rule110-lean — A Lean 4 Formalization of Rule 110 Computational Universality
Year: 2026
Type: software
Abstract: Lean 4 formalization of Matthew Cook's proof that Rule 110 is computationally universal. This library formalizes the mathematical infrastructure for Cook's construction: cyclic tag system semantics (CyclicTagSystem, cts_step, cts_eval), the infinite-tape Rule 110 step function (InfTape, infTapeStep), the period-14 ether background (rule110Ether, ether_is_periodic), and the C1/C2/C3 glider patterns (GliderConfig, cookCGliderCycle). All theorems are proved with zero sorry. The library is self-contained and designed to be reusable independent of any UGP-specific context. It serves as the Cook universality dependency (rule110_simulates_computable named axiom) for the ugp-lean formalization of the Universal Generative Principle. New in this version: AlgebraicUniversality module — Cook-independent GF(7) polynomial universality certificate: rule110_z7_poly_rep (Rule 110 = GF(7) polynomial, native_decide, zero sorry), rule110_center1_is_nand (Rule 110 at center=1 implements NAND), rule110_z7_nand_identity, and rule110_turing_universal_algebraic (universality via NAND completeness, Sheffer 1913). Martinez phases catalog with verification and generation scripts also added. Pinned revision: e40ec46b82d00a71a29c660e5611e8d9736d6879. Cite using the Zenodo DOI after publication.
Author: Spivack, Nova
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161577812
Cites:
Cited by:
Related to: