# Backend Lowering Registry and Semantic Plan Cache
P186 separates semantic operator registration from backend lowering registration while keeping the existing `OperatorRegistry` facade compatible.
## Registry Boundary
`OperatorRegistry` still owns semantic operators: names, signatures, contracts, and layer behavior.
`BackendLoweringRegistry` owns backend-specific lowering rules:
- lowering rule id
- semantic operator name
- backend name
- supported representations
- supported domains
- mathematical lowering capabilities
- required evidence
- lowering obligations
The facade `OperatorRegistry` now composes both pieces. It still rejects lowerings for unknown semantic operators, but the backend lowering registry can also be used independently by later backend packages and plugin-style lowering providers.
## Cache Key Boundary
`PlanCacheKey` now records:
- semantic graph digest
- shape class
- domains
- representations
- contracts
- backend name
- backend fingerprint
- backend capability vector
- mathematical constraint fingerprint
- capability version
- selected lowering rule ids
This means cache entries invalidate when any of these change:
- graph semantics or shape class
- mathematical domain or contract constraints
- backend capability descriptors
- selected lowering rule ids
The key intentionally keeps semantic operator identity separate from backend lowering identity. Two plans may share the same semantic graph digest while having different lowering rule ids or backend capability versions.
## Proof Replay Fingerprint
`proof_replay_plan_fingerprint` includes the new cache fields. This keeps proof/audit artifacts bound to the backend and mathematical constraints that produced the plan, not just to graph shape and backend name.
## Non-Claims
P186 does not add a persistent disk cache, distributed cache invalidation, backend plugin loading, or kernel compilation cache. It defines the in-memory registry and key structure needed for later backend modularity and audit-bound caching.