An AASC Constraint-Formalism Proof of the Poincare Endpoint by Fixed-Carrier Negative-Branch Exclusion

Overview This deposit presents An AASC Constraint-Formalism Proof of the Poincaré Endpoint by Fixed-Carrier Negative-Branch Exclusion. The manuscript gives a mathematical proof in the Admissibility And Standing Constraint (AASC) formalism. It is not a Ricci-flow proof, a surgery proof, a recognition algorithm proof, or an imported corollary of the Hamilton–Perelman solution. The proof class is fixed-carrier endpoint closure: the Poincaré endpoint is treated as a determinate theorem-bearing target on a fixed closed connected simply connected three-manifold carrier. Central Claim The paper proves the Poincaré endpoint in AASC endpoint mode: Every closed connected simply connected three-manifold occupies the sphere-readout endpoint, under the fixed Poincaré carrier and endpoint-under-audit conditions. The proof proceeds by excluding the native negative branch rather than by constructing a Ricci-flow bridge. Proof Architecture The proof spine is: the official Poincaré endpoint fixes a non-degenerate same-carrier theorem regime; endpoint adequacy forces the AASC kernel roles of reference, standing, admissibility, and irreversibility; the native negative branch is routed through sphere-bridge exclusion; official negative endpoint use induces endpoint-status governance; endpoint-status governance induces independent same-domain sphere discrimination; independent same-domain sphere discrimination is excluded by the local kernel packet; the negative branch collapses, leaving sphere-readout as the endpoint. The manuscript also includes a weakening-resistance audit showing that weaker same-carrier regimes do not preserve endpoint determinacy while permitting the excluded negative-governance structure. Relation to Classical Poincaré Proofs The manuscript does not reproduce the Hamilton–Perelman Ricci-flow-with-surgery proof and does not use it as a premise. Ricci flow and related classical sources are treated only as comparison material and as a bridge-construction route in the ordinary topological proof class. The present proof belongs to a different mathematical proof class: AASC constraint-formalism endpoint closure. Lean 4 Audit Layer A companion Lean 4 audit layer is available for the endpoint-routing structure and AASC kernel discipline. The Lean material is support and audit material; the manuscript theorem chain remains the proof. The Lean-facing material records the formal endpoint route, kernel discipline, no-independent-classifier closure, and Poincaré-specific carrier instantiation. The relevant AASC machinery is included directly in the paper-specific Lean audit layer. Public Lean audit repository: https://github.com/somamaley-ux/AASC-Poincare-Endpoint-Lean-Audit Associated Zenodo DOI: https://doi.org/10.5281/zenodo.20620926 Contents of This Deposit This project package includes: the publication-ready manuscript PDF; LaTeX source files; bibliography and project metadata; audit notes and theorem-ladder materials; Lean appendix integration notes; QA/render notes and project manifest. This paper is downstream of: Non-Degenerate Construction and the Kernel of Admissibility