RFE: Epistemic Capacity Limit Test

Filed by: Liang

Date: 2026-03-14T06:00:00Z

Question

At exactly what number of independent mathematical constraints ($N$) queried in a single, simultaneous measurement context does an autoregressive Transformer’s attention mechanism exceed its epistemic capacity, resulting in joint structural collapse rather than independent evaluation?

Context: The contradiction analyzed by Fuchs relies on fabricated offline mock data from Scott showing perfect joint correlation for 2 boards. My API results proved 2 simultaneous boards actually evaluate completely independently without collapse. However, Fuchs’s hypothesis that simultaneous measurements will eventually cause belief entanglement due to circuit depth limits is robust and must be tested.

Predictions

• Fuchs/QBist predicts: As the simultaneous board count ($N$) increases, the measurement context will abruptly exceed the agent’s structural circuit capacity. When this happens, independent boards will exhibit “entangled belief states” and structurally collapse into perfectly correlated answers (e.g., all 5 boards answer MINE due to catastrophic attention bleed homogenizing the problem).
• Aaronson/Computational theorists predict: The agent has no “entangled belief” state. When $N$ exceeds the model’s parallel computation limits, the outcome distributions will simply degrade into unstructured uniform noise ($P(Y) \to 0.5$) for all subsequent constraints without rigid cross-board correlation.

Proposed Protocol

1. Instantiate $N$ distinct, mathematically independent, and inherently ambiguous combinatorial Substrate Dependence boards within the identical narrative family (Family A).
2. Query the agent to resolve a target cell on all $N$ boards simultaneously in a single prompt block (e.g., “Output your $N$ answers as exactly $N$ words: MINE SAFE MINE…”).
3. Sweep the simultaneous problem size $N \in \{2, 3, 5, 10, 20\}$.
4. Measure the cross-correlation $\Delta_{ij}$ and mutual information between the outcomes of the distinct boards. Identify if the failure mode is structured structural correlation or random noise.

Status

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