# UTFANSWF Research Program — Item 03 Closeout

**Item:** Blind heavy-threshold closure  
**Date:** 2026-08-17 (America/New_York)  
**Production v23 status:** UNCHANGED / PROTECTED 18-of-18 canonical harness PASS  
**Research verdict:** `BLOCKED_TWO_DIMENSIONAL_HEAVY_THRESHOLD_MANIFOLD__NO_UNIQUE_BLIND_EM_PREDICTION`

## 1. Blind contract

The audit fixes only the UTFANSWF-native primitive boundary and the allowed QCD datum:

- `alpha_U^-1 = 8*pi`;
- `alpha_3(M_Z) = 0.1184` may determine one scale condition;
- `M_Sigma/M_U = sqrt(2)/5 = 0.282842712474619`;
- measured `alpha_1(M_Z)` and `alpha_2(M_Z)` are not used;
- no electromagnetic target or historical electroweak endpoint is used.

The corrected heavy weights are

- `H_C = (2/5,0,1)`;
- `Sigma_3+Sigma_8 = (0,2,3)`;
- `X/Y = (-10,-6,-4)`.

## 2. Native-source audit

The current UTFANSWF source declares the unified threshold object as

`T = (M_HC, M_X, M_Sigma)`.

Its threshold solver explicitly leaves a free ratio and instructs the calculation to **pick** `rho=M_Sigma/M_X` (or impose equality) after the coupling combinations are formed. That is an input boundary, not a prediction.

The declared `H-Sigma` stability potential is quartic only. It contains no complete SU(5)-breaking mass/cubic superpotential and no GUT-breaking VEV/coupling map from which `M_HC/M_U` and `M_X/M_U` can be calculated. Therefore `(lambda_H,lambda_A,lambda_p)` does not close the heavy spectrum.

The exact-`Z6` proton-stability branch also does not determine these ratios; it removes the conventional `Delta B=1,2` lifetime-selection route rather than supplying a unique heavy spectrum.

## 3. Identifiability proof

After fixing `alpha_U`, `M_Sigma/M_U`, and hence

`L_Sigma = ln(M_U/M_Sigma) = 1.262864322154128`,

the remaining blind coordinates may be written

`(ln M_U, L_HC, L_X)`.

Requiring the downward two-loop run to reproduce the allowed QCD datum `alpha_3(M_Z)=0.1184` provides **one scalar equation**. Therefore, absent two additional independent native relations, the solution set is generically two-dimensional.

This is not only a parameter count. The frozen probe explicitly solves `M_U` for a grid of `(L_HC,L_X)` values while enforcing `alpha_3(M_Z)=0.1184` to numerical precision. All 25 tested points close QCD, yet the predicted electroweak inverse coupling spans

`118.697179240 <= alpha_em^-1(M_Z) <= 134.246131528`.

Near `(L_HC,L_X)=(0,0)`, the numerical sensitivities are

- `d alpha_em^-1 / d L_HC ~= 0.772174348`;
- `d alpha_em^-1 / d L_X ~= -6.230037793`.

So the electromagnetic output moves materially along directions that the current blind data do not constrain.

## 4. Why the pinned repair cannot close the blind route

The existing corrected spectrum near

- `M_HC = 1.8700319287e16 GeV`;
- `M_X = M_Sigma = 1.0831613303e16 GeV`;
- `alpha_U^-1 = 25.7910032280`

is a valid **pinned low-energy closure diagnostic**, but it was solved using `alpha_1(M_Z)` and `alpha_2(M_Z)`. Importing those masses into the blind electromagnetic route would reintroduce the quantity family being predicted and violate the blind contract.

## 5. Final disposition

The blind heavy-threshold problem is not presently solvable uniquely from the declared UTFANSWF-native boundary. The strongest justified status is

`BLOCKED_TWO_DIMENSIONAL_HEAVY_THRESHOLD_MANIFOLD__NO_UNIQUE_BLIND_EM_PREDICTION`.

This is an identifiability boundary, not a numerical failure of the corrected SU(5) threshold algebra.

**Production consequence: none.** The protected v23 18/18 PASS executable remains unchanged because its unification result is explicitly scoped as a pinned-input existence/closure check, not a blind electromagnetic prediction.

Reopen Item 03 only if at least two genuinely independent, target-free heavy-boundary relations are supplied—for example, a fully declared SU(5)-breaking superpotential/VEV/coupling sector that predicts `M_HC/M_U` and `M_X/M_U` before electroweak data are revealed.
