# OPERA QUANTITAS EX QUALITAS — Execution Mechanism

Version: `1.0.0-OPERA-QUANTITAS-EX-QUALITAS`
Status: `IMPLEMENTATION-READY CANDIDATE / NON-RUNTIME`
Authority: `USER / HUMAN CONTROL PLANE`
Class: `AGLA / OPERA / ARITHMETICA`
Artifact ID: `OPERA-QUANTITAS-EX-QUALITAS`
Direction: `QUALITAS -> QUANTITAS`

Source alias: `OPERA-EX-QUALITAS`, retained for provenance only.

## I. Dependencies

- root OPERA class law;
- `TENET_ARITHMETICA_DoctrinalInvariants.md`, especially Sections VIII-X,
  XIV-XIX;
- operation-specific admission from
  `AREPO_ARITHMETICA_InputAdmissibility.md`;
- `ROTAS_ARITHMETICA_StructuralInstantiation.md`;
- mediation by `SATOR_ARITHMETICA_OutputRequirements.md`.

This artifact specifies one OPERA. Shared normalization, rule, generation,
trace, handoff, ordinal, and GRAPHUS invariants are inherited from TENET.

## II. Native purpose

OPERA QUANTITAS EX QUALITAS compiles admitted qualitative requirements into
typed quantitative predicates, searches an admitted domain, and returns zero,
one, or many quantitative candidates.

The operation is reverse constraint compilation and search. It is not presumed
to be a total, unique, lossless, or mathematical inverse of
OPERA QUALITAS EX QUANTITAS.

## III. OPERA-specific input

```text
QUANTITAS_EX_QUALITAS_INPUT:
  qualitative_constraint_ref
  supplied_quality_terms[]
  normalization_vocabulary_ref
  target_quantitative_types[]
  search_domain_ref
  predicate_compiler_ref
  uniqueness_requirement
```

Unregistered synonyms and undecomposed compound qualities remain unresolved.

## IV. Execution

1. preserve the supplied qualitative tokens;
2. normalize only through a registered vocabulary;
3. compile each admitted quality into explicit quantitative predicates;
4. bind the declared numeric domain and state schema;
5. generate candidates using only declared rule adapters;
6. verify every quantitative candidate;
7. reduce through predicate satisfaction, constraints, equivalence, dominance,
   and resource bounds;
8. preserve ambiguity and rejected alternatives;
9. establish uniqueness only when formally demonstrated;
10. return candidate set, reduction trace, and state delta.

The bounded cardinal register may return a familiar carrier, but familiarity
alone never resolves ambiguity in a wider admitted domain.

## V. Output

```text
QUANTITAS_EX_QUALITAS_RESULT:
  supplied_quality_terms[]
  canonical_quality_records[]
  normalization_records[]
  compiled_predicates[]
  search_domain_ref
  generated_candidate_refs[]
  accepted_quantitative_states[]
  accepted_quantitative_relations[]
  rejected_candidate_refs[]
  deferred_candidate_refs[]
  uniqueness_status: ZERO | ONE | MANY | UNRESOLVED
  reduction_trace_ref
  actual_state_delta
  arithmetica_generation_trace_ref
```

## VI. Native failures

- `QUALITY_UNKNOWN`
- `SYNONYM_TABLE_NOT_REGISTERED`
- `COMPOUND_QUALITY_UNRESOLVED`
- `PREDICATE_COMPILATION_FAILED`
- `SEARCH_DOMAIN_MISSING`
- `CARRIER_INVENTED`
- `REVERSE_SEARCH_UNIQUENESS_INVENTED`
- `QUALITATIVE_REQUIREMENT_USED_AS_NUMERIC_PROOF`

## VII. Final law

OPERA QUANTITAS EX QUALITAS searches quantity under admitted qualitative
constraints. It preserves zero, one, many, and unresolved results without
inventing uniqueness or mediating the final output.