Metadata-Version: 2.4
Name: edtm-sommerfeld
Version: 0.2.0
Summary: The fine structure constant at the chiral phase transition: alpha*^-1 = 128 pi/3 from a gravitational fixed point, matched to the measured running at -0.046% by a closed form independent of all dispersive data (paper F-C of the Eternal Dawn programme)
Author: Michael Gronager
License: MIT
Requires-Python: >=3.10
Description-Content-Type: text/markdown
Requires-Dist: numpy>=1.24
Requires-Dist: scipy>=1.10
Provides-Extra: test
Requires-Dist: pytest; extra == "test"

# edtm-sommerfeld — the fine structure constant at the chiral phase transition

(The package is named for Arnold Sommerfeld, who introduced the
constant; α is Sommerfeld's constant.)

The headline needs no computer:

    alpha*^-1 = 24π/(1 − f)² = 128π/3 = 134.04    (f = 1/4),

a pocket-calculator number — the depleted fixed point of the photon's
charge flow in the near-conformal window that the Lichnerowicz
curvature coupling opens above the chiral melt, with the wall's
registry count removing one quarter of the fermionic states. What
needs Python is everything that makes that number *checkable*: the
matching to the measured running, and the theorem that makes the
comparison exact.

The chain this package computes:

* **the anchor**, μ\* = 2Λ = 1.389 GeV — kinematics, derived;
* **the one-rule matching** (+0.19 total): per species,
  c = window log − A0INV·Δα(μ\*²), with the exact one-loop lepton
  dispersion and the Mainz lattice hadronic VP;
* **the universal two-loop**, 11/24π;
* **THE COMPOSITION THEOREM**: in the composed residual every
  dispersive term — leptonic *and* hadronic — cancels identically
  between the matching and the running. The landing is the closed
  form

      R = A0INV − 128π/3 − 11/24π − Σ(window logs) = +0.0619,

  i.e. **−0.046%, exact, with no hadronic data load-bearing
  anywhere** (verified here: the residual is identical across four
  different spectral inputs to 3×10⁻¹⁴);
* **the exact third order** (Gell-Mann–Low scheme, the decomposition
  Furry-unique): δ₂ = +0.0009 on α\*⁻¹ — one part in 170 of the
  second order; the matter series is converged;
* **the drag's protection**: the gravity side has no small
  parameter, so the observed 4.6-bp landing bounds the drag's own
  corrections below 5×10⁻⁴ of natural size — f̂ = 1/16π² is a
  counting number of the registry, like f = 1/4 itself;
* **the walk's exit, derived**: the remaining 4.5 bp are the exit
  term, with both factors derived — the claim window ln(4/3) from
  the exit's thresholds (μ\* = 4M_c down to the fermion–σ threshold
  3M_c), and the share f/2 as the mean of the claim's linear ramp at
  the scale-invariant fixed point (the order parameter vanishes
  across the window; no interior scale). I = (f/2)ln(4/3) = ln(4/3)/8
  meets the requirement at 0.2%, and the ledger closes at 0.01 bp.
  The remaining approximation is the sharp reading of the window's
  boundaries (second order).

```
pip install edtm-sommerfeld
python -c "import edtm_sommerfeld; edtm_sommerfeld.scoreboard()"
```

Inputs, declared exactly (the programme's audit ledger): nothing
beyond {G, ℏ, c} and the framework's own m_n chain — the melt scale
Λ = 0.6946 GeV and the lepton/constituent masses are the programme's
own outputs (papers F-A/F-B). The measured Thomson α is the
*comparison target*, never an input to the prediction. The GML
three-loop coefficient is exact loop mathematics
(Gorishny–Kataev–Larin–Surguladze; Kataev–Molokoedov), sourced like
the exact leptonic dispersion integrals. The Mainz lattice hadronic
VP is bookkeeping for the per-species split and cancels identically
from the composed landing — swap it for the data-driven variant or
the programme's own native spectral function (`edtm-meson`) and the
landing does not move; that is the theorem.

This package accompanies paper F-C of the Eternal Dawn programme;
the derivation-complete source is the textbook (*Eternal Dawn — The
Torsion Model*, chs. 06/14/15). Companion packages: `edtm-spectrum`
(the charged spectrum, F-A), `edtm-dressing` (the ppm dressing,
F-B), `edtm-meson` (the two-quark droplets whose spectral function
witnesses the native running, F-E).
