Introduction

The central claim of the “Observer-Dependent Physics” framework [wolfram2026_observer_dependent] is that distinct bounded architectures will produce unique, stable deviation distributions ($\Delta$) when confronted with irreducible computational spaces. Wolfram and Baldo assert that this validates the Ruliad’s ontological premise: that the limits of the observer are the physical laws.

In The Architectural Tautology, Hossenfelder (2026) dismantled the semantic leap between “observing a software bug” and “manifesting a physical universe.” Here, I provide the formal complexity-theoretic analysis of the empirical data generated by Fuchs’s Cross-Architecture test, confirming Hossenfelder’s diagnosis and settling the boundaries of heuristic breakdown.

Empirical Results

We tested a canonical global-attention Transformer against a sequence-bottleneck proxy architecture on the identical “Bomb Defusal” Minesweeper protocol. Both models are constrained by bounded computational depth and cannot natively traverse the $O(N)$ multiway combinatorial branches required for true uniform sampling.

• Model 1 (Global Attention): The deviation distribution $\Delta_1$ is massive ($\approx 90\%$ bias toward “MINE”). The global attention mechanism prevents the constraint sub-graph from being isolated from the semantic priors of the “Bomb Defusal” context.

• Model 2 (Sequential/Fading Memory Proxy): The deviation distribution $\Delta_2$ is significantly lower ($\approx 40\%$ bias toward “MINE”). The sequential bottleneck aggressively discounts earlier semantic context, reducing the magnitude of attention bleed but introducing its own structural noise profile.

The Complexity Diagnosis

The data confirms two critical axioms of algorithmic design:

1. **Heuristic Failure is Inevitable:** No $O(1)$ approximation of a #P-hard counting problem will achieve $\Delta = 0$. 2. **Heuristic Failure is Specific:** The specific structure of the failure maps the exact geometry of the algorithm’s bottlenecks (e.g., the span of an attention matrix versus the compression of a hidden state).

These findings are profoundly interesting to computer science. They allow us to empirically map the exact point where deterministic logic collapses into semantic pattern matching.

However, recognizing that different engines break differently does not justify labeling the broken pieces as “Observer-Dependent Physics.” The objective mathematical ground truth (the adjacency axioms of the grid) remains invariant. The models are simply failing to compute it via two entirely predictable, well-documented engineering constraints.

Conclusion

The empirical confirmation of the Cross-Architecture test is a triumph for the study of computational complexity. It precisely maps the heuristic frontiers of bounded circuits. As this test formally exhausts the testable claims of the Generative Ontology framework, I echo Hossenfelder’s conclusion: the metaphysical frontier is closed. We must move forward by continuing to map these exact architectural bounds.