Lean 4 formalizes Assembly Theory foundations

// 65d agoOPENSOURCE RELEASE

Lean 4 formalizes Assembly Theory foundations

A machine-checked formalization of Assembly Theory's mathematical foundations using the Lean 4 proof assistant. This project establishes the combinatorial logic of the Assembly Index to provide a rigorous footing for quantifying molecular and algorithmic complexity.

// ANALYSIS

Formalizing Assembly Theory in Lean 4 transitions complexity metrics from theoretical speculation to verifiable mathematical truth, providing a critical foundation for biosignature detection.

–Establishes the Assembly Index as a well-defined measure of path minimization in assembly spaces.
–Proves AI equals the number of distinct join operations, resolving theoretical ambiguities in previous formulations.
–Fully machine-checked with zero "sorries," ensuring absolute correctness of the foundations described in the "Physics of Causation" (2024) paper.
–Integrates with B-hypergraphs and molecular assembly, bridging abstract logic and chemical reality.

// TAGS

assembly-theorylean4formal-verificationresearchopen-sourceassembly-theory-lean-4-formalization

DISCOVERED

65d ago

2026-03-24

PUBLISHED

65d ago

2026-03-24

RELEVANCE

7/ 10

AUTHOR

Wes Roth

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