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Kobayashi2501 / A-Formal-Collapse-Resolution-of-the-Riemann-Hypothesis-via-AK-Theory

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This repository presents Version 2.5 of a formally complete, structurally reinforced, and type-theoretically encoded resolution of the Riemann Hypothesis (RH), formulated through Collapse Theory and the AK High-Dimensional Projection Structural Framework (AK-HDPST v12.5).

riemann-hypothesis zeta-function critical-line collapse-theory topological-moduli-collapse sha-obstruction ext-class-cohomology functorial-resolution langlands-correspondence collapse-rh-theorem zfc-compatible-proof ak-high-dimensional-projection
  • Updated Aug 4, 2025
  • TeX

Kobayashi2501 / navier-stokes-global-regularity

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This repository presents Version 8.0, a fully formal, logically closed, and collapse-theoretic resolution of the global regularity of the 3D incompressible Navier–Stokes equations on R³, developed under the AK High-Dimensional Projection Structural Theory (AK-HDPST)

latex mathematics navier-stokes pde fluid-dynamics numerical-analysis persistent-homology topological-data-analysis mathematical-physics millennium-problem collapse-theory ak-high-dimensional-projection
  • Updated Jul 23, 2025
  • TeX

Kobayashi2501 / collapse-hodge-ak-theory

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ia Collapse Theory and AK High-Dimensional Projection This repository presents Version 2.0 of a formal, categorical, and type-theoretic resolution of the Hodge Conjecture, formulated through Collapse Theory and the AK High-Dimensional Projection Structural Framework (AK-HDPST).

category-theory algebraic-geometry persistent-homology formal-proof hodge-conjecture collapse-theory ak-theory high-dimensional-projection ext-class
  • Updated Jul 15, 2025
  • TeX

Kobayashi2501 / Structural-Proof-of-the-BSD-Conjecture-via-AK-Theory

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This repository presents Version 4.0 of a formal, type-theoretic, and fully machine-verifiable proof of the Birch and Swinnerton-Dyer (BSD) Conjecture, built upon the framework of Collapse Theory and the AK High-Dimensional Projection Structural Theory (AK-HDPST) v14.5.

elliptic-curves algebraic-number-theory collapse-theory bsd-conjecture birch-swinnerton-dyer zeta-correspondence topological-collapse ext-class-elimination functorial-proof type-theoretic-formalization collapse-bsd-theorem ak-high-dimensional-projection
  • Updated Aug 1, 2025
  • TeX

dawnfield-institute / dawn-field-theory

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A post-symbolic physics framework modeling intelligence, collapse, and emergence through entropy flow.

reinforcement-learning information-theory agent-based-modeling bayesian-optimization open-research quantum-field-theory field-theory qbe early-stage research-prototype collapse-theory post-symbolic-ai entropy-based-intelligence infodynamics non-symbolic-ai open-agi superfluid-dynamics dawn-collective
  • Updated Aug 26, 2025
  • Python

Kobayashi2501 / Collapse-Theoretic-Resolution-of-the-Black-Hole-Information-Paradox

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AK-HDPST resolves BHIP by reinterpreting information loss as a structural typing failure — not as a violation of physics, but as the breakdown of projectability across a categorical boundary.

type-theory category-theory formal-verification persistent-homology quantum-gravity collapse-theory ak-theory black-hole-information-paradox entropy-and-information functorial-projection
  • Updated Jul 18, 2025
  • TeX

Kobayashi2501 / Collapse-Theoretic-Proof-of-the-ABC-Conjecture

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via Collapse Theory and AK High-Dimensional Projection This repository contains Version 2.0 of a formally verifiable, obstruction-theoretic proof of the ABC Conjecture, based on:

persistent-homology diophantine-equations collapse-theory abc-conjecture radical-inequality collapse-energy-decay ext-class-trivialization sheaf-theoretic-collapse type-theory-in-number-theory categorical-collapse collapse-abc-theorem ak-high-dimensional-projection
  • Updated Aug 3, 2025
  • TeX

Kobayashi2501 / the-M-Conjecture

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The M Conjecture proposes a collapse-theoretic foundation for understanding: Motives Mirror Symmetry The category of motives 𝕄_mot By reinterpreting them as functorially-generated fixed points of structural degeneration in the AK Collapse Theory.

category-theory homotopy-type-theory cohomology motives collapse-theory ak-theory mirror-symmetry derived-categories structural-mathematics functorial-simplification
  • Updated Jul 23, 2025
  • TeX

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