• 1 Overview ▶
    • 1.1 What this project is
    • 1.2 What it is trying to find out
    • 1.3 Goals, in order of ambition
    • 1.4 How to read this blueprint
    • 1.5 Coverage caveat
  • 2 Haar Measure Foundation ▶
    • 2.1 Self-Duality on Compact Groups
  • 3 Functional Equation ▶
    • 3.1 Completed Riemann Zeta Function
  • 4 Shadow Symmetry = Time Reversal ▶
    • 4.1 The Three-Step Proof
  • 5 Riemann Hypothesis (Pathway 2) ▶
    • 5.1 Two-Zeros Argument
    • 5.2 Spectral Multiplicity
  • 6 thm:link6 Formalized
  • 7 Celestial Holography ▶
    • 7.1 Shadow Discontinuity = Loop Integrand
    • 7.2 Tree-to-Loop Topology (Shadow-Pair Sewing)
    • 7.3 Loops from Cuts (canonical replacement series)
    • 7.4 Dispersion Reconstruction: the Mechanism Behind sewing_identity
  • 8 Adèlic \(L^2\) Regularization
  • 9 Spectral Weil Formula
  • 10 Cesàro Regularization and the Weil Positivity Criterion
  • 11 L2 Constraint ▶
    • 11.1 \(L^2(K^1)\) Forces \(\mathrm{Re}(s) = \tfrac {1}{2}\)
  • 12 The Half-Flip: CPT, Time Reversal, and Complete Positivity ▶
    • 12.1 Wigner time reversal squares to \(-1\)
    • 12.2 Antiunitary conjugation is transposition
    • 12.3 Transposition is positive but not completely positive
    • 12.4 Entanglement bounds (same module family)
  • 13 Standard Model — Three Generations ▶
    • 13.1 Division Algebra Tower
  • 14 Standard Model — Dark Matter Abundance
  • 15 Arithmetic and Quantum-Information Miscellanea (from ONON5213.tex)
  • 16 Quantum Gravity — Born Rule from Haar
  • 17 Quantum Gravity — Celestial Spectral Weight and All-Loop Bound
  • 18 General Relativity — Rigidity
  • 19 Thread HT — Prime–Archimedean Heat Trace (Elementary Layer) ▶
    • 19.1 Complete Monotonicity and Laplace Bookkeeping
    • 19.2 Subordination
    • 19.3 Bridge to Thread L, and the Archimedean Laplace Transform
    • 19.4 Honest Boundary
  • 20 The Digamma Function
  • 21 Local-Field Shadow Kernels ▶
    • 21.1 The \(d=2\) Cut vs. the Spherical Weyl Coefficient
    • 21.2 The Global Eisenstein Coefficient
  • 22 The Golden Ratio as the Minimal Hyperbolic Sector of \(PSL_2(\mathbb {Z})\)
  • 23 Local Shadow Kernels and the Finite-Prime Weil Kernel
  • 24 Thread Weil-Semiboundedness
  • 25 Formalized Content Not Yet Written Up Individually ▶
    • 25.1 Riemann Hypothesis — Supporting Tower
    • 25.2 Thread Weil-Parity
    • 25.3 Number Theory — Arithmetic Layer
    • 25.4 Celestial Holography — Further Results
    • 25.5 Quantum Gravity — Further Results
    • 25.6 Standard Model — Further Results
    • 25.7 General Relativity — Further Results
    • 25.8 Cosmology
    • 25.9 String Theory
    • 25.10 Thread S — Signature and Inertia
    • 25.11 Yang–Mills
    • 25.12 Core Theorems and Grassmannian Geometry
  • 26 Axiom Inventory ▶
    • 26.1 Physics Inputs (now hypotheses, not axioms)
    • 26.2 Mathlib-Gap Axioms
    • 26.3 Retired Axioms
    • 26.4 The True-Stub Convention (not axioms, not sorries)
  • Dependency graph
  • 1 Overview
    • 1.1 What this project is
    • 1.2 What it is trying to find out
    • 1.3 Goals, in order of ambition
    • 1.4 How to read this blueprint
    • 1.5 Coverage caveat
  • 2 Haar Measure Foundation
    • 2.1 Self-Duality on Compact Groups
  • 3 Functional Equation
    • 3.1 Completed Riemann Zeta Function
  • 4 Shadow Symmetry = Time Reversal
    • 4.1 The Three-Step Proof
  • 5 Riemann Hypothesis (Pathway 2)
    • 5.1 Two-Zeros Argument
    • 5.2 Spectral Multiplicity
  • 6 thm:link6 Formalized
  • 7 Celestial Holography
    • 7.1 Shadow Discontinuity = Loop Integrand
    • 7.2 Tree-to-Loop Topology (Shadow-Pair Sewing)
    • 7.3 Loops from Cuts (canonical replacement series)
    • 7.4 Dispersion Reconstruction: the Mechanism Behind sewing_identity
  • 8 Adèlic \(L^2\) Regularization
  • 9 Spectral Weil Formula
  • 10 Cesàro Regularization and the Weil Positivity Criterion
  • 11 L2 Constraint
    • 11.1 \(L^2(K^1)\) Forces \(\mathrm{Re}(s) = \tfrac {1}{2}\)
  • 12 The Half-Flip: CPT, Time Reversal, and Complete Positivity
    • 12.1 Wigner time reversal squares to \(-1\)
    • 12.2 Antiunitary conjugation is transposition
    • 12.3 Transposition is positive but not completely positive
    • 12.4 Entanglement bounds (same module family)
  • 13 Standard Model — Three Generations
    • 13.1 Division Algebra Tower
  • 14 Standard Model — Dark Matter Abundance
  • 15 Arithmetic and Quantum-Information Miscellanea (from ONON5213.tex)
  • 16 Quantum Gravity — Born Rule from Haar
  • 17 Quantum Gravity — Celestial Spectral Weight and All-Loop Bound
  • 18 General Relativity — Rigidity
  • 19 Thread HT — Prime–Archimedean Heat Trace (Elementary Layer)
    • 19.1 Complete Monotonicity and Laplace Bookkeeping
    • 19.2 Subordination
    • 19.3 Bridge to Thread L, and the Archimedean Laplace Transform
    • 19.4 Honest Boundary
  • 20 The Digamma Function
  • 21 Local-Field Shadow Kernels
    • 21.1 The \(d=2\) Cut vs. the Spherical Weyl Coefficient
    • 21.2 The Global Eisenstein Coefficient
  • 22 The Golden Ratio as the Minimal Hyperbolic Sector of \(PSL_2(\mathbb {Z})\)
  • 23 Local Shadow Kernels and the Finite-Prime Weil Kernel
  • 24 Thread Weil-Semiboundedness
  • 25 Formalized Content Not Yet Written Up Individually
    • 25.1 Riemann Hypothesis — Supporting Tower
    • 25.2 Thread Weil-Parity
    • 25.3 Number Theory — Arithmetic Layer
    • 25.4 Celestial Holography — Further Results
    • 25.5 Quantum Gravity — Further Results
    • 25.6 Standard Model — Further Results
    • 25.7 General Relativity — Further Results
    • 25.8 Cosmology
    • 25.9 String Theory
    • 25.10 Thread S — Signature and Inertia
    • 25.11 Yang–Mills
    • 25.12 Core Theorems and Grassmannian Geometry
  • 26 Axiom Inventory
    • 26.1 Physics Inputs (now hypotheses, not axioms)
    • 26.2 Mathlib-Gap Axioms
    • 26.3 Retired Axioms
    • 26.4 The True-Stub Convention (not axioms, not sorries)