| import numpy as np | |
| import matplotlib.pyplot as plt | |
| # PUH v11: Gravity Jacobian Shear Sim — Fold Distortion | |
| x = np.linspace(-10, 10, 1000) # Coordinate | |
| m_knot = 1 # Toy mass (knot) | |
| # Jacobian J(φ) = 1 - 2 G m / r (toy 1D shear) | |
| r = np.abs(x) + 1e-6 # Avoid singularity | |
| J = 1 - 2 * 6.6743e-11 * m_knot * 1.989e30 / (r * 1.496e11)**2 # G M / (c^2 r) normalized |
Author: Brian Martell
Date: December 13, 2025
PUH v11 derives gravity from E8 shear: S[φ] = ∫ dV_E8 √|J(φ)| Tr(φ T φ), J(φ)=det(∂φ/∂ξ) distortion yields R_μν - (1/2) R g_μν = 8π G T_μν with G = ℓ_P^2 (roots 240, √2 ℓ_P). Knots warp geodesics. Axioms 5/12 mass/vacuum. LISA h~10^{-22} PSR test. From July 14, 2025.
| @article{einstein1915, | |
| author = {Einstein, A.}, | |
| title = {Die Feldgleichungen der Gravitation}, | |
| journal = {Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.)}, | |
| pages = {844}, | |
| year = {1915} | |
| } | |
| @article{lisi2007, | |
| author = {Lisi, A. G.}, |
| % Gist-ready — upload as: puh_gravity_e8_derivation_v11.tex | |
| \documentclass[11pt,a4paper]{article} | |
| \usepackage[utf8]{inputenc} | |
| \usepackage{amsmath,amsfonts,amssymb,amsthm} | |
| \usepackage{siunitx} | |
| \usepackage{geometry} | |
| \usepackage{booktabs} | |
| \usepackage{xcolor} | |
| \usepackage{hyperref} | |
| \geometry{margin=1in} |
| import numpy as np | |
| import matplotlib.pyplot as plt | |
| # PUH v11: SM E8 Projection Sim — Rep Cycle | |
| dim = 248 | |
| roots = 240 | |
| gens = 3 | |
| omega = np.exp(2j * np.pi / 3) | |
| # T eigenvalues for SU(3) cycle |
Author: Brian Martell
Date: December 13, 2025
PUH v11 derives SM from E8: S[φ] = ∫ dV_E8 √|J(φ)| Tr(φ T φ) projects 248-dim to SU(3)^3 × SU(2) × U(1). T^3=I 3 gens, chiral knots i \slashed{D} ψ = m ψ (m=240/248 m_Pl), gauges A_μ root edges (α_s=0.1179 8/240), Higgs v=m_Pl / √(248/3)≈246.22 GeV. T averages θ_QCD=0. g-2 ~0.1% torque. From July 14, 2025.
| @article{lisi2007, | |
| author = {Lisi, A. G.}, | |
| title = {An Exceptionally Simple Theory of Everything}, | |
| journal = {arXiv e-prints}, | |
| eprint = {0711.0770}, | |
| year = {2007}, | |
| note = {E8 SM embedding} | |
| } | |
| @article{glashow1961, |
| % Gist-ready — upload as: puh_standard_model_e8_derivation_v11.tex | |
| \documentclass[11pt,a4paper]{article} | |
| \usepackage[utf8]{inputenc} | |
| \usepackage{amsmath,amsfonts,amssymb,amsthm} | |
| \usepackage{siunitx} | |
| \usepackage{geometry} | |
| \usepackage{booktabs} | |
| \usepackage{xcolor} | |
| \usepackage{hyperref} | |
| \geometry{margin=1in} |
| import numpy as np | |
| import matplotlib.pyplot as plt | |
| from scipy.integrate import odeint | |
| # PUH v11: Toy 1D Dirac Sim — Chiral Propagation in Fold | |
| hbar = 1 # Normalized | |
| m = 0.5 # Knot mass | |
| x = np.linspace(-10, 10, 1000) | |
| # Dirac in 1D: i ∂_t ψ = -i ∂_x σ_z ψ + m σ_x ψ (toy 2-comp spinor) |
Author: Brian Martell
Date: December 13, 2025
PUH v11 derives i ħ \slashed{∂} ψ = m ψ from E8 triality T^3=I: Cycles spinor reps in 248-dim (roots 240, √2 ℓ_P), γ^μ root Pauli, ∂_μ J(φ) shear, m = 240/248 m_Pl dilution. Chiral 2+2 from T eigenvalues. Axioms 5/10 knot/Ping. g-2 ~0.1% torque. From July 14, 2025.