# UTFANSWF v23 — Unified Embedding Preflight

## Purpose

This module makes the first complete executable handoff from SANSWF into the UTFANSWF unified layer. Execution label **0.4 / UTFANSWF** is a harness-ordering label only; historical row numbering is preserved.

## Active v23 boundary

The gate deliberately distinguishes **active v23 branches** from preserved historical branches. The old `datasets/unification_tau.yaml` file is retained unchanged for provenance but is explicitly marked `HISTORICAL_LEGACY_NOT_ACTIVE` in `datasets/v23_active_registry.json`.

The active v23 unified branch combines:

- explicit SU(5) representation anomaly cancellation;
- the Standard-Model anomaly-free decomposition per generation;
- a benchmark type-I seesaw consistency check;
- the protected two-loop `Sigma_3 + Sigma_8` unification-existence branch with pinned low-energy couplings;
- the exact-`Z6` proton-stability candidate carried by Row 28.

## SU(5) anomaly cancellation derived explicitly

The gate constructs the 24 fundamental `SU(5)` generators with `Tr(Ta Tb)=1/2 delta_ab`. It then constructs the antisymmetric two-index `10` representation on `wedge^2 5` and the `5bar` generators.

For each representation it computes

`D_abc = Tr(T_a {T_b,T_c})`.

Numerically, under the same fundamental normalization,

- `A(10)/A(5) = +1`;
- `A(5bar)/A(5) = -1`;
- `D_abc(10) + D_abc(5bar) = 0` to floating-point precision.

Thus each `10 + 5bar` generation is explicitly anomaly-free in the executable representation, rather than accepted only by assertion.

The gate independently checks the SM decomposition: `SU(3)^3`, `SU(3)^2 U(1)_Y`, `SU(2)^2 U(1)_Y`, `U(1)_Y^3`, gravitational-`U(1)_Y`, and the even SU(2)-doublet Witten parity all cancel per generation.

## Seesaw benchmark

The type-I seesaw formula is treated as a **benchmark parameterization**, not a solution of the full flavor problem. In a diagonal `M_R` basis with the implicit Casas-Ibarra-like choice `R=I`, the gate constructs

`Y_nu = sqrt(M_R) sqrt(m_diag) U^T / v_u`

for a deterministic orthogonal mixing matrix and verifies

`-v_u^2 Y_nu^T M_R^-1 Y_nu = -U m_diag U^T`.

For the largest declared benchmark values `M_R=1.2e15 GeV`, `m_nu=0.05 eV`, `v_u=174 GeV`, the exact single-scale Yukawa is approximately `1.40775`, below `sqrt(4*pi)`. The older `~1.44` shorthand is not used for those exact inputs.

## Protected two-loop unification existence branch

The active branch uses the same protected two-loop response encoded in the post-v22 proton-stability work:

- pinned low-energy couplings `(alpha1,alpha2,alpha3)=(0.01695,0.03377,0.1184)`;
- SM running to `M_SUSY=3 TeV`, then MSSM-like two-loop running;
- retained adjoint `Sigma_3+Sigma_8` threshold weight `(0,2,3)`;
- `M_Sigma/M_U = 1/(5 sqrt(1/2))`.

The gate minimizes the inverse-coupling spread and requires the relative spread to remain below `0.1%`. This is an **existence/consistency result using pinned low-energy couplings**, not a blind prediction of those couplings.

The rank-3/rank-2 split also reproduces `Tr(Y^2)=5/6` and `g1^2/gY^2=5/3`.

## Proton prediction propagation

The exact-`Z6` parent/residual anomaly and operator checks are recomputed so the unified layer cannot accidentally leave the old conventional proton-decay prediction active.

Active v23 candidate state:

- `DeltaB=1`: forbidden;
- `DeltaB=2`: forbidden;
- selection rule: `DeltaB=3*k`;
- isolated proton width under exact `Z6`: `0`;
- old finite single-proton lifetime forecast: `HISTORICAL_SUPERSEDED_BRANCH`.

The gate does not produce a trinucleon lifetime because the `DeltaB=3` Wilson coefficient/scale remains unfixed.

## Open UV boundary

The primitive candidate `alpha_U^-1=8*pi`, using only `alpha_3(M_Z)` to fix the scale, remains a separate blind UV-boundary diagnostic. It is run and reported, but it does **not** get converted into a pass by the pinned-input unification existence result. Its old 1% electromagnetic holdout gate remains missed at about 1.15%.

## PASS rule

UTFANSWF unified embedding is **Critical / Blocking** at the declared pinned-input boundary. PASS requires the SANSWF handoff, anomaly cancellation, seesaw benchmark consistency, protected unification existence, exact-Z6 structural propagation, and correct active/legacy dataset labeling.

A PASS here does not close the blind UV coupling-origin problem, the full flavor problem, SO(10)/heterotic numerical branches, or the `DeltaB=3` lifetime.
