Add ProofConcept package: certificates and proofs of algebraic facts#38
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antonleykin wants to merge 2 commits into
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Add ProofConcept package: certificates and proofs of algebraic facts#38antonleykin wants to merge 2 commits into
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A proof-of-concept Macaulay2 package modeling algebraic facts as logical
statements and their proofs as independently re-verifiable data:
* Statement: an atomic algebraic predicate (inIdeal, generates,
isGroebner) or a compound formula built with and/or/not;
* Implication: A ==> B;
* Certificate: an atomic proof — a witness checked cheaply and
independently (e.g. H with H*G = f for ideal membership, monomial
divisibility, or a nonzero normal form for non-membership);
* Proof: a tree of inference steps combining certificates by logical
rules (and-introduction, or-introduction) and the derived Buchberger
rule.
verify recomputes and re-checks the witness in each leaf and the side
conditions of each rule. Includes documentation and TEST blocks for the
three motivating cases (ideal membership, monomial-ideal membership,
Buchberger's criterion) and the logic layer.
https://claude.ai/code/session_01VSJyxL59SKiQ4ZPoAyKj8C
Companion document capturing the conversation that produced the package: the original request, the follow-up that turned proofs into a logical tree, the Macaulay2 findings that shaped the design, and the decisions made. https://claude.ai/code/session_01VSJyxL59SKiQ4ZPoAyKj8C
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A proof-of-concept Macaulay2 package modeling algebraic facts as logical
statements and their proofs as independently re-verifiable data:
isGroebner) or a compound formula built with and/or/not;
independently (e.g. H with H*G = f for ideal membership, monomial
divisibility, or a nonzero normal form for non-membership);
rules (and-introduction, or-introduction) and the derived Buchberger
rule.
verify recomputes and re-checks the witness in each leaf and the side
conditions of each rule. Includes documentation and TEST blocks for the
three motivating cases (ideal membership, monomial-ideal membership,
Buchberger's criterion) and the logic layer.
https://claude.ai/code/session_01VSJyxL59SKiQ4ZPoAyKj8C