The Engine Was Never About Chess: A Certified Universal Exact Solver by Retrograde Folding

One axiom. One operation. Zero free parameters. A Smithian Fold campaign solved ~1 billion chess endgame positions exactly by retrograde folding, zero error against the Syzygy oracle. This paper proves what that success means: the engine was never about chess. Retrograde folding is a domain-agnostic exact solver. Give it any finite state space, a move generator, and a terminal rule, and it returns the exact game-theoretic value of every state — win, loss, draw, with exact distance — and certifies itself against an independent oracle. States get a fold coordinate (index+1)/P traced to the One; terminals seed; retrograde induction propagates. Demonstrated beyond chess on the subtraction game (loss iff heap divisible by 4) and Nim (loss iff XOR of heaps is zero, Sprague-Grundy/Bouton), reproducing each closed-form oracle with zero disagreements. Exact, certified, general: one solver for all finite games. Machine-checked; reproduces from one command. A standalone result within the Smithian Fold Theory of Everything (SFTOE). Full corpus, code, and the run-it-yourself VERIFY.md protocol: https://github.com/MettaMazza/Smithian-Fold-Theory

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-29
DOI
https://doi.org/10.5281/zenodo.21028950
Citations
2
Primary Topic
Artificial Intelligence in Games
Type
article
Field-Weighted Citation Impact
26.08
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article

The Engine Was Never About Chess: A Certified Universal Exact Solver by Retrograde Folding

Maria Smith
2 citations
Zenodo (CERN European Organization for Nuclear Research)
Artificial Intelligence in Games
26.08
article

The Engine Was Never About Chess: A Certified Universal Exact Solver by Retrograde Folding

Maria Smith
article en
2 citations

Abstract

One axiom. One operation. Zero free parameters. A Smithian Fold campaign solved ~1 billion chess endgame positions exactly by retrograde folding, zero error against the Syzygy oracle. This paper proves what that success means: the engine was never about chess. Retrograde folding is a domain-agnostic exact solver. Give it any finite state space, a move generator, and a terminal rule, and it returns the exact game-theoretic value of every state — win, loss, draw, with exact distance — and certifies itself against an independent oracle. States get a fold coordinate (index+1)/P traced to the One; terminals seed; retrograde induction propagates. Demonstrated beyond chess on the subtraction game (loss iff heap divisible by 4) and Nim (loss iff XOR of heaps is zero, Sprague-Grundy/Bouton), reproducing each closed-form oracle with zero disagreements. Exact, certified, general: one solver for all finite games. Machine-checked; reproduces from one command. A standalone result within the Smithian Fold Theory of Everything (SFTOE). Full corpus, code, and the run-it-yourself VERIFY.md protocol: https://github.com/MettaMazza/Smithian-Fold-Theory

Zenodo (CERN European Organization for Nuclear Research)
Fano Labs (China) (CN)
Peace, Justice and strong institutions
Openalex Percentile: Top 1%
Artificial Intelligence in Games
26.08
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