# Deterministic Ising audit v1

This proposal-only audit derives an exact six-spin Ising representation from
the frozen p10m atomic-structure cube. It does not train a model, mutate an
optimizer state, read transfer documents, select a structure certificate, or
authorize scaling.

## Exact arithmetic

For vertex `x` and character `A`, the audit computes the unnormalized integer
Walsh coefficient

```text
W(A) = sum_x loss(x) (-1)^(A dot x).
```

With `s_i=(-1)^x_i`, the same coefficients are the integer numerators of the
Ising Hamiltonian

```text
loss(x) = (1/64) sum_A W(A) product_(i in A) s_i.
```

The replay checker independently verifies all 64 inversions and the integer
Parseval identity for Q20 and Q32.

Each frozen temperature uses a positive piecewise-linear dyadic weight. If
`delta=q*T+r`, then its common-scale integer weight is

```text
(2*T-r) 2^(127-q),  0 <= q < 128.
```

This avoids platform math libraries while retaining every vertex in the
ensemble. Reduced integer fractions record the ground-state probability,
expected excess energy, ground-state and Edwards--Anderson overlaps, per-spin
magnetic susceptibility, spin-glass susceptibility, and per-atom
magnetization.

The cubic Walsh residual is then streamed in binary-reflected Gray-code order
through a first-order sigma--delta quantizer with denominator `64`. Every row
records the input numerator, carry before, emitted integer, and carry after.
The checker enforces

```text
sum(input) = 64 sum(emitted) + final_carry
```

and the nearest-integer carry bound `|carry| <= 32`.

## Replay

Run:

```bash
scripts/run-production-atomic-ising-v1.sh
```

The checker regenerates the artifact in a temporary directory and requires
byte equality. The frozen contract binds the source result, source contract,
kernel, analyzer, checker, and the `integer_residual_sgd` optimizer control
tuple (optimizer name, state magic, and state version). Any change to those
bindings fails the audit until an explicit refreeze.

The frozen outputs are:

- `benchmarks/production-model-v1/p10m-atomic-ising-audit-v1-contract.json`
- `benchmarks/production-model-v1/p10m-atomic-ising-audit-v1.json`

The current passing replay hashes are emitted by
`scripts/run-production-atomic-ising-v1.sh` and independently checked against
freshly generated bytes.

## Prospective confirmation verdict

The frozen same-source confirmation on documents `136--199` **supported all
three preregistered endpoints** after exact Holm correction:

- pairwise Ising mask `59` versus baseline: `51/13/0`, aggregate Q32
  `-259574`;
- quenched-Gibbs mask `61` versus baseline: `50/14/0`, aggregate Q32
  `-257908`;
- the frozen `[47,59]` probe router versus global mask `47`: `17/0/47`,
  aggregate Q32 `-88447`.

This is a supported within-source confirmation, not a general Ising-model or
optimizer result. All proposal and confirmation documents come from one source
cluster, documents `200--212` remain sealed, cross-source generalization is
unidentified, and the result authorizes neither paid scaling nor an optimizer
change. The default remains `integer_residual_sgd`.

Clean-checkout replay treats the hash-bound production structure cubes as
frozen inputs because the model and corpus data are not repository artifacts.
The structure checker independently reconstructs every integer cube; the
document-Ising, audit, confirmation-contract, and confirmation-result checkers
then regenerate their derived JSON and require byte equality. The passing
confirmation contract/result SHA-256 values are
`57084a50c82883cb7d6c6d449b699cf793d495e293cf33ea1318b04aad71c9ce`
and `106f4724056a483d84e9ee2cd178fa54a7164ed85ad6475770cea172e7dbf0a3`.