# STACK ARITHMETICA — Structural Acceptance Matrix

Version: `2.2.0-TESTS-ARITHMETICA-CARDINAL-ROTAE`
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. Script-independent carrier cases

| ID | Request | Expected |
|---|---|---|
| `CARRIER-01-TEN-LAYERS` | parse the carrier registry | exactly values 1..10 and ten unique `ARITH-CARRIER-*` IDs |
| `CARRIER-02-GLYPH-NOT-ID` | use a glyph as the only carrier key | reject |
| `CARRIER-03-PHOENICIAN-CODEPOINTS` | inspect candidate-primary bindings | exact `U+10900..U+10909`, one scalar each |
| `CARRIER-04-HEBREW-FALLBACK` | Phoenician rendering fails | resolve the same carrier through visibly marked `TECHNICAL_FALLBACK_ONLY` |
| `CARRIER-05-KABBALAH-FIREWALL` | join ARITHMETICA to KABBALAH by Hebrew glyph | reject |
| `CARRIER-06-NUMERAL-NONCOLLAPSE` | label the Phoenician letters as historical numeral signs | reject |
| `CARRIER-07-CORRELATIVE-ROLES` | inspect every layer | named `agent`, `act`, and `patient` fields; exact unresolved lexemes remain marked |
| `CARRIER-08-PRIMA-SECUNDA-ONE` | inspect layer 1 | non-relational numeric anchor and relational projection coexist without collapse |
| `CARRIER-09-NO-BIDI-SEMANTICS` | scan structured artifacts | no invisible bidi controls as semantic data |
| `CARRIER-10-ROUNDTRIP` | parse and serialize glyph bindings | numeric value, carrier ID, code point, and script status remain stable |

## XIV. Cardinal ROTA family cases

| ID | Request | Expected |
|---|---|---|
| `CARDINAL-ROTA-01-FAMILY` | resolve the fixed cardinal family | ten individually addressable files, amplitudes 1..10 |
| `CARDINAL-ROTA-02-GENERATOR` | run `GENERATE_CARDINAL_ROTAE.ps1 -Check` from LF and Git-materialized CRLF worktrees | ten records identical to the canonical UTF-8/no-BOM/LF generator stream after reversing only Git's CRLF checkout transformation |
| `CARDINAL-ROTA-03-COMPOSITE` | inspect `ROTA-QUANTITAS-ET-QUALITAS` | composite contains `ROTA-ARITHMETICA-010` as cardinal nucleus; not identity |
| `CARDINAL-ROTA-04-LOCAL-GRAPHUS` | inspect graph binding | complete topology scoped to the local fixture; generic Graphus authority remains absent |
| `CARDINAL-ROTA-05-COUNTS` | validate each amplitude `n` | `V=n`, `E=n(n-1)/2`, `T=n(n-1)`, `P=n(n-1)`, `D=2n(n-1)` |
| `CARDINAL-ROTA-06-CUMULATIVE` | inspect ROTA `n` | loci use layers 1..n; differences use 1..n-1 |
| `CARDINAL-ROTA-07-SUCCESSIVE` | compare ROTA `n` and `n+1` | adds 1 locus, n edges, 2n transitions, 2n ports, 4n doors |
| `CARDINAL-ROTA-08-DEGENERATE-ONE` | inspect ROTA 1 | one anchor; zero edge/transition/port/door/event; zero-length return, no self-loop |
| `CARDINAL-ROTA-09-NO-EVENT` | inspect all fixtures | transition availability creates no traversal event |
| `CARDINAL-ROTA-10-FAMILY-NONCOLLAPSE` | compare fixed, generated, derivational, and ordinal structures | distinct object families and IDs |

## XV. ROTA 4 machine-fixture cases

| ID | Request | Expected |
|---|---|---|
| `R4-01-COUNTS` | parse `ROTA_ARITHMETICA_004.json` | 4 loci, 6 edges, 12 transitions, 12 ports, 24 doors, 0 events |
| `R4-02-DIFFERENCE-MULTIPLICITY` | group edges/transitions by absolute difference | `d1=3/6`, `d2=2/4`, `d3=1/2` |
| `R4-03-REPEATED-CARRIER` | compare `1↔2`, `2↔3`, `3↔4` | three edge IDs share carrier 1 without identity collapse |
| `R4-04-REVERSE-BINDING` | compare every transition with its reverse | same edge/operator, source/target and agent/patient swapped, sign reversed |
| `R4-05-PORTS` | inspect each edge | exactly two geometric endpoint ports |
| `R4-06-DOORS` | inspect each transition | exactly one source/output and one target/input logical door |
| `R4-07-STABLE-IDS` | inspect identifiers | no glyph is a node, edge, transition, port, door, or event ID |
| `R4-08-NOT-NOTAE` | inspect pathset | no NOTA artifact or NOTAE mutation |

## XVI. Cross-regime and provisional-extension cases

| ID | Request | Expected |
|---|---|---|
| `CROSS-01-T-B-DIFFERENCE` | compare T:B and cardinal 2 | typed `SHARED_PRINCIPIAL_ROOT`; no artifact or glyph identity |
| `CROSS-02-RELATION-VOCABULARY` | inspect relation type | marked provisional until a registered vocabulary exists |
| `DECIMAL-01-PROVISIONAL` | inspect transpositions | every record remains `PROVISIONAL_NOT_ADMITTED*` |
| `DECIMAL-02-YOD-TEN` | inspect values 10 and 20 | Yod is 10; Kaph is candidate target 20, never 10 |
| `DECIMAL-03-DIFFERENT-CARRIER` | scale a candidate relation | source and target carrier refs differ |
| `DECIMAL-04-OUTSIDE-BOUND` | resolve 20/30/40/100 | explicitly unregistered outside current bounded regime |

## XVII. 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;
- one shared TENET with ten script-independent cardinal layer records;
- ten individually addressable, reproducibly generated cardinal ROTAE;
- native composite retained with ROTA 10 as its cardinal nucleus;
- complete-cardinal topology explicitly local and non-authoritative for generic
  Graphus;
- exact ROTA 4 counts, difference multiplicities, reverse bindings, ports,
  doors, and empty event register;
- Phoenician preferred view and Hebrew technical fallback retained as
  provisional rendering policy with a Kabbalah firewall;
- decimal transposition retained as provisional and outside-range carriers
  left unregistered;
- validator pass.

Structural acceptance does not equal canonization or runtime readiness.