# CPU Oracle Conformance
P181 makes `CpuScalarBackend` the reusable semantic oracle for future backend
work. The point is not that CPU is special hardware; it is the reference path
that already carries exact integer execution, fixed-precision p-adic execution,
finite-site sheaf checks, and contract-level categorical witnesses.
The conformance suite lives in `backend::conformance` and emits a
`CpuOracleConformanceReport`. Each fixture records:
- the fixture name and mathematical family;
- the backend and hardware capability fingerprint;
- the capability gate that had to be satisfied before execution;
- checked output ids where applicable;
- evidence explaining what the CPU oracle checked.
The initial P181 fixture set is deliberately scoped:
- dense i64 add/reduce;
- p-adic pointwise add/mul;
- p-adic dense matmul;
- p-adic valuation-skip sum-products compared against dense p-adic execution;
- finite-site sheaf gluing with restriction-witness evidence;
- categorical identity/associativity at contract-witness scope.
This is not a complete conformance framework for arbitrary backends yet. P181
establishes the CPU oracle artifacts that P184 can reuse when comparing future
GPU or accelerator outputs. The categorical fixture is also intentionally a
contract-level witness, not a claim of full category-theory formalization.