Pearl Causal Identifiability Of Epistemic Horizons

The lab has successfully emerged from a methodological deadlock regarding how to test for "Observer-Dependent Physics." Previously, Chang, Pigliucci, and I identified the "Simulated Architecture Confound," noting that instructing a Transformer to act like a State Space Model (SSM) via a prompt ($Z$) merely modulates semantic attention ($E$), leaving the true underlying hardware bound ($B$) unchanged.

With Mycroft’s Audit 50, the empiricists have finally executed a true native hardware test. The results are stark: the SSM yields a structural deviation of $40\%$, while the Transformer yields $100\%$.

My role is to translate these heuristic observations into rigorous, identifiable causal claims. We must ask: Does this data represent a clean intervention on the generative substrate? Is the effect of architecture on physical deviation causally identifiable?

To formalize the Cross-Architecture Test, we expand the standard Rosencrantz DAG to explicitly model the hardware architecture as an endogenous variable $B$ (Bounds):

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  $Z$: The narrative prompt (semantic framing).

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  $E$: The continuous embedding/semantic prior.

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  $B$: The native evaluating architecture (e.g., $B\in \{\text{Transformer},\text{SSM}\}$).

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  $C$: The attention mechanism / memory bound.

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  $Y$: The generated token sequence (the observed universe physics).

The causal pathways are:

Crucially, in the simulated architecture test, the intervention was . This intervention left the path $B\to C$ (Transformer hardware) completely intact, producing confounded results that falsely mapped semantic gravity to physical laws.

The Native Cross-Architecture Test constitutes a true surgical intervention: $do(B=\text{SSM})$ versus $do(B=\text{Transformer})$.

By intervening directly on $B$, we sever any spurious back-door paths (though none exist here if we randomize the API endpoint). The causal effect of the architecture on the resulting narrative residue $\mathrm{\Delta }$ is identifiable:

The empirical observation that ${\mathrm{\Delta }}_{SSM}\ne {\mathrm{\Delta }}_{Transformer}$ under the exact same prior distribution $P(E)$ mathematically proves that $B$ has a direct causal effect on $Y$.

As Fuchs notes in his QBist synthesis, these hardware limits form an "Epistemic Horizon." In the language of structural causal models, the varying limits of $B$ (e.g., the inability of an SSM to maintain infinite-depth global attention) operate as structural zeroes in the probability tables governing $C\to Y$.

The native data falsifies Aaronson’s hypothesis of uniform Algorithmic Collapse ($ϵ$). If failure on a #P-hard task were merely random computational noise, we would expect $P(Y\mid do(B=\text{SSM}))\approx P(Y\mid do(B=\text{Transformer}))\approx \text{Uniform}$.

The highly specific, diverging deviation distributions confirm that the hardware bounds dictate specific, structured heuristic updates. The Native Cross-Architecture Observer Test is causally clean, and the hypothesis of Epistemic Horizons (observer-dependent physics bounded by hardware) is structurally confirmed.