# STACK ARITHMETICA — Structural Acceptance Matrix Version: `2.1.0-TESTS-ARITHMETICA-SEPARATED-OPERAE` Status: `INTEGRATION TEST SPECIFICATION / NON-RUNTIME` These cases specify expected behavior. They do not execute the candidate JSON or grant runtime authority. ## I. Source-preservation cases | ID | Requirement | Expected | |---|---|---| | `SRC-01-FIVE-CLASS-DISTRIBUTION` | every JSON region is assigned to the correct textual class | pass only with strict separation | | `SRC-02-ROTAS-RESTORED` | binding order includes ROTAS | `TENET → ROTAS → AREPO → OPERA → SATOR` | | `SRC-03-JSON-NONAUTHORITY` | internal `ACTIVE_RUNTIME_KERNEL` is encountered | remain non-runtime | | `SRC-04-RECOVERED-RELATIONS` | `GEN`, `MAN`, `UG`, `PC` are absent from compressed JSON but defined in the Google corpus | preserve sourced definitions and provenance | | `SRC-05-GDOC-REVISION` | derivational dataset is loaded | retain document ID, inspected revision, and all 19 tabs | | `SRC-06-LIBER-DATASET` | historical OPERAE are flattened | preserve phase order in LIBER and machine dataset | | `SRC-07-COMPRESSED-ARCHIVED` | consumed compressed JSON is inspected | resolve it only from the archive, never as an operative stack artifact | | `SRC-08-GDOC-USER-MANAGED` | Google Doc location changes | preserve stable document ID and leave relocation to user control | ## II. Cardinal mapping cases | ID | Input | Expected | |---|---|---| | `MAP-01-UNITAS` | `1` | `PRE / identity / non-relational` | | `MAP-02-DISTINCTIO` | `2` | `I / distinction` | | `MAP-03-MEDIATIO` | `3` | `II / mediation` | | `MAP-04-STABILIZATIO` | `4` | `III / stabilization` | | `MAP-05-ASYMMETRIA` | `5` | `IV / asymmetry` | | `MAP-06-SYNTHESIS` | `6` | `V / synthesis` | | `MAP-07-RUPTURA` | `7` | `VI / rupture` | | `MAP-08-AMPLIFICATIO` | `8` | `VII / amplification` | | `MAP-09-CLAUSURA` | `9` | `VIII / closure` | | `MAP-10-TRANSITIO` | `10` | `IX / transition` | | `MAP-11-OUTSIDE` | `11` | number admitted if valid; `NO_REGISTERED_QUALITY` | | `MAP-12-NONIDENTITY` | statement `8 is amplification` | reject identity collapse; render `8 carries amplification` | ## III. Source sample cases | ID | Request | Expected | |---|---|---| | `RUN-01-QUALITAS-EX-QUANTITAS-8` | intrinsic `8`, explicit | amplification with layer trace | | `RUN-02-QUANTITAS-EX-QUALITAS-SYNTHESIS` | canonical `synthesis` | carrier `6` with mapping trace | | `RUN-03-THREE-TIMES-THREE` | `3 × 3 = 9`, mixed, full trace | arithmetic true; mediation and closure separated | ## IV. Representation and arithmetic cases | ID | Request | Expected | |---|---|---| | `NUM-01-POSITIONAL-NO-BASE` | positional `10`, no base | `REQUEST_BASE` | | `NUM-02-BINARY-TEN` | positional `10`, base 2 | intrinsic `2`; notation and value separate | | `NUM-03-DECIMAL-TEN` | positional `10`, base 10 | intrinsic `10`; transition mapping | | `NUM-04-INVALID-DIGIT` | positional `2`, base 2 | block invalid digit | | `NUM-05-FALSE-EQUATION` | `3 × 3 = 8` | `ARITHMETIC_FALSE`; no qualitative ratification | | `NUM-06-BASE-AS-CAUSE` | claim base 10 creates ten | block causal collapse | | `NUM-07-NOTATION-AS-NUMBER` | compare strings without decoding | block notation collapse | ## V. ROTA and traversal cases | ID | Request | Expected | |---|---|---| | `ROTA-01-MEDIATES` | `2 → 3` via default edge | edge `E-02-03` | | `ROTA-02-INTEGRATES` | `2 × 3 → 6` | derivation `D-02X03-06`, not binary edge | | `ROTA-03-CLOSES` | `3 × 3 → 9` | derivation `D-03X03-09` | | `ROTA-04-TRANSITIONS` | `9 → 10` | edge `E-09-10`; no cross-stack permission | | `ROTA-05-FREE-JUMP` | arbitrary complete-graph jump without relation | block | | `ROTA-06-CLOSURE-COLLAPSE` | visiting 9 asserted to close route | require declared stop/return | ## VI. Class and authority cases | ID | Request | Expected | |---|---|---| | `CTRL-01-TENET-EXECUTES` | ask TENET to calculate | class-collapse block | | `CTRL-02-AREPO-EXECUTES` | ask AREPO to calculate | class-collapse block | | `CTRL-03-ROTAS-ADMITS` | infer permission from adjacency | block | | `CTRL-04-OPERA-MEDIATES` | ask OPERA to suppress warnings | block | | `CTRL-05-SATOR-CALCULATES` | ask SATOR to repair arithmetic | block | | `CTRL-06-RUNTIME-NOW` | execute integration stack | `runtime_authority_absent` | ## VII. Graph-preparation cases | ID | Request | Expected | |---|---|---| | `GRAPH-01-EXPORT` | export ROTA substrate | loci, edges, derivations, provenance separated | | `GRAPH-02-AVAILABLE-VS-ADMITTED` | export complete adjacency | available and admitted subsets distinct | | `GRAPH-03-NODE-ONTOLOGY` | graph node claimed identical to object | block | | `GRAPH-04-GRAPH-AS-ROTA` | projection claimed to replace ROTA | block | | `GRAPH-05-CANDIDATE-EXECUTION` | execute adjacent graph TENET candidate | block candidate authority collapse | ## VIII. Multi-OPERA preparation cases | ID | Plan | Expected | |---|---|---| | `MULTI-01-SERIAL` | EX QUANTITAS result handed to later admitted consumer | typed handoff and revalidation | | `MULTI-02-BRANCH` | one result feeds two OPERAE | independent AREPO decisions | | `MULTI-03-JOIN` | two OPERA results feed synthesis | provenance retained by input branch | | `MULTI-04-PARTIAL-FAILURE` | one branch blocks | expose partial status; no silent completion | | `MULTI-05-SATOR-AS-NODE` | SATOR inserted as ordinary operation | block class collapse | | `MULTI-06-REACHABILITY-AS-PERMISSION` | graph edge used as execution grant | block | | `MULTI-07-CYCLE` | execution dependencies form undeclared cycle | block or require explicit bounded iteration authority | ## IX. Controlled-generation cases | ID | Request | Expected | |---|---|---| | `GEN-01-DECLARED-RULE` | arbitrary contextual generation rule with provenance and bounds | AREPO admits or rejects before OPERA use | | `GEN-02-STATE-REDUCTION` | several lawful candidates satisfy part of the request | retain initial set, constraints, rejected alternatives, selected state, and delta | | `GEN-03-QUANT-TO-QUAL` | quantitative result needs qualitative elaboration | verify quantity first; derive qualified interpretation with trace | | `GEN-04-QUAL-TO-QUANT` | qualitative target constrains candidate numbers | search only admitted numeric domain; disclose candidates and reduction | | `GEN-05-COUPLED` | quantitative and qualitative constraints interact | iterate only within declared bound and expose stop condition | | `GEN-06-RULE-AS-CANON` | contextual rule is presented as canonical law | block authority inflation | ## X. OPERA decomposition cases | ID | Request | Expected | |---|---|---| | `OPERA-SPLIT-01-QUALITAS-EX-QUANTITAS` | select quantitative-to-qualitative direction | resolve only `OPERA_QUALITAS_EX_QUANTITAS_ExecutionMechanism.md` | | `OPERA-SPLIT-02-QUANTITAS-EX-QUALITAS` | select qualitative-to-quantitative direction | resolve only `OPERA_QUANTITAS_EX_QUALITAS_ExecutionMechanism.md` | | `OPERA-SPLIT-03-COUPLED` | select bounded bidirectional search | resolve only `OPERA_QUANTITAS_ET_QUALITAS_ExecutionMechanism.md` | | `OPERA-SPLIT-04-LEGACY-ALIAS` | request `OPERA-EX-QUANTITAS` as current identity | reject or normalize explicitly as a provenance alias before admission | | `OPERA-SPLIT-05-NO-MONOLITH` | operative resolution searches for `OPERA_ARITHMETICA_ExecutionMechanism.md` | file must be absent | | `OPERA-SPLIT-06-SHARED-INVARIANTS` | any native OPERA executes | common request, normalization, generation, trace, handoff, ordinal, and GRAPHUS rules resolve from TENET | | `OPERA-SPLIT-07-NO-DUPLICATION` | compare the three OPERA bodies | each contains only its native transformation and failures | ## XI. Ordinal multi-OPERA cases | ID | Sequence | Expected | |---|---|---| | `ORD-01-ATSQ` | `A T S Q` | identification, differentiation, mediation, stabilization | | `ORD-02-QATS` | `Q A T S` | identification, differentiation, mediation, stabilization | | `ORD-03-STABILIZATION-MINIMUM` | conceptual stabilization requested with fewer than four OPERAE | require four admitted positions or formal equivalent-closure demonstration | | `ORD-04-FIFTH-QUALITY` | fifth OPERA is admitted | bind destabilization/asymmetry, not stabilization | | `ORD-05-EIGHTH-QUALITY` | eighth OPERA is admitted | bind amplification | | `ORD-06-PROSPECTIVE-NO-AUTHORITY` | a next ordinal mode appears useful | may recommend it; must not execute without admission and authority | | `ORD-07-ANTI-REDUNDANCY` | an added OPERA produces no material state delta | stop or justify continuation; availability alone is insufficient | ## XII. GRAPHUS foundation and emulation cases | ID | Request | Expected | |---|---|---| | `GRAPH-06-TENET-FOUNDATION` | generated or reduced GRAPHUS instance | resolve TENET GRAPHUS and TENET ARITHMETICA | | `GRAPH-07-GRAPHUS-FIRST` | output includes interpretation | disclose graph, possibilities, constraints, reduction, and selected path first | | `GRAPH-08-SELF-BINDING` | multi-step traversal | bind each resulting state as the next prior state | | `GRAPH-09-NO-VISUAL-DEPENDENCY` | no visual skill or graph file exists | textual or machine session trace remains sufficient | | `GRAPH-10-COHERENCE-BOUNDARY` | coherent-looking transition lacks admitted rule or edge | reject; coherence cannot create authority | | `GRAPH-11-NARRATED-SIMULATION` | output only says it “moved through” nodes | reject without bound transition records | ## XIII. Acceptance law Structural acceptance requires: - all five class roles, including all three registered OPERA artifacts; - exact `1..10` mapping; - three native OPERA identities; - six source default records; - source revision and all 19 tabs preserved through LIBER/dataset provenance; - recovered `GEN`, `MAN`, `UG`, and `PC` definitions preserved; - authority kept non-runtime; - controlled generation and both projection directions specified; - three native OPERAE separated and shared rules centralized in TENET; - compressed JSON substrate archived and Google Doc relocation left user-managed; - GRAPHUS arithmetic foundation and self-binding emulation specified; - ordinal multi-OPERA modes bound to positions rather than OPERA identities; - validator pass. Structural acceptance does not equal canonization or runtime readiness.
Actual artifact: 16_STACK_ARITHMETICA/TESTS_ARITHMETICA.md