# OPERA QUALITAS EX QUANTITAS — Execution Mechanism

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

Source alias: `OPERA-EX-QUANTITAS`, 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 not duplicated here.

## II. Native purpose

OPERA QUALITAS EX QUANTITAS receives admitted quantitative carriers,
relations, derivations, matrices, or state-space subsets and produces
traceable qualitative elaborations.

It does not claim that a number is identical to a quality. It does not use
qualitative fit as proof of arithmetic truth.

## III. OPERA-specific input

In addition to the shared request envelope defined by TENET:

```text
QUALITAS_EX_QUANTITAS_INPUT:
  quantitative_input_ref
  quantitative_carriers[]
  quantitative_relations[]
  declared_layer
  declared_base
  projection_rule_refs[]
  requested_qualitative_scope
```

The quantitative input must already be admitted and truth-checkable.

## IV. Execution

1. normalize quantitative representations under the TENET normalization law;
2. verify each quantitative statement independently;
3. bind available cardinal mappings without inventing absent qualities;
4. classify admitted relations and patterns;
5. apply only declared qualitative projection rules;
6. generate candidate elaborations;
7. test candidates against scope, provenance, coherence, and constraints;
8. retain, reject, defer, or deduplicate each candidate with reason;
9. return the reduced qualitative set and state delta.

A carrier in `1..10` may use the bounded cardinal register. A carrier outside
that register remains quantitatively valid but returns
`NO_REGISTERED_QUALITY` unless another admitted projection rule applies.

## V. Output

```text
QUALITAS_EX_QUANTITAS_RESULT:
  intrinsic_quantitative_records[]
  original_carriers[]
  quantitative_truth_status
  cardinal_mapping_records[]
  candidate_elaborations[]
  accepted_elaborations[]
  rejected_elaborations[]
  deferred_elaborations[]
  projection_rule_refs[]
  reduction_trace_ref
  actual_state_delta
  confidence_and_limits
  arithmetica_generation_trace_ref
```

## VI. Native failures

- `NORMALIZATION_FAILED`
- `BASE_REQUIRED`
- `ARITHMETIC_FALSE`
- `NUMBER_QUALITY_COLLAPSE`
- `QUALITY_INVENTED_OUTSIDE_REGISTER`
- `PROJECTION_RULE_MISSING`
- `QUALITATIVE_FIT_USED_AS_NUMERIC_PROOF`
- `QUALITATIVE_BRANCH_UNTRACED`

## VII. Final law

OPERA QUALITAS EX QUANTITAS elaborates quality from verified quantity under
declared projection rules. It neither proves quantity through interpretation
nor mediates the final output.