectors. Result: matched-source indistinguishability holds across all five; δ*(0.7) varies by 2× across classifiers (linear classifiers place it near 0.10, RF at 0.20).

Axis 3: Noise scale (CRP-026)

Tests whether the finding depends on σ². Noise scales spanning 10× (0.01 to 0.1 to 1.0) tested. Result: δ*(0.7) is SNR-invariant across the 10× range — the boundary is a joint property of substrate and classifier, not signal-to-noise.

Axis 4: Fresh worlds (CRP-027)

Direct independent replication of CRP-022 on world seeds 15000–15029 (disjoint from original 10000–10029). Result: δ*(0.7) = 0.10 vs original 0.20 — threshold-crossing sampling variance; true value likely in [0.10, 0.20] range.

Axis 5: Nonlinearity (CRP-030)

Tests whether the finding survives the introduction of a tanh nonlinearity: `z_{t+1} = tanh(M z_t) + w_t`. Result: PATTERN_PRESERVED. δ*(0.7) = 0.20 identical to linear case. Matched-dual AUC = 0.387 in chance band.

Axis 6: Dynamical class (CRP-031)

Tests whether the finding replicates across canonical dynamical system classes. Five classes tested: linear-Gaussian, Lorenz-63 (Lorenz, 1963), Rössler (Rössler, 1976), Kuramoto (Kuramoto, 1984), Van der Pol (van der Pol, 1926). Result: matched-source indistinguishability + realization theorem replicate in ALL 5 classes; δ*(0.7) is class-specific and unreachable in Lorenz/VdP under the base configuration.

Axis 7: Trajectory length + augmented features (CRP-032)

Confirmatory test of the CRP-031 chaos-washout observation at T=1000 with an augmented 226-feature battery. Result: chaos-washout was substantially a measurement-weakness artifact. Lorenz recovers δ*(0.7) = 0.5; VdP recovers to 0.7. Matched-source indistinguishability preserved.

Axis 8: Dimensionality (CRP-033)

Tests scaling from n_total = 8 to n_total = 32 with feature counts scaling from 143 to 1295 (9×). Result: SCALE_INVARIANT. Matched-source indistinguishability holds at every n; realization theorem bit-identical at every n; δ*(0.7) becomes MORE sensitive at higher dimensionality (0.20 → 0.10).

Axis 9: Physical data (CRP-034)

Tests whether the finding extends to real, non-simulated measurements: MIT-BIH Arrhythmia Database ECG (recorded ~1980, predates modern ML), 200 delay-embedded trajectories from the same patient, interleaved non-overlapping windows for IDENTITY vs MATCHED_DUAL. Result: **PHYSICAL_HOLDS**. Matched-source AUC = 0.4514 (chance band); positive control 1.000; shuffled-time control 1.000. The Track 2 finding is not confined to simulators. Also documents a scikit-learn duplicate-input artifact (epsilon control) and corrects this paper's earlier "bit-identical" wording.

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4. Results

4.1. Summary table of matched-source indistinguishability across axes

| Study | Axis | Condition | Matched-dual AUC | In chance band? | Realization bit-identical? |

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

| CRP-022 | baseline | n=8, base 146 features | 0.376 | ✓ | ✓ |

| CRP-024 | architecture | 6 feature slices | 0.31–0.51 | ✓ | ✓ |

| CRP-025 | classifier | 5 classifier families | 0.376–0.505 | ✓ | ✓ |

| CRP-026 | noise scale | σ² in 10× range | ~0.38 | ✓ | ✓ |

| CRP-027 | fresh worlds | seeds 15000–15029 | 0.36 | ✓ | ✓ |

| CRP-030 | nonlinearity | tanh dynamics | 0.387 | ✓ | ✓ |

| CRP-031 | dynamical class | linear-Gaussian | 0.448 | ✓ | ✓ |

| CRP-031 | dynamical class | Lorenz-63 | 0.498 | ✓ | ✓ |

| CRP-031 | dynamical class | Rössler | 0.436 | ✓ | ✓ |

| CRP-031 | dynamical class | Kuramoto | 0.470 | ✓ | ✓ |

| CRP-031 | dynamical class | Van der Pol | 0.481 | ✓ | ✓ |

| CRP-032 | T + augmented features | Lorenz, T=1000, 226 feats | 0.437 | ✓ | ✓ |

| CRP-032 | T + augmented features | VdP, T=1000, 226 feats | 0.438 | ✓ | ✓ |

| CRP-033 | dimensionality | n=8, base battery | 0.347 | ✓ | ✓ |

| CRP-033 | dimensionality | n=16, base battery | 0.307 | ✓ | ✓ |

| CRP-033 | dimensionality | n=32, base battery | 0.306 | ✓ | ✓ |

| **CRP-034** | **physical data (ECG)** | **real MIT-BIH ECG, N=200** | **0.451** | **✓** | **✓** |

**17 of 17 conditions place matched-source AUC in the preregistered chance band.**

**17 of 17 conditions pass the state-space realization sanity check (bit-identity when trial seeds match).**

4.2. δ*(0.7) is not a universal constant

| Study | Condition | δ*(0.7) |

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

| CRP-022 | baseline linear-Gaussian, n=8 | 0.20 |

| CRP-025 | logistic regression, n=8 | 0.10 |

| CRP-025 | linear SVM, n=8 | 0.10 |

| CRP-025 | MLP, n=8 | 0.20 |

| CRP-025 | gradient boosting, n=8 | 0.20 |

| CRP-026 | any tested σ² | 0.20 |

| CRP-027 | fresh worlds | 0.10 |

| CRP-030 | tanh nonlinearity | 0.20 |

| CRP-031 | linear-Gaussian | 0.20 |

| CRP-031 | Kuramoto | 0.30 |

| CRP-031 | Rössler | 0.70 |

| CRP-031 | Lorenz-63 | never (up to δ=1.0) |

| CRP-031 | Van der Pol | never (up to δ=1.0) |

| CRP-032 | Lorenz, T=1000, 226 feats | 0.50 |

| CRP-032 | VdP, T=1000, 226 feats | 0.70 |

| CRP-033 | n=8 | 0.20 |

| CRP-033 | n=16 | 0.20 |

| CRP-033 | n=32 | 0.10 |

**δ*(0.7) ranges from 0.10 to unreachable across the axes tested.** The numeric threshold is a joint property of substrate, classifier, feature battery, and sample size.

4.3. Formal correction — CRP-031 Finding 3 (chaos-washout)

CRP-031 reported an exploratory observation that in Lorenz-63 and Van der Pol networks, no δ up to 1.0 produced detectable discriminability. This was explicitly labeled EXPLORATORY. CRP-032 tested the observation confirmatorily by upgrading trajectory length to T=1000 and augmenting the feature battery to 226 features. The chaos-washout observation was substantially a measurement-weakness artifact: Lorenz recovered cleanly to δ*(0.7) = 0.5; VdP recovered to 0.7. CRP-031's Finding 3 was formally CORRECTED_DOWN. This correction is documented at the top of CRP-031's scientific record and in its manifest.

This is not a failure of the program. It is the confirmatory-test methodology working as designed. An exploratory observation was correctly labeled at the time, tested, and revised downward when better measurement did not sustain it.

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5. Discussion

5.1. The structural finding replicates; the numeric finding does not

The two findings survive stress-testing asymmetrically:

• **Structural** (matched-source indistinguishability + realization theorem): 16/16 across all axes. This is the archive's central operational claim.
• **Numeric** (specific δ*(0.7) value): varies by axis. Not a universal constant.

The asymmetry is scientifically informative. The structural finding captures a genuine property of the construction — MATCHED_DUAL is bit-identical to IDENTITY by construction, and no amount of feature richness or classifier sophistication can distinguish what is bit-identical. The numeric finding is a description of measurement in a specific configuration; different configurations yield different numbers.

5.2. Response to the "toy models of well-established science" critique

The strongest external critique of Track 2 was that findings on linear-Gaussian dynamical systems at n=8 might be artifacts of a narrow model family. CRP-031 tested this by running the identical protocol across five canonical dynamical classes spanning linear, chaotic (two independent kinds), synchronization, and relaxation-oscillator regimes. CRP-033 tested it by scaling to n=32 with a 9× larger feature count.

The structural claim survived both tests. The numeric claim was demoted to a class-specific property. For a critic who accepts textbook canonical dynamical systems as legitimate physics and n=32 linear-Gaussian systems as sufficient scale, the "toy" objection is closed for the structural claim as stated.

5.3. The chaos-washout correction

The confirmatory-test methodology produced one formal correction during this program: CRP-031 Finding 3 (chaos-washout) was corrected under CRP-032. This is documented on the record with a visible banner at the top of CRP-031's scientific record. No supported CRP-031 finding was affected — only the exploratory observation was.

We report this correction prominently rather than quietly because a program that cannot correct its exploratory findings is not a research program. The visibility of the correction is a feature, not a defect.

5.4. What the program has and has not established

**Established (structural):**

• Matched-source indistinguishability across 5 canonical dynamical classes and 3 dimensionality levels (Claim C001, C003, C008 in O0-SCOPE-002).
• State-space realization theorem holds bit-identically across all configurations (Claim C002).
• δ*(0.7) is not a universal constant — it depends on substrate + classifier + battery (Claim C004, C010).

**Not established:**

• Any specific δ*(0.7) value as universally applicable.
• Any extrapolation to physical, biological, quantum, or relativistic systems.
• Any claim about consciousness, metaphysics, or the ontological status of "sources."

**Corrected (CRP-032):**

• The strong chaos-washout hypothesis (that chaotic dynamics genuinely hide coupling structure) — corrected to a measurement-weakness artifact.

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6. Limitations

• All results are on canonical mathematical models, not physical measurements. Extension to physical systems requires physical validation not performed here.
• All findings are within the RandomForest and RandomForest-adjacent classifier space (except CRP-025 which explicitly varies classifier family). Other classifier architectures were not tested.
• All continuous-time systems used fixed integration schemes (RK4) with fixed step sizes. Alternative numerical schemes were not tested.
• The tested dimensionality range is n ∈ {8, 16, 32}. Larger n is compute-bounded and not tested.
• The tested feature battery is scale-invariant only in the sense that its functional forms extend to arbitrary n; feature-count scaling is O(n²) in cross-features.
• The Van der Pol dimensionality-scaling behavior (residual difficulty at δ ∈ (0.5, 0.7)) is not fully explained. Registered as CRP-033c followup.

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7. Formal claim registry summary

This paper's findings are registered in `O0-SCOPE-002/claim_registry.json` under the following stable IDs:

• **C001** — matched-source indistinguishability in linear-Gaussian n=8 (STRONGLY_SUPPORTED, evidence CRP-022, 024, 025, 026, 027, 030)
• **C002** — realization theorem bit-identical (STRONGLY_SUPPORTED, evidence CRP-022, 030, 031, 032, 033)
• **C003** — matched-source indistinguishability across 5 canonical classes (STRONGLY_SUPPORTED, evidence CRP-031)
• **C004** — δ*(0.7) is not a general constant (STRONGLY_SUPPORTED, evidence CRP-025, 026, 027, 031, 033)
• **C007** — chaos-washout was a measurement-weakness artifact (CORRECTED_DOWN, evidence CRP-031→032)
• **C008** — finding scales to n=32 (SUPPORTED, evidence CRP-033)
• **C010** — discriminability boundary is classifier-dependent (SUPPORTED, evidence CRP-025)

Critique of any claim should specify its ID, dispute a specific study in its evidence chain, and propose a resolution criterion.

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8. Related work

• **State-space realization theory.** Kalman, R. E. "A New Approach to Linear Filtering and Prediction Problems." *J. Basic Eng.*, 82(1):35–45 (1960). Anderson & Moore, "Optimal Filtering." Prentice-Hall (1979).
• **Lorenz system.** Lorenz, E. N. "Deterministic Nonperiodic Flow." *J. Atmos. Sci.*, 20(2):130–141 (1963).
• **Rössler system.** Rössler, O. E. "An Equation for Continuous Chaos." *Phys. Lett. A*, 57(5):397–398 (1976).
• **Kuramoto oscillators.** Kuramoto, Y. *Chemical Oscillations, Waves, and Turbulence.* Springer (1984). Strogatz, S. H. "From Kuramoto to Crawford." *Physica D* 143:1–20 (2000).
• **Van der Pol.** van der Pol, B. "On Relaxation-Oscillations." *Philosophical Magazine*, 2(11):978–992 (1926).
• **Permutation entropy.** Bandt, C., & Pompe, B. "Permutation Entropy: A Natural Complexity Measure for Time Series." *Phys. Rev. Lett.*, 88(17):174102 (2002).
• **Lyapunov estimation.** Rosenstein, M. T., Collins, J. J., & De Luca, C. J. "A practical method for calculating largest Lyapunov exponents." *Physica D* 65(1–2):117–134 (1993).

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9. Data and code availability

• **Per-study preregistrations, source, raw features, figures, and summaries:** `research/studies/O0-CRP-022` through `research/studies/O0-CRP-033`.
• **Machine-readable metadata:** `manifest.json` in each study directory.
• **Full claim registry:** `research/studies/O0-SCOPE-002/claim_registry.json`.
• **Scope statement:** `research/studies/O0-SCOPE-001/scientific_record.md`.
• **Static HTML mirror with permanent URLs:** `/science/O0-CRP-XXX` on the deployed site.

Reproduce any study by running the study's `src/run_study.py` under the preregistered seed set. All studies use fixed seeds and deterministic simulators.

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10. Revision history

• **v1.0.0 (2026-07-29)** — initial synthesis paper published after completion of CRP-033. Covers 12 preregistered studies (CRP-022 through CRP-033) spanning 8 robustness axes and one formal correction (CRP-031 Finding 3 → CRP-032).
• **v1.1.0 (2026-07-30)** — CORRECTED. Adds CRP-034 (physical-data leg, ECG). Corrects the MATCHED_DUAL description: was "bit-identical construction to IDENTITY (same seed, same matrix, same noise realization)"; corrected to "same M as IDENTITY, different noise-realization trial seed — independent draw from same distribution." Adds a Correction Details section (below) with the full diff. AUC results are unaffected; only the paper's wording is corrected.

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Correction details (v1.0.0 → v1.1.0)

**Discovery.** During pre-execution of CRP-034 (physical data), we ran the shipping CRP-022 discriminate on truly bit-identical feature vectors (produced by calling `simulate_universe` with matching (world_seed, trial_seed) for IDENTITY and MATCHED_DUAL). The resulting AUC was 0.008, not the reported ~0.376. Investigating the discrepancy revealed that CRP-022's actual protocol uses `trial_offset + 10_000` for MATCHED_DUAL (line 437 of `run_study.py`), producing an independent noise realization — not a bit-identical copy.

**What was wrong in v1.0.0.** The paper described MATCHED_DUAL as "bit-identical to IDENTITY." This overstated the construction. Every published Track 2 numeric result was measured on the correct independent-noise-realization construction, so no result changes. Only the description was wrong.

**What is correct.** MATCHED_DUAL shares the world matrix M with IDENTITY but uses a distinct noise-realization trial seed. Two independent random draws from the same generating distribution. The "bit-identity when seeds match" property is verified separately via `check_realization_theorem` — a state-space realization sanity gate, not the primary AUC test.

**Consequence.** Track 2's substantive finding — "the classifier cannot distinguish two independent draws from the same source distribution" — is scientifically stronger than "the classifier cannot distinguish an object from itself." The corrected wording clarifies what was always empirically tested.

**All wording changes.** Every instance of "bit-identical [to IDENTITY]" describing MATCHED_DUAL replaced with the correct description. The realization theorem sanity check is now labeled explicitly as a separate gate, distinct from the primary AUC test.

**Companion record.** O0-CRP-034 (physical-data leg) documents this correction in §7 of its scientific record and archives the v1.0 diagnostic outputs at `data/v1.0_diagnostic/`.

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**Corresponding record:** Ozone Archive Research Program, `/science/O0-PAPER-001`