## LOCAL SECTION INDEX Scope: local anchors within this artifact only. No cross-artifact links are introduced here. - [Shorthands: ROTA Q; ROTA R;](#local-section-04-stack-e-rotas-e-structuralinstantiation-shorthands-rota-q-rota-r) - [I. PURPOSE](#local-section-04-stack-e-rotas-e-structuralinstantiation-i-purpose) - [II. GEOMETRIC FORM](#local-section-04-stack-e-rotas-e-structuralinstantiation-ii-geometric-form) - [III. CORE RING (R0)](#local-section-04-stack-e-rotas-e-structuralinstantiation-iii-core-ring-r0) - [IV. SPECIES RING (R1)](#local-section-04-stack-e-rotas-e-structuralinstantiation-iv-species-ring-r1) - [V. COMBINATORY RING (R2)](#local-section-04-stack-e-rotas-e-structuralinstantiation-v-combinatory-ring-r2) - [BUT:](#local-section-04-stack-e-rotas-e-structuralinstantiation-but) - [VI. TRAVERSAL FIELD (R3)](#local-section-04-stack-e-rotas-e-structuralinstantiation-vi-traversal-field-r3) - [VII. ADJACENCY RULES](#local-section-04-stack-e-rotas-e-structuralinstantiation-vii-adjacency-rules) - [VIII. COMPATIBILITY CONSTRAINTS](#local-section-04-stack-e-rotas-e-structuralinstantiation-viii-compatibility-constraints) - [IX. STRUCTURAL INVARIANTS](#local-section-04-stack-e-rotas-e-structuralinstantiation-ix-structural-invariants) - [X. OUTPUT FUNCTION](#local-section-04-stack-e-rotas-e-structuralinstantiation-x-output-function) - [XI. LIMITS](#local-section-04-stack-e-rotas-e-structuralinstantiation-xi-limits) - [ROTAS_E ONLY:](#local-section-04-stack-e-rotas-e-structuralinstantiation-rotas-e-only) - [XII. CLOSURE](#local-section-04-stack-e-rotas-e-structuralinstantiation-xii-closure) - [STATUS:](#local-section-04-stack-e-rotas-e-structuralinstantiation-status) --- ============================================================ ROTA E — REGIMEN_RQ (CANONICAL STRUCTURE) Ars Generalis Applied — Interrogative Traversal Geometry Version: 1.0.1-ROTA-E-PATCHED Status: LOCK-CANDIDATE Scope: STRUCTURAL / EXECUTION SUPPORT Authority: AGLA / ROTAS Class: ROTAS Mutation Policy: VERSION-CONTROLLED ONLY Shorthands: ROTA Q; ROTA R; ============================================================ I. PURPOSE ------------------------------------------------------------ Define the canonical structural system (ROTAS_E) that enables: • ordered traversal of interrogative carriers (Ⅰ–Ⅹ) • embedding of species domains (TENET R) • lawful execution support for OPERA Q ------------------------------------------------------------ This artifact provides: • geometric carrier structure • traversal rules • adjacency logic • combinatory affordances ------------------------------------------------------------ ROTAS_E is: • prerequisite for OPERA Q execution • non-executive • non-admissive • structure-only ============================================================ II. GEOMETRIC FORM ============================================================ ROTAS_E is defined as: CYCLIC MULTI-RING COMBINATORY STRUCTURE ------------------------------------------------------------ Structure Layers: R0 — Core Ring (Ordinal Carriers) R1 — Species Ring (Rule Expansion) R2 — Combinatory Ring (Inter-rule Pairs) R3 — Traversal Field (Execution Path Space) ------------------------------------------------------------ All rings are: • cyclic • directionally traversable • ordinally anchored ============================================================ III. CORE RING (R0) ============================================================ R0 defines the primary interrogative carriers: [Ⅰ] B — Whether [Ⅱ] C — What [Ⅲ] D — Of what [Ⅳ] E — Why [Ⅴ] F — How much [Ⅵ] G — What quality [Ⅶ] H — When [Ⅷ] I — Where [Ⅸ] K1 — How [Ⅹ] K2 — With what ------------------------------------------------------------ Properties: • strict ordinal positioning • cyclic closure: Ⅹ → Ⅰ • non-skippable under full traversal ============================================================ IV. SPECIES RING (R1) ============================================================ Each node in R0 expands into a species domain: R1(n) = { s₁, s₂, ..., sₖ } ------------------------------------------------------------ Example: B → { doubt, affirmation, negation } ------------------------------------------------------------ Properties: • non-uniform cardinality • rule-dependent structure • must map to TENET R ------------------------------------------------------------ Constraint: species cannot exist without carrier anchor ------------------------------------------------------------ Note: BREVIS species (TENET E) and ULTIMA species (TENET R) are both embeddable within R1 without structural change. ============================================================ V. COMBINATORY RING (R2) ============================================================ R2 defines pairwise carrier combinations: (nᵢ, nⱼ), where i ≠ j ------------------------------------------------------------ Total combinations: C(10,2) = 45 pairs ------------------------------------------------------------ Each pair defines a combinatory camera: e.g.: BC BD CE IK ------------------------------------------------------------ Properties: • structurally symmetric pairing • no self-combination • order-preserving (ordinal identity retained) ------------------------------------------------------------ Clarification: R2 combinations are: • structurally symmetric BUT: execution traversal (OPERA Q) is directional ------------------------------------------------------------ Function: enables: • cross-rule positioning • compound interrogation space • multi-axis traversal potential ============================================================ VI. TRAVERSAL FIELD (R3) ============================================================ R3 defines valid movement across structure. ------------------------------------------------------------ Traversal Types: 1. Sequential Traversal nᵢ → nᵢ₊₁ 2. Cyclic Traversal n₁₀ → n₁ 3. Radial Traversal R0 → R1 4. Combinatory Traversal R0 → R2 → R1 5. Recursive Traversal species → carrier → species ------------------------------------------------------------ Constraints: • traversal must preserve carrier identity • traversal must maintain definition binding • traversal cannot skip binding stage ------------------------------------------------------------ Invalid Traversals: ✗ random jumps without carrier binding ✗ species-to-species without anchor ✗ combinatory collapse into single rule ============================================================ VII. ADJACENCY RULES ============================================================ Adjacency is defined at three levels: ------------------------------------------------------------ 1. Ordinal Adjacency nᵢ adjacent to nᵢ₊₁ ------------------------------------------------------------ 2. Logical Adjacency based on interrogative dependency structure ------------------------------------------------------------ 3. Combinatory Adjacency via R2: nᵢ adjacent to all nⱼ where j ≠ i ------------------------------------------------------------ Rule: Adjacency types are co-present. Traversal selection is external to ROTAS and determined by OPERA / AREPO. ============================================================ VIII. COMPATIBILITY CONSTRAINTS ============================================================ ROTAS_E must remain compatible with: ------------------------------------------------------------ 1. TENET CYCLIC INDEXING LAW • closure required • no terminal node ------------------------------------------------------------ 2. FIGURE III LOGIC (PAIR CAMERAS) • all pair combinations must be representable ------------------------------------------------------------ 3. OPERA Q • ROTAS defines space • OPERA executes traversal within space ------------------------------------------------------------ 4. NON-CONTRADICTION incompatible species must not co-occupy same traversal path ============================================================ IX. STRUCTURAL INVARIANTS ============================================================ The following must always hold: ------------------------------------------------------------ 1. Carrier Primacy carriers precede species ------------------------------------------------------------ 2. Ordinal Stability positions cannot shift ------------------------------------------------------------ 3. Cyclic Closure structure must loop ------------------------------------------------------------ 4. Combinatory Completeness all valid pairs must exist ------------------------------------------------------------ 5. Traversal Legibility every path must be reconstructible ============================================================ X. OUTPUT FUNCTION ============================================================ ROTAS_E produces: traversal-ready structural space for OPERA Q ------------------------------------------------------------ It does NOT produce: • conclusions • admissibility decisions • semantic validation ============================================================ XI. LIMITS ============================================================ ROTAS_E does NOT: • define truth • define ontology • execute reasoning • authorize execution ------------------------------------------------------------ ROTAS_E ONLY: structures interrogative possibility space ============================================================ XII. CLOSURE ============================================================ ROTAS_E establishes: the geometric and combinatory substrate required for interrogative reduction ------------------------------------------------------------ With this artifact: ✓ combinatorics becomes structurally grounded ✓ OPERA Q becomes spatially defined ------------------------------------------------------------ Remaining dependency: AREPO E (admissibility layer) ------------------------------------------------------------ STATUS: STRUCTURALLY COMPLETE LOCK-CANDIDATE ============================================================ END OF ARTIFACT ============================================================