ROTO-NO-TSURUGI (Lot Sword Theorem) v12.4 — Audit-Ready Reduction of 3D Navier–Stokes Global Regularity to KZ-A1 (via ESS 2003)

Package: ROTO-NO-TSURUGI (Lot Sword Theorem) v12.4 Programme: GQV / Navier–Stokes (R^3) Millennium Track Author: Hisashi Suga (Ikigakusha/Gaasu 13/COME HERE GAASU FOREST/Independent Researcher) Format: Strict ASCII | No LaTeX | Copy-safe Governance: NO OVERCLAIM This upload provides an audit-ready logic chain isolating a single explicit sufficient condition for excluding finite-time singularities in 3D Navier–Stokes (R^3), using a pinned external theorem. Core target (KZ-A1): For any suitable weak solution (Leray–Hopf + local energy inequality) on R^3 x (0,T), establish the critical bound ess supt in (0,T) ||u(t)||L^3(R^3) < infinity. Pinned bridge (ESS 2003, contrapositive form used): If the above L^infty_t L^3_x bound holds for a suitable weak solution on (0,T), then T is not a singular time. What this package provides (B route): An audit-ready reduction: if KZ-A1 holds on every finite interval for all suitable weak solutions, then the standard global regularity statement follows (via the ESS bridge). A minimal SI clarifies definitions (singular time, first singular time, ess sup conventions) and the limited use of weak–strong uniqueness as a standard bridge. What this package does NOT provide: No proof of KZ-A1. No claim of uniqueness among all weak solutions. No claim that KZ-A1 is equivalent to the Millennium problem. Included artefacts: Theorem file (Route B: audit-ready reduction) Supplement (SI) with minimal definitions and pin-map README and RUNLOG (audit context) SHA256 manifest(s) for integrity checking