mtft 0.8.0

Modular Time Field Theory — falsifiability engine, modular geometry, gauge-Higgs unification, dark sector, LHC confrontation, information geometry, arithmetic computation, and sonification.

MTFT — Modular Time Field Theory

Fundamental constants from the integers. Zero free parameters.

_{μN(y) over gauge groups SU(2)…SU(16), computed entirely from wn = Σd|n (log d)/d. The wall at small y is confinement; uniform positivity is the mass-gap statement. Open the interactive 3D navigator →}

MTFT proposes a modular time field τ(x) = t_R / t_U mapping spacetime to the upper half-plane ℍ, with SL(2,ℤ) symmetry and the modular curve X₀(143) (genus 13, level 11×13) as the arithmetic backbone. Coupling constants, the gauge tower, dark-sector profiles, and a Riemann-Hypothesis toolkit all emerge from one weight sequence — no fitted parameters anywhere in the pipeline.

The Three-Ensemble Program (v0.7 → v0.8)

One weight sequence, three assemblies, three classical RH criteria — all installable, all cross-certified by independent audit:

Ensemble	Object	Curvature output	RH criterion
Laplace	Σ wₙ e^(−2πyn)	μ_N(y) = (1/4π²)[T″(y) − Re T″(y−i/N)] — exact	Th 1: limsup|Δκ·X^(−3/2)| < ∞
Dirichlet	Z_D(β) = −ζ(β)ζ′(β+1) — exact	g_D = ∂²log ζ(β) + ∂²log(−ζ′(β+1))	Speiser (1935): ζ′ ≠ 0 in 0 < Re s < ½
Critical	log ξ at s = 1	Li coefficients λₙ, three independent methods	Li (1997): λₙ ≥ 0 for all n

from mtft import dirichlet_curvature, li_criterion_report, hadamard_zetaprime_check

dirichlet_curvature(3.0)     # exact split: ζ piece + ζ′ piece (48.59%)
li_criterion_report(12)      # λ₁..λ₁₂ with the Bombieri–Lagarias caveat attached
hadamard_zetaprime_check(3)  # ∂²log(−ζ′) = 2/(s−1)² − Σ(s−ρ′)⁻²; residual 4e−9
                             # at s=3, certified < 1e−5 across s ∈ [3,10]

The Legend — python -m mtft.legend

mtft computes artifacts of the number line. The Legend is its map key: every function tagged by nature, Arithmetica Generale primitive signature (⟳ ÷ Σ ↑ ∂), epistemic status (Df/Pp/Pr/Conj/Heur/Cert × EXACT/CERTIFIED/DIAGNOSTIC/PHENO), and derivation chain. Zero free parameters means every chain terminates in the integers — and you can watch:

$ python -m mtft.legend trace alpha_inverse
alpha_inverse  [Pr, CERTIFIED(3.5ppm)]
   └─ monster_order  [Pr, EXACT]  └─ integers  → It was always the integers.
   └─ genus_13       [Pr, EXACT]  └─ X0_143 └─ N_143 └─ integers  → ...
   └─ dim_S2_11      [Pr, EXACT]  └─ X0_143 └─ N_143 └─ integers  → ...

$ python -m mtft.legend status        # epistemic audit of the whole surface
$ python -m mtft.legend status EXACT  # just the bedrock you can build on

No other scientific package can ship trace honestly: everyone else's chains end in a fitted constant.

Machine Certificates (Tier 11)

The Jacobian Conjecture counterexample (July 2026) ships as a self-certifying, dependency-free module — its own exact-arithmetic engine re-derives the whole mechanism (constant Jacobian, S₃ monodromy, non-surjective image) on every call. A counterexample cannot be faked:

import mtft
cert = mtft.jc_verify_all(verbose=True)   # det DF = -2, degree 3, JC false n>=3

Installation

pip install mtft            # fresh install
pip install --upgrade mtft  # already installed? pip won't upgrade unless asked

Quick Start

import mtft

# ── Modular forms on X₀(143) ──────────────────────────────
C = mtft.X0(143)                     # the modular curve, LMFDB-anchored
C.genus                              # 13
mtft.dedekind_eta(1j)                # 0.7682254223260566 = Γ(1/4)/(2π^(3/4))

# ── Gauge-Higgs via Hosotani holonomy ─────────────────────
h = mtft.HosotaniMTFT()
h.find_vacuum()                      # the Hosotani angle θ₀
h.gauge_masses()                     # m_W, m_Z, m_H from the holonomy

# ── Mass gap / stiffness ──────────────────────────────────
mtft.filtered_moment_identity(0.18174, N=3)   # exact to machine precision

# ── Falsifiability: the honest scorecard ──────────────────
mtft.falsify.honest_report()         # 23 pre-registered zero-parameter
                                     # predictions, ppm deviations, no cherry-picking

# ── Arithmetic computation (v0.7.0) ───────────────────────
from mtft.arithmetic_machine import decompose_turing_machine
decompose_turing_machine()           # a TM as a five-primitive AG object

CLI: python -m mtft verify | report | tower | screen | info

Package Structure — 35 modules in 16 tiers

Tier	Modules	What lives here
0	constants arithmetic	wₙ weights, X₀(143) structural constants
1	modular modular_curve forms x0_143	Modular geometry, LMFDB-validated newforms
2	hosotani tano_metric	Gauge-Higgs unification, the Tano metric
3	particles koide decay	Spectrum phenomenology
4	lattice burning_ship	Lattice gauge, Burning Ship fermions
5	dimensional_bridge cosmology dark_sector	Bridges & the dark sector
5b	falsify	23 pre-registered predictions, honest scorecard
5c	tower	SU(N) landscape
5d	riemann	Explicit formula, corrected RH diagnostic, Speiser–Hadamard lab
5e	lhcb_analysis	ROOT-bridge confrontation (uproot)
6	quantum	Topological qudits
7	crypto monster_hash	SL(2,ℤ)-sponge hashing
8	info_geometry jacobian	Fisher–Rao curvature, Jacobian engine
9	arithmetic_machine arithmetic_wick busy_beaver music viz	Computation as arithmetic, Wick bridge, sonification
10	critical_ensemble	Li coefficients λₙ — three cross-certified methods
11	jc_counterexample estimator_standards legend	Machine certificates, A.7 estimator standards, the Legend

Key Identities

α⁻¹        = ln|M| + genus − 1/11 + O(10⁻⁴)          Monster ↔ fine structure
μ_N(y)     = (1/4π²)[T″(y) − Re T″(y − i/N)]          mass gap = twisted-curvature gap (exact)
Z_D(β)     = −ζ(β)·ζ′(β+1)                            Dirichlet ensemble closed form (exact)
∂²log(−ζ′) = 2/(s−1)² − Σ_ρ′ (s−ρ′)⁻²                Hadamard over ζ′ zeros (certified < 1e−5, s ∈ [3,10])
λ₁         = 1 + γ/2 − ½ln(4π)                        critical-ensemble anchor (exact)

Visuals

viz/ ships the gallery: hero_stiffness.png + stiffness_navigator.html (regenerate with python viz/make_hero.py), plus React components — X0_143_BurningMandelbrot.jsx, MTFT_HyperbolicTiling.jsx, MTFT_MonsterFingerprint.jsx, mtft_enneper.jsx.

Testing

pytest          # 401 tests: LMFDB anchors, exact identities, audit regressions

Every numerical claim above is a test. The suite gates PyPI publication — nothing ships if anything fails.

Citation

See CITATION.cff. GitHub's "Cite this repository" button does the formatting.

License

MIT — see LICENSE.