mtft 0.4.1

Modular Time Field Theory — core data structures, modular geometry, gauge-Higgs unification, dark sector, and information geometry

MTFT — Modular Time Field Theory

A Python library implementing the core data structures and computational tools for Modular Time Field Theory (MTFT).

Overview

MTFT proposes a modular time field τ(x) = t_R / t_U mapping spacetime to the upper half-plane ℍ, unifying dark matter, particle masses, and cosmic structure through:

• Modular symmetry — SL(2,ℤ) acting on τ
• Gauge-Higgs unification — Higgs = A_τ holonomy via the Hosotani mechanism
• τ-vortex dark matter — logarithmic τ-profiles give flat rotation curves with no dark particles
• Information geometry bridge — Fisher-Rao curvature of the logistic map connects chaos → geometry → dynamics

The Three-Layer Architecture

Counting   →  Logistic map orbits, figurate-number degeneracies
Geometry   →  Fisher-Rao metric, Ricci curvature R_core
Dynamics   →  SM masses, dark matter halos, decay rates, cosmology

Connected by the spectral determinant identity:

det(1 − q^{1/m} P_m) = η(τ)^{−1/m} θ₃(0,τ)^{1/m}

linking Fredholm determinants (chaos/RG) to CFT partition functions.

Installation

pip install -e .              # minimal (numpy only)
pip install -e ".[full]"      # with scipy + matplotlib
pip install -e ".[dev]"       # with pytest + ruff

Quick Start

import mtft

# ── Modular forms ─────────────────────────────────────
tau = 0.1 + 1.5j
eta = mtft.dedekind_eta(tau)
j   = mtft.forms.j_invariant(tau)
print(f"η(τ) = {eta:.6f}")
print(f"j(τ) = {j:.2f}")

# Verify the spectral determinant identity
result = mtft.forms.verify_spectral_identity(tau, m=2)
print(f"Spectral identity relative error: {result['relative_error']:.2e}")

# ── Hosotani mechanism ────────────────────────────────
hp = mtft.HosotaniPotential(fermion_fraction=0.4, kappa_ew=0.05)
theta0 = hp.find_vacuum()
masses = hp.gauge_masses()
print(f"Vacuum θ₀ = {theta0:.4f}")
print(f"m_W = {masses['m_W']:.2f} GeV  (PDG: 80.37)")
print(f"m_Z = {masses['m_Z']:.2f} GeV  (PDG: 91.19)")

# ── Particle spectrum ─────────────────────────────────
sm = mtft.StandardModel()
top = sm.by_name("Top")
print(f"Top quark: m = {top.mass_GeV} GeV, κ = {top.kappa}")

# Full κ-hierarchy
for name, kappa in sm.kappa_hierarchy():
    print(f"  {name:15s}  κ = {kappa:.2e}")

# ── Dark sector ───────────────────────────────────────
import numpy as np
halo = mtft.TauVortexHalo(A=1e20, r0=1e30)
r = np.logspace(31, 35, 100)
v = halo.v_circular(r)
print(f"v_∞ = {halo.v_infinity:.4e} (flat rotation velocity)")

# ── Information geometry ──────────────────────────────
R = mtft.info_geometry.R_core()
print(f"R_core (Feigenbaum) = {R:.4f}")

# ── Cosmology ─────────────────────────────────────────
cosmo = mtft.FriedmannMTFT(Omega_tau=0.25)
hist = cosmo.expansion_history()

Package Structure

mtft/
├── constants.py       # PDG masses, SM parameters, physical constants
├── modular.py         # τ-field, SL(2,ℤ), hyperbolic geometry
├── forms.py           # Dedekind η, Jacobi θ₃, Eisenstein, spectral det
├── hosotani.py        # Effective potential, vacuum finder, EWSB
├── particles.py       # SM particle database with κ-couplings
├── dark_sector.py     # τ-vortex halos, rotation curves, Tully-Fisher
├── info_geometry.py   # Fisher-Rao metric, Ricci curvature, logistic map
└── cosmology.py       # Modified Friedmann, perturbations, G(t) oscillation

Key Equations

Component	Equation
Modular time field	τ(x) = t_R(x)/t_U(x) ∈ ℍ
Hyperbolic metric	ds² = (dx² + dy²)/y², K = −1
W mass	m_W = κ_EW |sin θ_H| / (2R_τ)
Fermion mass	m_f = κ_f |sin θ₀| / R_τ
τ-vortex density	ρ_τ(r) = A²/(2r²)
Flat rotation	v²_∞ = 2πGA²
Tully-Fisher	v⁴ ∝ M_BH ∝ M_baryonic
R_core bridge	m_τ² = c_m |R_core|

Testing

pytest tests/ -v

License

MIT

Citation

If you use this package in research, please cite:

@software{mtft2025,
  title  = {MTFT: Modular Time Field Theory Python Package},
  author = {Roger},
  year   = {2025},
  url    = {https://github.com/roger/mtft}
}