# UTFANSWF v22 - SU(5) Threshold / 1-over-137 Repair Audit

Status: repair candidate. No new physics and no fitted parameter introduced.

## Corrections made

1. Corrected the minimal supersymmetric SU(5) heavy-threshold weights to
   - H_C: (2/5, 0, 1)
   - Sigma: (0, 2, 3)
   - X,Y: (-10, -6, -4)
2. Corrected the second unification combination to
   C2 = -(1/(2*pi)) [24 ln(mu/MX) + 12 ln(mu/MSigma)].
3. Corrected the rho-parametrized solutions:
   - ln(mu/MX) = -(pi/18) C2 + (1/3) ln(rho)
   - ln(mu/MSigma) = -(pi/18) C2 - (2/3) ln(rho)
4. Corrected the main-text factor-of-two normalization where the formula used ln(mu/M) rather than ln(mu^2/M^2).
5. Retired the legacy heavy-mass/proton-lifetime PASS claims that depended on the inconsistent threshold algebra.
6. Corrected the legacy NZ/PPC inequality: 56.67 > 26.29, so that legacy diagnostic is not a PASS. The active Row 22 NZ-sandwich gate is separate and remains unchanged.

## Repaired reproducibility diagnostic

Command:

    python -m harness.gate_row27_unification_alpha

Pinned inputs used by the canonical repair diagnostic:
- alpha1(MZ) = 0.01695
- alpha2(MZ) = 0.03377
- alpha3(MZ) = 0.1184
- MZ = 91.1876 GeV
- MSUSY = 3 TeV
- matching scale = 9.8e15 GeV
- rho = MSigma/MX = 1
- two-loop gauge-only SM -> MSSM running
- one-loop MSbar -> DRbar scheme conversion at MSUSY

No tan(beta), top-Yukawa value, SUSY threshold spectrum, or electromagnetic target is fitted.

The corrected round-trip closure gives:
- MHC = 1.8700319e16 GeV
- MX = MSigma = 1.0831613e16 GeV
- alphaU^-1 = 25.7910032
- residual spread among the three threshold-corrected inverse gauge couplings: ~3.6e-15

This is a closure diagnostic, not an independent low-energy prediction, because the measured low-energy gauge couplings are inputs to the solve.

## Legacy spectrum check

Using the old published spectrum (MHC=1.08e18 GeV, MX=1.11e16 GeV, MSigma=1.73e16 GeV) with the repaired threshold map and alpha3 alone as the UV normalization gives a predicted electroweak electromagnetic inverse coupling near 129.71 in the canonical gauge-only repair diagnostic, versus the bundle target 127.9405. The old spectrum therefore does not survive the repaired blind matching test.

## 1/137 test

Status: BLOCKED_BY_UV_BOUNDARY.

The test is deliberately not forced closed. A genuine UTFANSWF prediction requires an independent UTFANSWF-native condition that fixes alphaU and the GUT/SUSY matching data before using the measured electromagnetic coupling. V22 does not currently supply that boundary condition or a native nonperturbative MZ -> q=0 vacuum-polarization bridge.

The earlier exploratory tan(beta) fit is not used in this repair.

## Source provenance for the threshold repair

The corrected one-loop decoupling structure follows the standard minimal supersymmetric SU(5) heavy-threshold coefficients. A primary reference is:

W. Martens, L. Mihaila, J. Salomon, M. Steinhauser, "Minimal Supersymmetric SU(5) and Gauge Coupling Unification at Three Loops," arXiv:1008.3070, especially Eqs. (2)-(4).

The two-loop MSSM gauge-running structure follows standard supersymmetric RGE results, e.g. S. P. Martin and M. T. Vaughn, arXiv:hep-ph/9311340. The MSbar/DRbar conversion is treated as a standard scheme-matching step; no new UTFANSWF physics is introduced.
