# Mathematics-Bound Audit Traces
P188 adds a dedicated audit artifact for decisions that depend on both hardware/backend state and mathematical constraints.
## Artifact
The new artifact is:
```text
tokitai-math-bound-audit-trace
```
Version 1 fields:
- `plan_fingerprint`
- `backend_id`
- `device_kind`
- `capability_fingerprint`
- `p_adic_constraint_fingerprint`
- `sheaf_constraint_fingerprint`
- `lowering_rule_ids`
- `fallback_reason`
- `conformance_result`
- `benchmark_environment`
The artifact is schema-listed in `docs/schemas/tokitai-artifacts-v1.schema.json` and can be attached to proof replay trace manifests.
## Semantics
`capability_fingerprint` binds the trace to the backend capability identity used by the planner.
`p_adic_constraint_fingerprint` records fixed-precision p-adic planning resources when present, including prime, precision, valuation cutoff, equality digits, backend capability, and fallback state.
`sheaf_constraint_fingerprint` records finite-site cover-local constraints when a cover glue plan is present.
`lowering_rule_ids` records the selected backend lowering rules, making registry decisions reproducible.
`fallback_reason` is copied from planner/backend fallback evidence when a mathematical capability or backend execution path is unavailable.
`conformance_result` links cross-backend conformance runner output to the audit artifact.
`benchmark_environment` is optional and intended for later benchmark matrices. P188 uses it only as scoped metadata, not as a performance claim.
## Non-Claims
P188 does not add a new proof system or prove backend correctness. It makes existing backend and mathematical decision evidence reproducible in audit artifacts so future papers, patents, and release gates can inspect the execution boundary.