Polynomial, Determinant, and Formal-Derivative Identities for an Explicit Sextic Section: Lean Stage 1 Algebraic Certificates

REVIEW DRAFT: this deposit is a review draft, not peer reviewed, and makes no publication-of-record claim and no claim to resolve the Hodge conjecture or any Clay problem. We record seven Lean 4 kernel-checked commutative-algebra lemmas in Hodge.ExplicitResidueAlgebra: exact two-pair decomposition, binary split factorization, two Jacobian determinant factorizations, root and leading Wronskian coefficient nonvanishing for an explicit degree-24 section modulus in characteristic zero, and a formal-derivative Wronskian identity. This review draft documents theorem mappings, toolchain pins and reproduction. It does not construct Betti or Hodge cohomology, geometric ideals, cycle classes, or a residue-cycle theorem, and does not resolve the Hodge conjecture or any Clay problem. Mathematical source pin: e207394a9ed4255ad804860b8f69fde7e940dd54; later checked source head: fefe2ba9d87c900b538d02c13f7f51f375fcd285; manuscript integration merge: 82a630d110dd80cdebcb708ecbd150d7c41ac473. The documented Lean verification uses pinned cached dependencies; it is not a clean dependency rebuild. The repository Paper workflow builds a different manuscript; these note PDFs were rebuilt and inspected separately with Tectonic.