# OPERA QUANTITAS ET QUALITAS — Execution Mechanism

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

## 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 coupled OPERA. It composes the two directional
capabilities without merging their identities or duplicating their mechanisms.

## II. Native purpose

OPERA QUANTITAS ET QUALITAS alternates verified quantitative elaboration and
qualitatively constrained quantitative search when the objective requires
both surfaces to converge.

It is not an automatic sequence of the other two OPERAE. One AREPO admission
must explicitly select this coupled artifact and declare a bounded convergence
policy.

## III. OPERA-specific input

```text
QUANTITAS_ET_QUALITAS_INPUT:
  quantitative_seed_refs[]
  qualitative_constraint_refs[]
  quantitative_rule_refs[]
  qualitative_projection_rule_refs[]
  convergence_policy:
    maximum_cycles
    required_state_delta
    stable_equivalence_ref
    closure_condition
  requested_logical_form
```

## IV. Execution

1. verify and bind the quantitative seeds;
2. generate admitted qualitative elaborations;
3. compare them with the qualitative constraint set;
4. compile surviving qualitative constraints into quantitative predicates;
5. search and reduce the admitted quantitative domain;
6. compare the resulting quantitative states with prior-cycle states;
7. repeat only while the convergence policy permits and a material delta
   exists;
8. bind declared ROTA edges, derivations, or hypertransitions;
9. construct an optional source-bounded proposition or syllogism;
10. return the coupled state, cycle trace, unresolved conflicts, and stop
    reason.

A cycle in the derivation graph is not progress. Every revisit requires a
state delta. Arithmetic truth is verified before any qualitative proposition.

## V. Output

```text
QUANTITAS_ET_QUALITAS_RESULT:
  quantitative_records[]
  quantitative_truth_status
  qualitative_records[]
  coupled_cycles[]:
    cycle_ordinal
    input_state_ref
    qualitative_delta
    compiled_predicate_refs[]
    quantitative_delta
    output_state_ref
  rota_bindings[]
  relation_provenance[]
  logical_form
  logical_record
  convergence_status
  unresolved_elements[]
  rejected_alternatives[]
  actual_state_delta
  termination_reason
  arithmetica_generation_trace_ref
```

## VI. Native failures

- `ARITHMETIC_PARSE_FAILED`
- `ARITHMETIC_FALSE`
- `COUPLED_ADMISSION_MISSING`
- `CONVERGENCE_POLICY_MISSING`
- `ROTA_BINDING_MISSING`
- `RELATION_PROVENANCE_MISSING`
- `LOGICAL_LAYER_CONTRADICTION`
- `QUALITATIVE_FIT_USED_AS_NUMERIC_PROOF`
- `CYCLIC_DERIVATION_AS_PROGRESS`
- `ZERO_DELTA_CYCLE_CONTINUED`

## VII. Final law

OPERA QUANTITAS ET QUALITAS performs a bounded coupled search while keeping
both directional surfaces distinguishable. It stops on closure, exhaustion,
budget, unresolved conflict, or absence of material delta and returns its
typed result to SATOR.