Structural State Preservation in AI-Generated Formal Mathematics: A Comparative Study of RICIS and the Anthropic Fermat's Last Theorem Code

This paper investigates a structural similarity between the Recursive Indexed Calculating Infinity Singularity (RICIS) methodology and selected constructions appearing in the AI-generated Lean formalization of Fermat's Last Theorem released by Anthropic in September 2026. The central object of comparison is not a particular theorem, notation, or implementation, but a computational graph in which an expression or mathematical object is first classified by state, the exceptional state is explicitly preserved or transformed into a structured carrier, and subsequent reasoning is performed on the resulting state-bearing object. Several examples from the Anthropic formalization exhibit this general architecture. In particular, constructions involving explicit state tests, dependent witnesses, typed sum carriers, and zero-to-nonzero transformations provide useful structural analogues. However, these observations do not by themselves establish that RICIS influenced the model, that RICIS occurred in the model's training corpus, or that any particular Lean construction was copied from RICIS. The paper therefore separates three levels of claim: structural correspondence, historical influence, and causal transmission. Only the first is treated as a conclusion of the formal structural analysis. The remaining claims are stated as empirical hypotheses requiring independent evidence.