What question did this study set out to answer?

The aim is to isolate conditions that prevent finite-time singularities in the 3D Navier-Stokes equations using a logical framework.

January 25, 2026Open Access

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

Key Points

The aim is to isolate conditions that prevent finite-time singularities in the 3D Navier-Stokes equations using a logical framework.
Developed an audit-ready logic chain isolating conditions for excluding singularities
Applied external theorem in the context of the Navier-Stokes equations
Used the ESS 2003 contrapositive form to establish critical bounds
Identified a sufficient condition (KZ-A1) for the absence of singular times
Established a link between KZ-A1 and global regularity statements
Provided artifacts for governance and integrity checking to ensure compliance and validation

Abstract

Package: ROTO-NO-TSURUGI (Lot Sword Theorem) v12. 4 Programme: GQV / Navier–Stokes (R³) 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 (R³), using a pinned external theorem. Core target (KZ-A1): For any suitable weak solution (Leray–Hopf + local energy inequality) on R³ x (0, T), establish the critical bound ess supₓ ₈₍ (₀, ₓ) ||u (t) ||₋℃ (ₑ℃) < infinity. Pinned bridge (ESS 2003, contrapositive form used): If the above Lⁱnftyₜ L³ₓ 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

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

Key Points

Abstract

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