# UTFANSWF — Global Nonperturbative Electromagnetic Frontier
## 2026-08-19

**Scope:** private research architecture checkpoint.  
**Production/public artifacts:** unchanged.

## Why Items 01 and 05 are one remaining problem

The two surviving boundaries are generated by the same QCD electromagnetic current-current sector.

### Vacuum channel — Item 01

Define the renormalized electromagnetic current \(J_\mu^R\). The vacuum polarization tensor is

\[
\Pi_{\mu\nu}(q)
=
\int d^4x\,e^{iqx}
\langle0|T\,J_\mu^R(x)J_\nu^R(0)|0\rangle .
\]

Its scalar vacuum-polarization function supplies the nonperturbative hadronic contribution to the running of the electromagnetic coupling,

\[
\Delta\alpha_{\rm had}^{(5)}.
\]

This is the remaining low-energy transport object in the blind 1/137 chain.

### Nucleon channel — Item 05

Using the same current,

\[
T_{\mu\nu}^{N}(p,q)
=
\int d^4x\,e^{iqx}
\langle N(p)|T\,J_\mu^R(x)J_\nu^R(0)|N(p)\rangle ,
\]

is the forward nucleon Compton tensor.

After the appropriate photon-kernel integration, renormalization/matching and finite-volume treatment, this channel supplies the nucleon electromagnetic self-energy. In the proton/neutron isoscalar-isovector basis it contains the missing absolute common response

\[
\Delta_+^{\rm QED}
=
\frac12\left(\Delta M_p^{\rm QED}+\Delta M_n^{\rm QED}\right),
\]

which cannot be determined from baryon mass splittings.

## Unified production object

The remaining UTFANSWF frontier can therefore be represented as

\[
\boxed{
\mathcal R_{\rm EM}^{\rm NP}
=
\left[
\Pi_{\gamma\gamma}^{\rm vac},
\;
T_{\gamma\gamma}^{p},
\;
T_{\gamma\gamma}^{n}
\right]
}
\]

computed with one common contract:

1. physical-point dynamical QCD ensembles;
2. a single renormalized electromagnetic current;
3. fixed quark-mass renormalization/matching convention;
4. connected and disconnected current contractions;
5. controlled continuum extrapolation;
6. controlled infinite-volume/QED finite-volume treatment;
7. common short-distance matching to perturbative QCD where required;
8. no proton mass or electromagnetic-alpha holdout used to tune the result.

## Existing pieces

Modern lattice calculations already demonstrate the two halves separately:

- physical-point CLS calculations determine the hadronic running of the electromagnetic coupling and, using a Euclidean-split lattice+pQCD construction, obtain a first-principles \(\Delta\alpha_{\rm had}^{(5)}(M_Z^2)\);
- second-order Feynman-Hellmann lattice methods directly compute the forward nucleon Compton tensor;
- physical-pion lattice calculations of the forward-Compton subtraction function have reached the nucleon isovector electromagnetic self-energy.

These establish feasibility of the operator class, but they do not yet provide the single matched physical-continuum vacuum+nucleon response package required by the strict UTFANSWF internal closure contract.

## Global consequence

The remaining research status is not

- Item 01 has an unrelated HVP problem, and
- Item 05 has an unrelated proton-QED problem.

Instead:

\[
\boxed{
\text{Item 01 + Item 05}
\longrightarrow
\text{one nonperturbative QCD electromagnetic response layer}.
}
\]

That is the correct global ownership.

## Current eight-item research disposition

1. Item 01 — upstream/EW normalization closed; **blocked only at the shared nonperturbative EM response frontier** for a strict first-principles no-external-hadronic-input closure.
2. Item 02 — **CLOSED** global source-complete distributed-H0 operator.
3. Item 03 — **CLOSED as conditional/self-consistent heavy-boundary candidate**; no unique ratio selector.
4. Item 04 — **CLOSED / PASS candidate** flavor dynamics; NZ P3 reversal globally invariant.
5. Item 05 — isoQCD + isovector bridge closed; **blocked only at the shared nonperturbative EM response frontier** for absolute charged-proton completion.
6. Item 06 — exact Z6 **CLOSED / PASS**; projector/heavy uniqueness **CLOSED / CLEAN FAIL**.
7. Item 07 — **CLOSED** at declared JWST/axion claim boundary.
8. Item 08 — **CLOSED** release/provenance synchronization.

## Verdict

`PASS_GLOBAL_REDUCTION__ITEM01_AND_ITEM05_SHARE_ONE_NONPERTURBATIVE_QCD_EM_RESPONSE_FRONTIER__NO_INTERNAL_ALGEBRAIC_SELECTOR_REMAINS`

No missing scalar coefficient should be fitted locally.
No public prediction is changed by this checkpoint.
