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Office Hours with Claude
Learn the mathematical and physics foundations of the Z² Framework
🎮 Interactive Visualizations
Explore Z₂ groups, torus topology, wave functions & more
📖 Notation Reference
All symbols used in the v8.8.8 paper with searchable index
📚 How to Learn
- • Complete Math first, then Physics
- • Each topic builds on the previous
- • Work through examples with pen and paper
- • Every topic shows its Z² framework connection
20
Documents
~50
Hours Total
100+
Concepts
1
Prerequisites
Algebra, calculus, complex numbers, Euler's formula
2
Linear Algebra
Vectors, matrices, eigenvalues, trace
3
Group Theory
Lie groups, SU(2), SU(3), U(1), Z₂ symmetry
4
Topology Basics
Manifolds, compactness, continuity
5
Differential Geometry
Metrics, curvature, geodesics
6
Algebraic Topology
Homology, Betti numbers (b₁ = 3)
7
Orbifolds
T³/Z₂ geometry, 8 fixed points
8
Index Theory
APS theorem, eta invariant
9
Intersection Theory
D-brane intersections, I_ab = 3
10
Classical Mechanics
Lagrangian, Hamiltonian, Noether's theorem
11
Special Relativity
Lorentz transformations, GPS proof
12
Quantum Mechanics
Wave functions, spin, uncertainty
13
Quantum Field Theory
Feynman diagrams, propagators, vacuum
14
Gauge Theory
Standard Model gauge structure
15
General Relativity
Einstein equations, curved spacetime
16
ADM Formalism
3+1 decomposition, Hamiltonian gravity
17
Cosmology
Ω_Λ = 13/19, dark energy
18
String Theory
Strings, D-branes, compactification
19
Holography
AdS/CFT, IR fixed points
🔗 Key Z² Connections
Z² = 32π/3
→
Orbifolds
Singularity resolution on T³/Z₂
α⁻¹ = 4Z² + 3
→
Index Theory
APS eta invariant + rank(G)
sin²θ_W = 3/13
→
Intersection Theory
D-brane intersection number
Ω_Λ = 13/19
→
Holography
Degrees of freedom counting
3 generations
→
Algebraic Topology
b₁(T³) = 3 Betti number
🏛️ The Four Pillars
α⁻¹ = 4Z² + 3
= 137.04 (0.004% error)
αₛ = 4/Z²
= 0.119 (1.24% error)
sin²θ_W = 3/13
= 0.2308 (0.17% error)
v = M_P·e^(-Z²)·α
= 249 GeV (1.12% error)