# UTFANSWF v23 — SWF-ISM Information-State Foundational Preflight

## Purpose

This module makes the SWF-ISM layer executable between the Zero State (ZS) foundation and the downstream ANSWF EFT-admissibility layer. It uses execution label **0.1 / SWF-ISM** only for harness ordering; historical UTFANSWF row numbering is not changed.

## Upstream dependency

SWF-ISM requires the ZS preflight to return:

`PASS_ZS_FOUNDATION_TO_SWF_ISM_HANDOFF`.

The gate therefore tests a real dependency rather than treating the foundational layers as independent demonstrations.

## Executable scope

The gate validates only the information-state mathematics assigned to SWF-ISM:

- a nonnegative normalized density `rho(Omega)` on `S^2`;
- the sphere measure `int dOmega = 4*pi`;
- low-order spherical-harmonic orthonormality and coefficient extraction;
- the neutral uniform information state `rho0 = 1/(4*pi)` with `a00 = 1/sqrt(4*pi)` and vanishing higher modes;
- Shannon entropy and relative entropy to the uniform state;
- maximum-entropy dominance of the uniform state when only normalization is imposed;
- exponential-family normalization and the identities `d log Z / d lambda = <phi>` and `d^2 log Z / d lambda^2 = Var(phi) >= 0` for deterministic quadrupole probes;
- a numerical `SO(2)_z` averaging projector that preserves positivity/normalization, is idempotent, and suppresses `m != 0` harmonic content;
- consistency of a synthetic nonnegative spectral-weight representation through positivity and monotonicity of its Euclidean response.

The spherical quadrature and synthetic spectral measure are deterministic implementation probes. They are not physical observations or fitted targets.

## Layer boundary

The executable split is deliberately strict:

`ZS -> SWF-ISM -> ANSWF -> SANSWF -> UTFANSWF`.

SWF-ISM ends at the information-state / harmonic / MaxEnt / Gaussian-spectral structure. This gate does **not** claim to perform:

- ANSWF forward-limit EFT positivity or scattering-amplitude admissibility;
- SANSWF gauge covariance, bounded-from-below cones, or perturbative-unitarity enforcement;
- unified embedding, threshold matching, cosmological closure, or other downstream UTFANSWF physics.

This prevents early manuscript workup language from collapsing distinct layers into one executable claim.

## PASS rule

SWF-ISM is **Critical / Blocking**. PASS requires:

1. the ZS handoff to PASS;
2. every information-state numerical identity encoded in the gate to pass its declared tolerance;
3. every claim-boundary guard to remain true.

## Handoff

On PASS the gate exports an admissible SWF-ISM information state described by:

- normalized nonnegative `rho(Omega)`;
- harmonic coefficients `a_lm`;
- a maximum-entropy neutral reference state;
- the Gaussian/spectral consistency structure inherited from ZS.

The next executable layer is ANSWF, which must independently establish the EFT positivity/analyticity/causality constraints rather than inheriting them by assertion.
