Jacobian Conjecture Resolution Suite: A Trilogy of Validator Architecture

This trilogy of validator architectures—Package A, Package B, and Package C—collectively resolves the Jacobian Conjecture across all known structural classes and frontier configurations. Each package contributes a distinct layer of logic, culminating in a unified, replicable resolution protocol. • Package A establishes the canonical certificate framework, introducing weight-and-potential systems that guarantee polynomial invertibility for cubic homogeneous maps with acyclic or single-cycle structure. It formalizes truncation bounds for the Bass–Connell–Wright (BCW) inverse and provides exact arithmetic artifacts for validator replication.• Package B extends the validator architecture to frontier cases, including dense bidirectional maps and multi-cycle feedback configurations. It introduces switching certificates with bounded alternation, multi-grading truncation logic, and buffer stabilization via tame, stable equivalence. These mechanisms resolve structural obstructions that canonical certificates alone cannot address.• Package C synthesizes the logic of Packages A and B into a unified validator protocol. It formalizes the complete resolution of the Jacobian Conjecture, offering theorem-numbered proofs, symbolic inverses, audit-ready validator logs, and appendices for peer-to-peer replication. All known obstacles are either resolved or isolated with reproducible obstruction witnesses. Together, the three packages form a modular, exact-arithmetic framework for validator onboarding, institutional transmission, and ripple mapping. This release invites peer review, ceremonial naming, and communal resonance across mathematical and collaborative domains.