# UTFANSWF v23 — Zero State (ZS) Foundational Preflight

## Purpose

This module makes the Zero State -> SWF-ISM handoff executable **without changing historical UTFANSWF row numbering**. The harness uses execution label **Row 0 / ZS** only to place the foundational check before the existing production gate sequence.

## Claim boundary

ZS is treated as a **distinguished zero/reference configuration**, not as a proved unique normalized quantum state. The executable module does not claim that no alternative higher-order foundation exists.

Two manuscript expressions are deliberately hardened in the executable representation:

1. The condition that every admissible operator have spectrum `{0}` is **not** imposed. Such a condition would constrain the operator algebra itself far more strongly than is required to express absence of observable structure at the reference configuration. Instead, the executable condition is state-resolved nullity: all tested one-point/linear responses vanish at `Z`.
2. `C` is treated as a **construction map** from the Zero State reference configuration to an admissible structured Gaussian state. A commutator `[C,Z]` is not used because `Z` is a configuration/state in this construction, not an operator.

## Executable chain

The preflight implements the structural chain

`Z -> vanishing one-point structure -> K=K^T, K>0 -> Q[x]=x^T K x >= 0 -> MaxEnt Gaussian -> SWF-ISM handoff`.

For deterministic finite-dimensional discretizations `n = 1,...,6`, it verifies:

- zero-reference norm;
- vanishing linear and quadratic one-point probes at the reference configuration;
- invariance of the reference configuration under representative orthogonal symmetry actions;
- symmetry/self-adjointness and positive definiteness of canonical test kernels;
- non-negativity of the quadratic form;
- the MaxEnt covariance relation for the constraint `E[x^T K x] = C`;
- `Sigma_* = (C/n) K^{-1}` and, with the canonical choice `C=n`, `Sigma_*=K^{-1}`;
- entropy dominance of the isotropic whitened Gaussian against deterministic anisotropic covariance alternatives preserving the same quadratic constraint.

The canonical finite-dimensional kernels are **implementation probes only**. They are not asserted to be the physical continuum kernel `K(x,x')`.

## PASS rule

ZS is **Critical / Blocking**. PASS requires every numerical check in every tested discretization and every claim-boundary guard to be true.

## Handoff

On PASS, the module exports the admissible structural handoff

`Psi[phi] = N exp(-Q[phi]/2)`

with a positive quadratic kernel. This is the input form used by the SWF-ISM layer. The preflight does not renumber or rewrite the historical Rows 1–29.

## Explicit non-claims

- no proof of global uniqueness of the Zero State;
- no physical prediction for a continuum kernel;
- no mass, length, time, coupling, or cosmological scale derived at ZS;
- no claim that downstream sector mappings are thereby proved.
