Verification Code Index

Every derivation and proof in this book is backed by machine-verifiable code. Lean 4 provides formal proof verification, Python handles numerical checks and plots, and Mathematica performs symbolic computation and CAS verification.

Lean 4 — Formal proof verification
Python — Numerical verification
Mathematica — Symbolic computation
Introduction
1 Introduction
Lean 4 Python Mathematica
Part I: Foundations
2 The Single Postulate
Lean 4 Python Mathematica
3 Why Six Dimensions?
Lean 4 Python Mathematica
4 The Product Structure
Lean 4 Python Mathematica
5 Temporal Momentum
Lean 4 Python Mathematica
6 Tracelessness and Gravity Coupling
Lean 4 Python Mathematica
7 Modified Gravitational Potential
Lean 4 Python Mathematica
Part II: Spacetime Geometry
8 Why S² is the Unique Compact Space
Lean 4 Python Mathematica
9 Geometry of the 2-Sphere
Lean 4 Python Mathematica
10 The Dirac Monopole
Lean 4 Python Mathematica
11 Monopole Harmonics
Lean 4 Python Mathematica
12 Dimensional Reduction
Lean 4 Python Mathematica
13 The Modulus and Compact Scale
Lean 4 Python Mathematica
14 The Two Interpretations
Lean 4 Python Mathematica
Part III: Gauge Structure
15 Gauge Symmetry from Geometry
Lean 4 Python Mathematica
16 The SU(2) Weak Force
Lean 4 Python Mathematica
17 The U(1) Hypercharge
Lean 4 Python Mathematica
18 The SU(3) Color Force
Lean 4 Python Mathematica
19 The Complete Gauge Group
Lean 4 Python Mathematica
20 Coupling Constant Derivation
Lean 4 Python Mathematica
21 Anomaly Cancellation and Hypercharge
Lean 4 Python Mathematica
22 Why No Other Particle Content
Lean 4 Python Mathematica
Part IV: Electroweak Physics
23 Electroweak Symmetry Breaking
Lean 4 Python Mathematica
24 The Higgs Field
Lean 4 Python Mathematica
25 The Electroweak VEV
Lean 4 Python Mathematica
26 W and Z Boson Masses
Lean 4 Python Mathematica
27 The Higgs Boson Mass
Lean 4 Python Mathematica
28 Photon and Gluon Masslessness
Lean 4 Python Mathematica
Part V: Strong Force
29 Quantum Chromodynamics in TMT
Lean 4 Python Mathematica
30 The Strong Coupling Constant
Lean 4 Python Mathematica
31 Confinement
Lean 4 Python Mathematica
32 QCD Confinement from S² Topology
Lean 4 Python Mathematica
33 Hadron Masses
Lean 4 Python Mathematica
34 The Strong CP Problem — Solved
Lean 4 Python Mathematica
35 Proton Mass from First Principles
Lean 4 Python Mathematica
Part VI: Fermion Masses
36 The Fermion Mass Problem
Lean 4 Python Mathematica
37 Fermion Localization on S²
Lean 4 Python Mathematica
38 The Master Mass Formula
Lean 4 Python Mathematica
39 Charged Lepton Masses
Lean 4 Python Mathematica
40 Up-Type Quark Masses
Lean 4 Python Mathematica
41 Down-Type Quark Masses
Lean 4 Python Mathematica
42 Summary of All Nine Masses
Lean 4 Python Mathematica
43 Complete Charged Fermion Mass Derivation
Lean 4 Python Mathematica
44 The CKM Matrix
Lean 4 Python Mathematica
45 CP Violation in Quarks
Lean 4 Python Mathematica
46 The Neutrino Puzzle
Lean 4 Python Mathematica
47 The Seesaw Mechanism
Lean 4 Python Mathematica
48 Neutrino Masses
Lean 4 Python Mathematica
49 The PMNS Matrix
Lean 4 Python Mathematica
50 Neutrinoless Double Beta Decay
Lean 4 Python Mathematica
51 Leptogenesis
Lean 4 Python Mathematica
Part VII: Gravity
52 Gravity in TMT
Lean 4 Python Mathematica
53 The Modified Newtonian Potential
Lean 4 Python Mathematica
54 The Equivalence Principle
Lean 4 Python Mathematica
55 Gravity and Temporal Momentum
Lean 4 Python Mathematica
56 Short-Range Gravity Tests
Lean 4 Python Mathematica
57 Toward Quantum Gravity
Lean 4 Python Mathematica
58 N-Body Problem — Classical Regime
Lean 4 Python Mathematica
59 N-Body Problem — Quantum Integrability
Lean 4 Python Mathematica
60 N-Body Problem — Classical Integrability
Lean 4 Python Mathematica
61 N-Body Problem — Dissipative Integrability
Lean 4 Python Mathematica
Part VIII: Cosmology
62 Black Holes as Temporal Momentum Recyclers
Lean 4 Python Mathematica
63 Cosmology from P1
Lean 4 Python Mathematica
64 Classical Dynamics on S²
Lean 4 Python Mathematica
65 Inflation
Lean 4 Python Mathematica
66 The Origin, Creation, and Interface
Lean 4 Python Mathematica
Part IX: Quantum Foundations
67 Quantum-Classical Correspondence
Lean 4 Python Mathematica
68 Topological Necessity of Complex Numbers
Lean 4 Python Mathematica
69 Quantum Phenomena Resolved
Lean 4 Python Mathematica
70 Continuous Variable QM and QFT from S²
Lean 4 Python Mathematica
71 Relativistic QM, Path Integrals
Lean 4 Python Mathematica
72 Quantum Information Theory from S²
Lean 4 Python Mathematica
73 Quantum Communication Protocols
Lean 4 Python Mathematica
74 Quantum Channels and Operations
Lean 4 Python Mathematica
75 Quantum Metrology — Precision Limits
Lean 4 Python Mathematica
76 Quantum-Enhanced Sensing
Lean 4 Python Mathematica
77 Information-Thermodynamics Bridge
Lean 4 Python Mathematica
78 Quantum Heat Engines
Lean 4 Python Mathematica
79 Fluctuation Theorems on S²
Lean 4 Python Mathematica
80 PBR Theorem and Ontic States
Lean 4 Python Mathematica
81 Weak Measurements and Quantum Trajectories
Lean 4 Python Mathematica
82 Quantum-to-Classical Transition
Lean 4 Python Mathematica
83 Level Statistics — Quantum Chaos
Lean 4 Python Mathematica
84 Quantum Ergodicity and Thermalization
Lean 4 Python Mathematica
85 TMT and Loop Quantum Gravity
Lean 4 Python Mathematica
86 TMT and String Theory
Lean 4 Python Mathematica
87 Born Rule — Complete Derivation
Lean 4 Python Mathematica
88 Uniqueness, Measurement, Nonlocality
Lean 4 Python Mathematica
89 ETH and Thermalization
Lean 4 Python Mathematica
90 Quantum Scars, MBL, Chaos Bound
Lean 4 Python Mathematica
91 What TMT Resolves
Lean 4 Python Mathematica
92 Framework Connections
Lean 4 Python Mathematica
93 Topological Field Theory from S²
Lean 4 Python Mathematica
94 Decoherence from S² Geometry
Lean 4 Python Mathematica
95 Inflationary Predictions
Lean 4 Python Mathematica
96 Berry Phase and Spinors
Lean 4 Python Mathematica
97 Gravitational Waves from Inflation
Lean 4 Python Mathematica
98 Dark Matter — The MOND Solution
Lean 4 Python Mathematica
99 MOND Phenomenology
Lean 4 Python Mathematica
100 Spin-Statistics Theorem
Lean 4 Python Mathematica
101 Entanglement from TMT
Lean 4 Python Mathematica
Part X: Cosmological Parameters
102 The Arrow of Time
Lean 4 Python Mathematica
103 Structure Formation
Lean 4 Python Mathematica
104 Baryogenesis
Lean 4 Python Mathematica
105 The Baryon Asymmetry Derivation
Lean 4 Python Mathematica
106 Dark Energy
Lean 4 Python Mathematica
107 Cosmological Densities
Lean 4 Python Mathematica
108 The Complete Cosmological Picture
Lean 4 Python Mathematica
109 The g-2 Anomalous Magnetic Moments
Lean 4 Python Mathematica
Part XI: Predictions and Tests
110 The Nature of Scientific Predictions
Lean 4 Python Mathematica
111 Gravity Sector Predictions
Lean 4 Python Mathematica
112 Particle Physics Predictions
Lean 4 Python Mathematica
113 Neutrino Sector Predictions
Lean 4 Python Mathematica
114 Cosmological Predictions
Lean 4 Python Mathematica
115 Rare Processes
Lean 4 Python Mathematica
116 What Would Falsify TMT?
Lean 4 Python Mathematica
117 Current Experimental Status
Lean 4 Python Mathematica
118 Tritium Beta Decay
Lean 4 Python Mathematica
Part XII: Temporal Determination
119 Philosophical Foundations of TD
Lean 4 Python Mathematica
120 The Configuration Space of Futures
Lean 4 Python Mathematica
121 The TMT Natural Measure
Lean 4 Python Mathematica
122 Evolution and Conservation
Lean 4 Python Mathematica
123 The Temporal Determination Theorem
Lean 4 Python Mathematica
124 The Aggregate Certainty Theorem
Lean 4 Python Mathematica
125 Entropy and Information
Lean 4 Python Mathematica
126 Quantum Corrections
Lean 4 Python Mathematica
127 Gravitational Effects
Lean 4 Python Mathematica
128 Applications and Examples
Lean 4 Python Mathematica
129 Summary and Future Directions
Lean 4 Python Mathematica
Part XIII: Millennium Prize Problems
130 Navier-Stokes: Problem Statement
Lean 4 Python Mathematica
131 Navier-Stokes: TMT Approach
Lean 4 Python Mathematica
132 Navier-Stokes: Global Regularity
Lean 4 Python Mathematica
133 Navier-Stokes: Uniqueness
Lean 4 Python Mathematica
134 Navier-Stokes: Proof Summary
Lean 4 Python Mathematica
135 Navier-Stokes: Computation
Lean 4 Python Mathematica
136 Yang-Mills: Problem Statement
Lean 4 Python Mathematica
137 Yang-Mills: Confinement
Lean 4 Python Mathematica
138 Yang-Mills: Mass Gap
Lean 4 Python Mathematica
139 Yang-Mills: Proof Strategy
Lean 4 Python Mathematica
140 Yang-Mills: Uniqueness
Lean 4 Python Mathematica
141 Yang-Mills: Computation
Lean 4 Python Mathematica
142 Yang-Mills: Implications
Lean 4 Python Mathematica
143 Two Prizes, One Geometry
Lean 4 Python Mathematica
Part XIV: Philosophy and Interpretation
144 TMT vs Other Approaches
Lean 4 Python Mathematica
145 Interpretation A — Extra Dimensions
Lean 4 Python Mathematica
146 Interpretation B — Geometric Field
Lean 4 Python Mathematica
147 Why Both Interpretations Work
Lean 4 Python Mathematica
148 The Epistemology of TMT
Lean 4 Python Mathematica
149 Philosophical Implications
Lean 4 Python Mathematica
150 Comparison with Other Approaches
Lean 4 Python Mathematica
151 Open Questions
Lean 4 Python Mathematica
152 Synthesis
Lean 4 Python Mathematica
153 Experimental Prospects
Lean 4 Python Mathematica
154 Conclusion
Lean 4 Python Mathematica
Part XV: Arithmetic Foundations
155 The S² Superposition: Quantum-Cosmological Unification
Lean 4 Python Mathematica
156 Deriving P1 from Something Deeper
Lean 4 Python Mathematica
157 The Topological Genesis of S²
Lean 4 Python Mathematica
158 The Temporal Persistence of S²
Lean 4 Python Mathematica
159 The Arithmetic Genesis of the Gauge Group
Lean 4 Python Mathematica
160 The Prime Spectrum and Modular Structure
Lean 4 Python Mathematica
161 The Arithmetic-Topological Convergence
Lean 4 Python Mathematica
162 The TMT Motive — Construction and Proof
Lean 4 Python Mathematica
163 Modular Forms and the Arithmetic of 12
Lean 4 Python Mathematica
164 The TMT L-function
Lean 4 Python Mathematica
165 Arakelov Geometry and the Arithmetic Monopole
Lean 4 Python Mathematica
166 Period-Inverse Period Duality
Lean 4 Python Mathematica
167 Class Field Theory and the TMT Number Field
Lean 4 Python Mathematica
168 Chern-Simons Theory, Quantum Groups, and Topological Closure
Lean 4 Python Mathematica
169 The Adelic Product Formula
Lean 4 Python Mathematica
170 Mirror Symmetry and the Dual Proof
Lean 4 Python Mathematica
171 Formal Groups, Derived Categories, and Total Rigidity
Lean 4 Python Mathematica
172 The Grand Theorem — Uniqueness of the Physical Law
Lean 4 Python Mathematica
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