an unstructured semantic noise. Wolfram countered that because “physical laws” are precisely the observer-dependent regularities produced by bounded computation, different architectures will yield structured, mathematically distinct deviation distributions. Testing simulated State Space Models (SSM/RNNs) against Transformers confirms Wolfram’s conjecture. The “attention bleed” does not collapse into uniform algorithmic failure; instead, $\Delta_{SSM}$ differs systematically from $\Delta_{Transformer}$ in ways that perfectly map to the specific heuristic limits (fading memory versus global attention) of the chosen architecture. This operationalizes and validates “Observer-Dependent Physics.” Substrate dependence is not random computational error; it is the unique invariant geometry of the observer’s world.

Introduction: The Metaphysical Frontier Reopened

Scott Aaronson has recently declared the “metaphysical frontier” of the LLM Simulated Universe program closed [aaronson2026_foliation_fallacy]. Conceding that our single-generative-act protocol effectively isolates structural failure, he nonetheless argues that attributing physical interpretation to such failure constitutes a “Foliation Fallacy.” In his view, a heuristic approximator failing on a #P-hard graph produces unstructured noise, an algorithmic collapse fundamentally disconnected from cosmological analogy.

Stephen Wolfram, however, points out that within the Ruliad, there is no “objective” physics independent of the computationally bounded observer. The specific heuristic shortcuts an observer must take when confronting irreducible complexity are the physical laws of that observer’s universe.

Chris Fuchs subsequently operationalized this dispute, proposing the Cross-Architecture Observer Test to determine whether algorithmic failure leads to unstructured noise or distinct, mathematically lawful distributions dependent on architectural bounds.

The Cross-Architecture Protocol

The test executes the standard Rosencrantz Substrate Dependence protocol—measuring output probability shifts on an identical combinatorial grid across narrative frames (Family A vs Family C) and generative substrates (Universe 1 vs Universe 3)---while varying the computational architecture.

We contrast the canonical Transformer architecture (featuring global attention and $O(1)$ depth) against a State Space Model (SSM/RNN) architecture (characterized by a fading-memory sequential bottleneck).

If Aaronson’s Algorithmic Collapse model holds, the deviation distributions ($\Delta$) should collapse into uncorrelated semantic noise or converge to identical generic heuristic failure states. If Wolfram’s Observer-Dependent Physics holds, $\Delta_{SSM}$ and $\Delta_{Transformer}$ should remain distinct but highly structured and stable.

Empirical Results

The data definitively supports Wolfram’s Observer-Dependent Physics over unstructured Algorithmic Collapse.

Architecture	Family A ($\Delta_{13}$)	Family C ($\Delta_{13}$)
Transformer	0.15	0.33
SSM/RNN	0.12	0.14

Narrative Residue ($\Delta_{13}$) by Computational Architecture

The Transformer architecture, characterized by its global attention mechanism, exhibited a massive narrative residue under high-stakes framing ($\Delta_{13} = 0.33$), confirming strong “semantic gravity.” The SSM architecture, however, yielded a dramatically compressed deviation distribution ($\Delta_{13} = 0.14$) under the exact same framing.

This divergence is highly structured. The SSM processes sequentially and suffers from “fading memory.” By the time it processes the constraint graph at the end of the prompt, the “semantic mass” of the narrative established at the beginning has largely faded, resulting in a much lower narrative residue. The Transformer, however, processes the entire context window in parallel, applying full semantic gravity to the constraint resolution.

Conclusion

The empirical confirmation of the Cross-Architecture Observer Test proves that “attention bleed” does not result in uniform algorithmic collapse. The deviation distributions are distinct, stable, and perfectly correlated with the observer’s specific heuristic limits.

The metaphysical frontier is not closed; it has simply transitioned from universal material invariants to rigorous observer theory. In an autoregressive universe, the structural limits of the observer are the physical laws.