# UTFANSWF v23 — ANSWF EFT Positivity / Admissibility Preflight

## Purpose

This module makes the ANSWF layer executable between SWF-ISM and SANSWF. It uses harness execution label **0.2 / ANSWF** only; historical UTFANSWF row numbering is unchanged.

## Upstream dependency

ANSWF requires:

`PASS_SWF_ISM_INFORMATION_STATE_FOUNDATION_TO_ANSWF_HANDOFF`.

## Conditional foundation

The forward-dispersion argument is conditional on the standard S-matrix assumptions stated in the manuscript: analyticity at fixed regulated momentum transfer, crossing, unitarity/optical-theorem positivity, suitable polynomial boundedness/subtractions, and an IR-safe treatment of gravity.

ANSWF does **not** claim to derive those assumptions from the Zero State or SWF-ISM. It checks the EFT sign consequences once those assumptions are imposed.

## Executable checks

The gate validates:

- a deterministic positive absorptive/spectral density gives positive twice-subtracted forward curvature;
- zero absorptive strength gives zero curvature, explicitly preventing an unconditional strict-positivity overclaim;
- for the stated single-scalar normalization, `A_fwd = 4 c4 s^2 / Lambda^4` implies `d^2 A/ds^2 = 8 c4/Lambda^4`, so the curvature sign follows `c4`;
- the two-field condition `A >= 0`, `B >= 0`, `C + sqrt(A B) >= 0` agrees with a dense numerical angular scan of the quartic form;
- subtraction of the known synthetic graviton-like `s^2/t` pole recovers the regular amplitude and curvature at several positive `t` values;
- the current `datasets/positivity_wilsons.yaml` inputs are finite/positive, including a positive `c_phi4` margin.

The synthetic absorptive density and gravity-pole parameters are implementation probes only. They are not measured cross sections, a prediction of Newton's constant, or a fitted physical amplitude.

## Layer boundary

ANSWF is the **EFT admissibility** layer. It does not absorb the downstream SANSWF responsibilities:

- gauge covariance;
- bounded-from-below scalar-potential cones;
- perturbative partial-wave unitarity;
- anomaly cancellation and unified symmetry embedding.

## PASS rule

ANSWF is **Critical / Blocking**. PASS requires the SWF-ISM handoff, all encoded positivity/admissibility checks, and all non-overclaim guards.

## Handoff

On PASS the gate hands an EFT-admissible slice to SANSWF, where gauge/symmetry and dynamical stability conditions must be checked independently.
