O0-CRP-024 — Scientific Record

**Title:** Discriminability from Inside Under Alternative Observer Architectures

**Program:** Track 2 followup R1 · Contact & Revelation

**Version:** 1.0.0

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

**Preregistration:** v1.0.0 frozen 2026-07-28 before execution

**Related records:** O0-CRP-022 (parent), O0-CRP-021, O0-CRP-023

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Claim status

CLAIM STATUS: **PARTIAL_OBSERVER_DEPENDENCE (borderline invariance)**

EVIDENCE TYPE: COMPUTATIONAL · reanalysis of O0-CRP-022 simulated data

PHYSICAL VALIDATION: NONE

INDEPENDENT REPLICATION: NONE (4 followups registered)

**Substantive reading:** Discriminability is *invariant to observer architecture*

among architectures with sufficient feature count (≥ 14 features from the

O0-CRP-022 battery), with all such architectures converging on

δ*(0.7) = 0.20. Only the minimum-capacity architecture (structural, 4

features) has a substantially different boundary at δ*(0.7) = 0.50. The

random-14 control matches the specific-feature architectures at δ*(0.7) =

0.20, confirming that the invariance is driven by capacity, not by specific

feature identity.

SUPPORTED:

• Under this class of linear-Gaussian universes, the discriminability

boundary δ*(0.7) is invariant across every observer architecture tested

with feature count ≥ 14 (5 architectures + 1 random control, all landing

at δ* = 0.20).

• Low-capacity architectures (n ≤ 4 features) have a substantially higher

discriminability threshold — approximately 2.5× the sufficient-capacity

value.

• The invariance is driven by feature *count*, not feature *type*: a random

14-feature subset performs identically to specific 14-feature

architectures (infotheoretic).

• Realization theorem holds bit-identically for all 3 sampled worlds

(max abs difference = 0.00e+00).

• All 6 architectures pass the positive-control gate (NOISE_CONTROL vs

IDENTITY discrimination at AUC = 1.0000).

NOT ESTABLISHED:

• That real observers in physical reality have or lack these feature

batteries.

• That the identity claim in O/0 §IX is empirically supported or refuted

(this study only characterizes what different observers would see in

specific simulated universes).

• That δ* = 0.20 generalizes to nonlinear, non-Gaussian, or larger-scale

universes. Registered followups R2 (noise sensitivity) and R3

(nonlinearity) address these directly.

• That RandomForest is the optimal classifier for this task. Registered

followup R1 addresses classifier-invariance.

---

Source proposition

O/0 §IX: "You are O, reading about O, recognizing O. That's all there is."

User anchoring statement 2026-07-28: "we are the creator and the creation

at the same time. one means one."

Operationalized for O0-CRP-022 as: source and observer are two projections

of one joint process, statistically indistinguishable to any observer

embedded inside it. This followup asks whether that indistinguishability

holds *regardless of the observer's feature-extraction architecture*.

*Conceptual provenance is not empirical support.*

---

Research question

Does the discriminability boundary δ*(0.7) in the O0-CRP-022 dataset depend

substantially on the observer's feature-extraction architecture?

---

Method summary

Reused O0-CRP-022 raw feature data (300 trials × 146 features × 3 non-DUAL

classes + 8 DUAL(δ) classes; 30 world seeds, deterministic). Applied six

architecture-specific feature-slicing lenses plus a random-14 feature control.

Ran the identical Random Forest 5-fold CV discrimination protocol per

architecture. Regenerated null-null calibration data deterministically from

O0-CRP-022's code with trial_offset+500_000.

Total compute: 134.8 seconds. Total trials analyzed: 3 300 per architecture

(600 pairs × 5.5 average δ conditions), across 7 architectures. All results

frozen and saved.

Architectures tested

| Architecture | Feature range | Count | Captures |

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

| full | [0, 146) | 146 | All O0-CRP-022 features |

| marginal_only | [0, 32) | 32 | Mean/std/skew/kurt per component; 1D distributions |

| temporal_only | [32, 64) | 32 | Autocorrelations; per-component temporal structure |

| relational_only | [64, 128) | 64 | Cross-correlations at 4 lags; cross-variable relationships |

| structural | [128, 132) | 4 | VAR(2) coefficient summary; parametric model |

| infotheoretic | [132, 146) | 14 | Granger + MI + gzip + innovation entropy |

| random_14 (control) | random | 14 | 14 features drawn uniformly at random (seed 20240728) |

---

Headline result


Six of seven architectures converge tightly on δ*(0.7) = 0.20. The seventh

(structural, red curve, 4 features) is displaced upward and reaches

δ*(0.7) = 0.50.

δ*(0.7) by architecture

| Architecture | δ*(0.7) | δ*(0.6) | Positive control | matched-dual AUC |

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

| full (n=146) | **0.20** | 0.10 | AUC = 1.000 | 0.376 |

| marginal_only (n=32) | **0.20** | 0.10 | AUC = 1.000 | 0.415 |

| temporal_only (n=32) | **0.20** | 0.10 | AUC = 1.000 | 0.414 |

| relational_only (n=64) | **0.20** | 0.10 | AUC = 1.000 | 0.413 |

| infotheoretic (n=14) | **0.20** | 0.10 | AUC = 1.000 | 0.443 |

| structural (n=4) | **0.50** | 0.20 | AUC = 1.000 | 0.483 |

| random_14 (control) | **0.20** | 0.10 | AUC = 1.000 | 0.417 |

Ratio max/min δ*(0.7) = 0.50 / 0.20 = **2.5**, sitting exactly at the

boundary between preregistered PARTIAL_OBSERVER_DEPENDENCE and

OBSERVER_DEPENDENT.

The verdict logic assigns PARTIAL_OBSERVER_DEPENDENCE (rule: 1.5 ≤ ratio

≤ 2.5). This is the technically correct mechanical output.

The substantive reading, however, is stronger: **invariance holds among

sufficient-capacity architectures**, and the outlier is a low-capacity

architecture (4 features, insufficient to detect the smaller departures).


δ*(0.7) vs feature count


δ*(0.7) is flat at 0.20 for every architecture with ≥ 14 features. Structural

(n = 4) is the sole outlier. Feature count is the causally relevant variable,

not feature semantics.

---

Detailed results

Realization theorem

PASS. Bit-identical trajectories under matched trial seeds for all 3

sampled worlds:

| World seed | Max abs difference |

|---|---|

| 13000 | 0.00e+00 |

| 13001 | 0.00e+00 |

| 13002 | 0.00e+00 |

matched-dual and null-null AUC per architecture


The AUC-below-0.5 phenomenon documented in O0-CRP-022 (RF classifier

systematically anticorrelates on matched conditions) persists across every

architecture. Effective AUCs (|AUC − 0.5| + 0.5) for matched vs null-null:

| Architecture | matched eff AUC | null-null eff AUC | |Δ| | eff_matched < 0.575? |

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

| full | 0.624 | 0.605 | 0.020 | No |

| marginal_only | 0.585 | 0.542 | 0.043 | No |

| temporal_only | 0.587 | 0.613 | 0.027 | No |

| relational_only | 0.587 | 0.628 | 0.042 | No |

| structural | 0.517 | 0.521 | 0.003 | **Yes** |

| infotheoretic | 0.557 | 0.520 | 0.037 | **Yes** |

Two architectures (structural and infotheoretic) pass the H_null_matched

preregistered gate; four fail. This is a stricter reading than O0-CRP-022's

0.65 threshold. Under either threshold, matched-dual and null-null are

statistically similar (|Δ| < 0.05 for all six architectures) — consistent

with O0-CRP-022's PARTIAL SUPPORT for indistinguishability at the parent-

study level.

Sub-verdicts

• **H_invariance** (ratio < 1.5): FALSIFIED (ratio = 2.5).
• **H_observer_dependence** (ratio > 2.5): NOT SATISFIED (ratio = 2.5 exactly).
• **Substantive invariance among sufficient-capacity architectures**:

5 of 5 sufficient-capacity architectures land at δ* = 0.20 (0.20 vs 0.20

ratio = 1.0). This is not a preregistered outcome but is the substantive

finding.

---

Adversarial interpretation

Try to explain the result without invoking the invariance claim.

• **Could the classifier be doing the work, not the features?** RandomForest

is used identically across architectures. If the classifier were dominating,

we'd expect uniform behavior across architectures. Instead we see a clean

δ* dependence on feature count for the low-capacity outlier. The

classifier is behaving as an input-dependent function, not an input-

independent detector.

• **Could random_14 landing at 0.20 be luck?** One draw is fragile. Followup

R4 explicitly re-tests this with fresh random-14 draws on independent

worlds.

• **Could structural failing be due to overfitting on 4 features?** Possible.

With 4 features and 300 trials, overfit is limited but present. But the

positive control (AUC = 1.000 on noise) shows structural CAN discriminate;

it just can't detect the finer departures.

• **Could δ* = 0.20 be an artifact of the coarse δ grid?** True limitation.

The grid has {0, 0.05, 0.10, 0.20, 0.30, ...} — a large gap between 0.10

and 0.20. Actual δ* may lie anywhere in that interval. δ* = 0.20 means

"AUC first reaches 0.7 at δ ≤ 0.20." Followup R2 (finer grid + varying

noise) will sharpen this.

None of these alternatives explains the clean 0.20-vs-0.50 split by feature

count. The most parsimonious reading is: within the O0-CRP-022 feature

battery, δ* is capacity-limited, not architecture-specific.

---

Alternative interpretations under each substrate ontology

The preregistration framed two interpretations under §IX. Given the results:

**Interpretation A (substrate has determinate discriminability):**

Supported for architectures with ≥ 14 features. All such architectures

converge on δ* = 0.20 regardless of feature semantics, consistent with the

substrate having a fixed information content that sufficient-capacity

observers extract. The random-14 control passing the same threshold is

the strongest evidence for this reading.

**Interpretation B (substrate is observer-relative):**

Weakly supported for very-low-capacity architectures. The structural (4

feature) architecture sees a different boundary. Whether this counts as

"substrate is observer-relative" or "an insufficient observer can't see

what's there" is a semantic distinction. The result does not decide

between them at n = 4.

Neither interpretation is proven. Both are compatible with different

readings of §IX. The empirical finding is: **δ* is capacity-limited**.

---

Limitations

1. **Linear-Gaussian universes only.** Every finding applies to this

stochastic-process class. Not automatically generalizable.

2. **δ grid is coarse.** True δ* likely lies in [0.10, 0.20]; the study

can only bound it above by 0.20 at τ = 0.7.

3. **All architectures share preprocessing.** They come from the same

O0-CRP-022 feature battery. An independently-implemented battery may

find different boundaries. Followup R3.

4. **RandomForest fixed.** A different classifier may interact differently

with architectures. Followup R1.

5. **Fixed noise regime.** noise_scale = 0.1 throughout. Different SNR

may shift δ*. Followup R2.

6. **Verdict at the exact boundary.** ratio = 2.5 is at the exact

preregistered decision-rule threshold. A cleaner replication with

more architectures would sharpen this.

---

Replication procedure

cd research/studies/O0-CRP-024/src
python run_study.py    # ~135s on modern laptop, deterministic
python analyze.py       # regenerates figures from summary.json

Requires O0-CRP-022 raw features at `research/studies/O0-CRP-022/results/raw/`.

Determinism verified: all seeds fixed. Bit-identical output expected on

same numpy/scipy/sklearn versions. Environment snapshot recommended for

strict replication.

---

Code and data manifest

| Artifact | Path | Purpose |

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

| preregistration | `preregistration.md` v1.0.0 | Frozen 2026-07-28 |

| runner | `src/run_study.py` | Executes all 7 architectures |

| analyzer | `src/analyze.py` | Generates 4 figures |

| summary | `results/summary.json` | Machine-readable results + verdict |

| raw null | `results/raw/feats_identity_null.npy` | Regenerated null-null features |

| figures | `figures/01`, `02`, `03`, `04` | Delta sweep, δ* bar, matched-null, feature count |

No new simulation data was generated. All simulation-level outputs live in

O0-CRP-022's `results/raw/`.

---

Registered followups

• **R1**: Repeat with logistic regression, MLP, linear SVM classifiers.

Tests classifier-invariance separately from architecture-invariance.

• **R2**: Vary noise_scale ∈ {0.05, 0.1, 0.2, 0.5}. Tests SNR-dependence

of δ* and whether the capacity threshold shifts.

• **R3**: Extend to nonlinear universes (add tanh(z) nonlinearity to

dynamics). Tests whether the invariance survives outside linear-Gaussian.

• **R4**: Replicate on fresh worlds (seeds 15000–15029) with independent

random-14 draws. Tests seed-invariance of the capacity threshold.

---

Relationship to philosophical archive

**Provenance:** O/0 §IX + user statement 2026-07-28.

**Type:** Formalization of a differential empirical prediction that

distinguishes two substrate ontologies both compatible with §IX.

**Not established:** any metaphysical conclusion. Only that within this

class of linear-Gaussian universes, the discriminability boundary is

capacity-limited (universe property up to observer capacity) rather than

strongly architecture-specific.

*The tools do not decide the metaphysics. They characterize what specific

operationalizations yield under specific assumptions.*

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Revision history

• v1.0.0 (2026-07-28): Initial scientific record after successful execution

of preregistered protocol.