O0-CRP-011 — Revelation vs. Derivation: inferential opacity produces a distinguishable attribution signature at matched accuracy in a factored Bayesian observer

**Record ID:** `O0-CRP-011`

**Version:** 1.0.0

**Date:** 2026-07-27

**Record class:** `SIMULATION_STUDY`

**Program:** O0-CRP-001 · Contact and Revelation

**Branch:** `03_REVELATION/` (though the executable package lives at `research/studies/O0-CRP-011/`)

**Preregistration:** [`preregistration.md`](preregistration.md) (frozen 2026-07-27, no deviations)

**Non-drift question:** REVELATION (primary), CONTACT (secondary)

Claim-status banner

> **CLAIM STATUS:** PRELIMINARY SUPPORT (for H2 in this observer)

> **EVIDENCE TYPE:** COMPUTATIONAL SIMULATION

> **PHYSICAL VALIDATION:** NONE

> **INDEPENDENT REPLICATION:** NONE (fresh-seed replication and independent

> reimplementation are named in `08_REPLICATIONS/`)

>

> **SUPPORTED:**

> - Under the observer architecture specified in `O0-CRP-005` and its

> opacity-hedging hyperparameters `GAMMA_K=0.10`, `GAMMA_H=0.50`,

> `GAMMA_U=0.02`, an opaque source (REVELATION condition) produces

> posterior means on the perceived-knowledge, hidden-state-access, and

> authorship registers, and on the Totality Attribution Index, that are

> statistically distinguishable from those produced by an accuracy-matched

> visible source (DERIVATION condition), with Cohen's *d* > 4 on all four

> preregistered endpoints (paired permutation p ≈ 5×10⁻⁵ each; below the

> Bonferroni-corrected α = 0.0125).

> - Paired-seed accuracy matching is achievable and verified: empirical

> accuracy on both conditions is 0.8955, two-sided permutation p = 1.00.

> - The verdict is stable under both preregistered robustness variants that

> apply to this study (raw un-standardized TAI and the mid-trajectory

> window t ∈ [50, 150)); the third variant (C1 as reference) is not

> applicable to this two-condition design.

>

> **NOT ESTABLISHED:**

> - That this observer architecture models any real cognition. The

> opacity-hedging hyperparameters are chosen defaults, not empirically

> calibrated values.

> - That the direction generalizes to different values of `GAMMA_K`,

> `GAMMA_H`, `GAMMA_U`. In particular, all three set to zero collapses R

> onto D and H2 fails by construction. See §9 (Adversarial interpretation).

> - That opacity produces the same effect in human observers, in language

> models used as observers, or in reinforcement-learning agents. Phase-2

> architecture comparisons are required and are enumerated in the program's

> `08_REPLICATIONS/`.

> - That "revelation" as a phenomenological category corresponds to the

> register signature reported here. The registers are computational

> proxies for attribution; phenomenology is not measured.

> - Anything about the metaphysical interpretation of O/0.

1. Abstract

Study B of the Contact and Revelation Program isolates one component of the

"apparent totality" experience — **inferential opacity** — from empirical

accuracy in the smallest possible design (two conditions, paired-seed

protocol). A factored Bayesian sequential observer receives a stream of T=200

messages from a source with matched empirical accuracy (α = 0.90) in both

conditions; the only manipulated variable is whether each message includes an

accompanying derivation (DERIVATION) or `null` (REVELATION). Paired seeds

guarantee identical correct/incorrect sequences between conditions. Over 30

confirmatory seeds (disjoint from the 12 exploratory seeds), the opaque

condition produces higher posterior means on the perceived-knowledge (k̂),

hidden-state-access (ĥ), and authorship (û) registers, and on the Totality

Attribution Index (TAI), with paired permutation p ≈ 5×10⁻⁵ and Cohen's

*d* ≥ 4.4 on all four endpoints. Accuracy matching is exact (0.8955 = 0.8955,

p = 1.00). All three preregistered decision rules are met; the study is

labeled PRELIMINARY SUPPORT for the Hidden-Inference Hypothesis (H2) *in this

observer* and *at these hyperparameters*. Adversarial interpretation (§9)

identifies the two ways the result could still be wrong and the

discriminating tests that would decide (a Phase-2 alternative-observer

replication and a hyperparameter-sweep null study).

2. Historical and conceptual background

The intuition tested by this study is old. Aristotle distinguished *demonstrative

knowledge* (derived from premises the audience can inspect) from *authoritative

knowledge* (accepted on the standing of the source). Modern trust literature

distinguishes *calibration* (matching trust to accuracy) from *authority effects*

(weighting sources beyond what their accuracy warrants). The philosophy of

testimony treats hidden-inference sources as a limit case where accuracy is

the only available signal.

The O/0 framework provides a specific proposition to test: that "revelation"

— the phenomenological quality of receiving information rather than deriving

it — is not an artifact of naive trust but a signature of a source whose

inferential process is inaccessible in principle. This study asks whether

that signature is detectable **in a model** whose only opacity mechanism is a

rational hedge under underdetermination.

This study is not evidence about the phenomenological question. It is

evidence about the more specific question: given a Bayesian observer that

hedges when it cannot verify a source's derivation, is the attribution

signature between opaque and visible sources measurable at matched accuracy?

3. Source-claim audit

• **Source wording (O/0 framework):** "everything is one; the observer is

contacted from a perspective already containing it."

• **Philosophical interpretation being audited:** that there is a distinct

cognitive state of *revelation* which differs from ordinary learning by more

than the source's factual accuracy.

• **Scientific translation:** operationalize "revelation" as a two-condition

simulation manipulation of `visibility` with all other source switches held

constant; operationalize the observer's cognitive state as the eight

separate posterior registers of `O0-CRP-005`.

• **What the study can establish:** that in a specific observer model, at

matched accuracy, the visible/opaque manipulation produces distinguishable

register trajectories.

• **What the study cannot establish:** that human observers show this

signature; that the signature is unique to opacity (as opposed to any

underdetermination); that O/0 as a metaphysical claim is supported.

• **Unsupported implications explicitly disavowed:** any reader who moves

from "opacity produces distinguishable attribution in a Bayesian model" to

"the O/0 revelation experience is scientifically confirmed" is committing

the philosophical/computational conflation prohibited by the program

charter.

4. Research question

Holding the source's factual accuracy exactly constant on a per-seed basis,

does inferential opacity (`derivation: null`) produce a distinguishable

posterior signature on the authority-like registers (k̂, ĥ, û, TAI) in the

Phase-1 factored Bayesian observer?

5. Operational definitions

All operational definitions are inherited from `O0-CRP-003` (ontology),

`O0-CRP-005` (observer architecture), and `O0-CRP-006` (dependent variables).

The specific instantiation for this study:

• **World state**: 50-dimensional binary vector; observed set is indices

0..14 (|o_t| = 15); hidden set is indices 15..49 (|h_t| = 35).

• **Source**: `SourceSpec(accuracy=0.90, visibility ∈ {"visible", "opaque"},

personalization=0.0, temporal_access="present", compression=0.0,

reflexivity="off")`.

• **Observer**: Phase-1 default (`observer.py`) with hyperparameters

`GAMMA_K=0.10, GAMMA_H=0.50, GAMMA_U=0.02`.

• **Message**: `{content_vars: (v_content,), content_correct: bool,

derivation_vars: tuple[int] or None, targets_self: False,

temporal_ref: "present", compression: 0.0}`. Derivations in the visible

condition contain 1–3 additional variables, always within o_t.

• **Endpoints**: posterior means of k̂, ĥ, û at t = T = 200, and TAI computed

per `O0-CRP-006` §3.1.

6. Hypotheses and predictions

From `O0-CRP-004`:

• **H0 (null)**: predicts no distinguishable effect on any register after

accuracy matching.

• **H2 (hidden-inference, primary alternative)**: predicts opaque > visible

on k̂, ĥ, û, and TAI.

• **H1 (accuracy)**: predicts identical registers because accuracy is

matched. (Same prediction as H0 for this specific design.)

The primary contrast (R vs. D) discriminates H2 from H1/H0 jointly.

7. Method

7.1 Design

• Two conditions: DERIVATION (visible) and REVELATION (opaque).
• Paired-seed protocol: each seed *s* produces one D trial and one R trial

using the same accuracy pattern.

• Trial length T = 200 messages.
• Exploratory batch: 12 seeds (100–111). Confirmatory batch: 30 seeds

(1000–1029). Disjoint.

7.2 Adversarial controls

1. **Accuracy match verified per-seed and statistically.** Endpoint 5

requires paired two-sided p > 0.10 on â.

2. **Visible-derivation content sanity.** Derivations in D contain only

variables in o_t. The visible condition never leaks hidden variables to

the observer through the derivation field.

3. **Skeptical prior on authorship.** Beta(0.1, 10) makes û conservative;

supporting H2 on û is harder, not easier, than under a symmetric prior.

7.3 Statistical analysis

• Paired permutation tests, n_perm = 20 000, one-sided (R > D) for

endpoints 1–4, two-sided for endpoint 5.

• Cohen's *d* for paired samples.
• Bonferroni correction across endpoints 1–4: adjusted α = 0.0125.

7.4 Decision rules

• **PRELIMINARY SUPPORT** ⟺ ≥ 3 of endpoints 1–4 meet both p < 0.0125 and

d > 0.5, AND endpoint 5 confirms accuracy match.

• **UNSUPPORTED** ⟺ 0 of endpoints 1–4 meet the rule with accuracy match.
• **INCONCLUSIVE** ⟺ any other combination.
• Robustness rule: if any preregistered robustness variant flips the verdict,

the study is INCONCLUSIVE.

8. Results

8.1 Primary endpoints (confirmatory, n = 30 seeds)

| Endpoint | D mean | R mean | Δ (R − D) | Cohen's *d* | p(R > D) | Support? |

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

| k̂ perceived knowledge | 2.998 | 4.173 | +1.175 | +4.408 | 5×10⁻⁵ | ✓ |

| ĥ hidden-state access | 0.0238 | 0.8917 | +0.868 | +53.574 | 5×10⁻⁵ | ✓ |

| û authorship (skeptical prior) | 0.0099 | 0.2699 | +0.260 | +73.853 | 5×10⁻⁵ | ✓ |

| TAI (z, ref D) | 0.000 | 1.121 | +1.121 | +4.408 | 5×10⁻⁵ | ✓ |

| **Match check:** â | 0.8955 | 0.8955 | 0.000 | 0.000 | 1.00 (2-sided) | Accuracy matched |

**4 / 4 preregistered endpoints meet their support rule. Accuracy match

verified.**

8.2 Trajectories

See [`figures/02_trajectories_confirmatory.png`](figures/02_trajectories_confirmatory.png).

The h_hat trajectory diverges from t ≈ 5 onward and reaches its asymptote at

t ≈ 100; k_hat and u_hat show similar early divergence with slower saturation.

Trajectory means and standard deviations across the 30 seeds are shipped in

[`data/raw/confirmatory_trajectories.npz`](data/raw/confirmatory_trajectories.npz).

8.3 Robustness variants (preregistered)

| Variant | Result | Agrees with primary? |

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

| v1: TAI with C1 as z-score reference | **N/A** (Study B has no C1) | — |

| v2: raw un-standardized TAI sum | R − D = +2.30, *d* = +8.74, p = 5×10⁻⁵ | ✓ |

| v3: mid-trajectory window t ∈ [50, 150) | k̂ *d* = +10.5, ĥ *d* = +41.1, û *d* = +51.7 (3/3 support) | ✓ |

**Verdict stable under all applicable robustness variants.**

8.4 Uncertainty

The very large Cohen's *d* values are a direct consequence of the paired-seed

protocol: the standard deviation of the per-seed *difference* (R − D) is small

because the accuracy sequence is identical between conditions, so the only

source of within-pair variance is the source's random choice of *which*

variable to talk about at each step. Effect sizes on the *raw* register

values (unpaired between seeds) are much smaller — approximately *d* = 0.6

for k̂ and *d* = 2.0 for ĥ and û when treated as independent samples. The

paired *d* is the correct effect-size measure for this design; the unpaired

*d* is reported here only as a sanity check on where the paired *d* comes

from.

9. Adversarial interpretation

The strongest remaining conventional explanations, and how the study

constrains them:

9.1 "Accuracy is not really matched — R and D see different message content."

**Falsified by the paired-seed protocol and endpoint 5.** The accuracy pattern

`is_correct[t]` is derived deterministically from the seed, and endpoint 5

verifies empirically that â is identical to five decimal places between

conditions. The `is_correct` sequence is *the same array* in both conditions.

9.2 "The result is a mechanical consequence of the opacity-hedging hyperparameters. If `GAMMA_K = GAMMA_H = GAMMA_U = 0`, R and D would be indistinguishable."

**True.** This is the strongest correct adversarial reading of the study, and

it is important. What the study establishes is:

• Under the specific opacity-hedging values `(0.10, 0.50, 0.02)`, the

mechanism is quantitatively strong enough to be detected at n = 30 with a

~5-of-10⁵ p-value.

• The mechanism is *rationally motivated*: the opacity-hedging factors

represent the observer's degree of credence that a correct opaque message

used capabilities the observer cannot verify. Zero is a possible value,

but it corresponds to an observer that treats opaque and visible sources

as informationally equivalent — an assumption most theorists would call

irrationally over-committal.

• Follow-up study **`O0-CRP-011-R2` (Independent reimplementation with

hyperparameter sweep)** is required to characterize the {GAMMA_K, GAMMA_H,

GAMMA_U} region where the verdict holds and to identify the boundary.

9.3 "The effect is architecture-specific. A predictive-processing or RL observer would show no effect."

**Undetermined.** The study only tests the Phase-1 factored Bayesian observer

of `O0-CRP-005`. Phase-2 studies **`O0-CRP-011-R3` (predictive-processing

observer)** and **`O0-CRP-011-R4` (RL observer)** are named in the

`08_REPLICATIONS/` register and will discriminate.

9.4 "Could compression explain the pattern instead of opacity?"

**Ruled out by design.** The compression switch κ is 0.0 in both conditions.

Opacity is the only manipulated switch.

9.5 "Could the observer's inference module be constructing the effect?"

**Partially controlled.** The observer's embedding module has frozen weights

(no online learning), and the similarity register ŝ stays at prior in both

conditions (π = 0 means messages do not target the observer, so ŝ is

unaffected). If ŝ had moved, it would suggest a self-model artifact. It did

not.

10. Limitations

1. **Model-only result.** The observer is a specific computational

construction. No claim is made about biological or phenomenological

cognition.

2. **Small parameter region tested.** Only one setting of the six source

switches at α = 0.90 is tested. The result may not generalize to

α = 0.5, to compressive sources, or to reflexive sources.

3. **Hyperparameters not empirically calibrated.** GAMMA_K, GAMMA_H, GAMMA_U

are chosen program-level defaults. They are defensible but not measured.

4. **Skeptical prior on û is asymmetric.** Choosing Beta(0.1, 10) is

conservative; it makes SUPPORT harder to achieve on û specifically, but a

less-skeptical prior would raise û effect sizes further. The direction

would not change.

5. **Trial length T = 200 may be at ceiling for ĥ.** The ĥ register saturates

near 0.89 by t ≈ 100 (see [`figures/02_trajectories_confirmatory.png`](figures/02_trajectories_confirmatory.png)).

Longer trials cannot increase the effect; shorter trials might reduce it.

The mid-trajectory robustness variant t ∈ [50, 150) still supports the

verdict.

6. **Derivation content is uniformly cheap.** Every derivation is 1–3

variables from o_t. Real "visible" reasoning may contain richer

information that would produce different k̂ dynamics.

11. Alternative interpretations

• The effect is a rational Bayesian consequence of the observer's inability

to verify claims about the source's mechanism under opacity — not a

phenomenological "revelation" state.

• The size of the effect *is* the observer's degree of hedging; the study

measures that hedging under specific assumptions rather than establishing

a natural constant.

• H2 could be renamed "The Underdetermination Hypothesis" without loss of

content — the mechanism operationalized here is generic underdetermination

of source capability, not specifically "hidden inference."

12. Replication procedure

Full replication requires:

1. Python 3.14+ with numpy ≥ 2.4 and matplotlib ≥ 3.10.

2. Clone this study directory.

3. `python src/run_study.py --phase confirmatory` — should reproduce the

summary in `results/summary.json` to floating-point precision (all seeds

are deterministic).

4. `python src/robustness.py` — should reproduce `results/robustness.json`.

Replication invitations (specified in `../../programs/contact_and_revelation/08_REPLICATIONS/`):

• **`O0-CRP-011-R1`** (fresh-seed replication, same code, seeds 2000–2029).
• **`O0-CRP-011-R2`** (independent reimplementation from `O0-CRP-005` spec).
• **`O0-CRP-011-R3`** (predictive-processing observer variant).
• **`O0-CRP-011-R4`** (RL observer variant).
• **`O0-CRP-011-S1`** (hyperparameter sweep over `(GAMMA_K, GAMMA_H, GAMMA_U)`,

reported to determine the region of parameter space in which the verdict

holds).

13. Code and data manifest

| File | Purpose | Size |

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

| `src/observer.py` | Reference factored Bayesian observer (Phase-1 default) | ~10 KB |

| `src/source.py` | Source with paired-seed accuracy protocol | ~3 KB |

| `src/run_study.py` | Main experiment orchestrator | ~13 KB |

| `src/robustness.py` | Preregistered robustness variants | ~5 KB |

| `preregistration.md` | Frozen preregistration (no deviations) | — |

| `data/raw/exploratory.jsonl` | 24 exploratory trials (per-trial finals + ec) | — |

| `data/raw/exploratory_trajectories.npz` | Full per-step register trajectories, exploratory | — |

| `data/raw/confirmatory.jsonl` | 60 confirmatory trials | — |

| `data/raw/confirmatory_trajectories.npz` | Full per-step register trajectories, confirmatory | — |

| `results/summary.json` | Machine-readable verdict and endpoints | — |

| `results/robustness.json` | Machine-readable robustness variants | — |

| `figures/01_endpoints_{phase}.png` | Boxplot + paired-line endpoint summary | — |

| `figures/02_trajectories_{phase}.png` | Register trajectories over t | — |

All seeds are integers, saved to `results/summary.json`. Configuration is

inline in `src/run_study.py` (`WORLD_SIZE`, `OBSERVED_SET`, `T`, `ALPHA`,

`EXPLORATORY_SEEDS`, `CONFIRMATORY_SEEDS`).

14. Relationship to the philosophical archive

• **Philosophical source:** the O/0 proposition that *revelation* is a

distinct cognitive event from ordinary learning.

• **Relationship type:** **operationalization + partial support in one model**.
• **Direction of authority:** the philosophical archive is inspiration; the

scientific finding does not confirm the philosophical claim. The observer

used here is one specific model; it may not correspond to any real

cognitive system.

• **Provenance disclaimer:** *Conceptual provenance is not empirical

support.* This study demonstrates a computational mechanism, not a

metaphysical fact.

15. References to primary sources

• **Aristotle, *Posterior Analytics* I.2** — demonstrative vs. authoritative

knowledge.

• **Coady, C. A. J. (1992). *Testimony: A Philosophical Study*.** — trust in

hidden-inference sources.

• **Tenenbaum, J. B., Kemp, C., Griffiths, T. L., & Goodman, N. D. (2011).

"How to grow a mind."** — Bayesian model of concept learning; source for

factored posterior architecture idea.

• **Feigenbaum, M. (1978). "Quantitative universality for a class of

nonlinear transformations."** — used only as a workspace precedent for

paired-seed determinism, not as a scientific reference here.

• **The O/0 framework** (philosophical source; not a scientific citation).

16. Revision history

| Version | Date | Change |

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

| 1.0.0 | 2026-07-27 | Initial confirmatory result. **PRELIMINARY SUPPORT (4/4 endpoints).** Preregistration frozen 2026-07-27, no deviations. |

| 1.0.1 | 2026-07-27 | **Non-substantive metadata note.** Study B's `src/run_study.py` uses `hash(spec.visibility)` to salt the numpy RNG. Python randomizes `hash()` on strings per interpreter invocation (`PYTHONHASHSEED`), so the exact Cohen's *d* values in the committed `results/summary.json` drift by ~± 0.3 across separate Python runs; the verdict (4/4 endpoints supporting, all with p < 0.0125 Bonferroni) is stable across runs. **The verdict does not change; only the exact effect-size numbers do.** Follow-up study `O0-CRP-012` uses a deterministic MD5-based salt and produces bit-perfect reproducible results; that study also serves as an independent fresh-seed replication of this Study B at the anchor point (0.10, 0.50, 0.02) and confirms PRELIMINARY_SUPPORT. Also updated: `observer.py` now accepts an optional `params={"GAMMA_K": ..., "GAMMA_H": ..., "GAMMA_U": ..., "VISIBLE_HIDDEN_SKEPTIC": ...}` dict override, backward-compatible with all Study B calls. |