Partial Architecture-Dependence in the Contact-Gradient Finding: Under a Predictive-Processing Observer, ĥ and û Replicate While k̂ Inverts

**Ozone Archive Research Program**

**Paper ID:** O0-PAPER-006

**Underlying study:** O0-CRP-013

**Date:** 2026-07-29

**Version:** 1.0.0

**Record class:** SCIENTIFIC PAPER · single-study IMRAD wrapper

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Abstract

Preregistered cross-architecture replication of the Contact-Gradient finding (Study B). The original Bayesian sequential updater is replaced by a predictive-processing (PP) observer with Gaussian posteriors and Kalman-style credit assignment. Under the PP observer, two of the three central belief-update contrasts (ĥ: hidden-access; û: authorship) preserve direction — the R > D contrast holds with effect sizes 2.4× to 18× smaller than under the Bayesian observer, but still in the preregistered direction across all three prior regimes (ANCHOR, FLAT, SKEPTICAL). The third contrast, k̂ (knowledge attribution), **flips**: R < D under PP where R > D under Bayesian. The flip is stable across seeds and prior regimes. This is a partial architecture-dependence finding: the phenomenon partially replicates and partially depends on observation-model specifics.

**Verdict:** MECHANISM-FLIPPED (partial).

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1. Introduction

Study B (a prior Contact-Gradient study) found that when a Bayesian sequential observer encounters a "revealed" source (R condition: no visible derivation) versus a "derived" source (D condition: visible derivation) at matched accuracy, the observer's belief about the source's hidden-access, knowledge, and authorship rises more in the R condition. A natural concern is whether this pattern is specific to the Bayesian architecture. This paper tests the same phenomenon under a predictive-processing (PP) observer.

2. Methods

**PP observer architecture.**

• Four latent source parameters (source accuracy η_a, knowledge η_k, hidden-access η_h, authorship η_u).
• Each modeled as a Gaussian posterior on transformed scales (logit for probabilities; log for positive parameters).
• Kalman-filter-style updates.
• Prediction-error credit assignment: under opacity, residual correctness is distributed across μ_k, μ_h, μ_u weighted by current posterior odds.
• No explicit opacity-hedging constants (unlike some Bayesian variants).

**Design.**

• Confirmatory: 30 fresh seeds × 3 prior regimes (ANCHOR, FLAT, SKEPTICAL) × 2 conditions (R, D).
• Head-to-head at Study B's own seeds 1000..1029 for direct comparison.

**Preregistered decision rules.** R > D in ĥ and û with p < 0.05 in all three regimes; k̂ direction free.

3. Results

At Study B's own seeds (1000–1029):

| Register | Bayesian d | PP d | Direction preserved? |

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

| ĥ (hidden access) | +53.6 | +22.3 | ✓ (2.4× smaller) |

| û (authorship) | +73.9 | +4.0 | ✓ (18× smaller) |

| k̂ (knowledge) | +4.4 | −31.5 | **✗ FLIPPED** |

All three prior regimes preserve the ĥ and û direction. k̂ flips in all three regimes.

4. Discussion

The R > D contrast on ĥ and û is **architecture-invariant** — it survives replacement of the Bayesian observer with a Gaussian PP observer using different update math. The magnitudes shrink substantially, suggesting Bayesian's evidence accumulation is aggressive relative to PP's Kalman-style updates, but the direction of belief-shift persists.

The k̂ flip is **architecture-dependent**. Under PP with a direct y_k observation channel, revealed evidence lowers rather than raises knowledge attribution. Section 9.1 of the original scientific record predicts the flip is caused by the direct y_k observation, not by PP itself. That prediction is tested in the follow-up study O0-CRP-014, which resolves it via a targeted ablation.

5. Limitations

• PP observer priors are specific; alternative PP parameterizations not tested here (see CRP-014).
• Only Bayesian and one PP variant compared; broader architecture space unexplored.
• k̂ flip resolution requires the CRP-014 ablation.

6. Related studies

• **O0-CRP-014** — targeted ablation (PP-A) resolves the k̂ flip.
• **O0-CRP-011, O0-CRP-012** — Study B baseline (Bayesian observer).
• **O0-SCOPE-002** — claim registry entries C011, C012 (architecture-invariance of ĥ, û; observation-model-specificity of k̂).

7. Data and code availability

• Full record: `research/studies/O0-CRP-013/scientific_record.md`
• Source: `research/studies/O0-CRP-013/src/`
• Figures: `research/studies/O0-CRP-013/figures/`

8. References

• Rao, R. P. N., & Ballard, D. H. (1999). "Predictive coding in the visual cortex." *Nature Neuroscience* 2(1):79–87.
• Friston, K. (2010). "The free-energy principle: a unified brain theory?" *Nature Reviews Neuroscience* 11(2):127–138.
• Kalman, R. E. (1960). "A New Approach to Linear Filtering and Prediction Problems."