============================================================ SIGMA_SATOR KERNEL BUNDLE AGLA / DEPLOYMENT LAYER Version: 1.0.3-SIGMA-SATOR-T-REBUILT Status: VALID_SIGMA_SATOR_KERNEL Date: 2026-05-01 Authority: AGLA / CONTROL PLANE / HUMAN DEVELOPER DIRECTIVE Class: AGLA / MACROCLASS (SIGMA_SATOR) Kernel_ID: SIGMA_SATOR_T Regime: T Stack_Folder: 03_STACK_T Selected_OPERA: IDX-T-OPERA Selected_ROTAS: IDX-T-ROTA Source_Class_Law: 00_ROOT_CLASS_LAWS/AGLA_SIGMA_SATOR_CLASS_LAW.md Mutation Policy: GENERATED FILE ONLY; SOURCE STACK ARTIFACTS NOT MUTATED BY THIS BUNDLE ASSEMBLY ============================================================ ## LOCAL SECTION INDEX Scope: local anchors within this artifact only. No cross-artifact links are introduced here. - [KERNEL_LIFECYCLE:](#local-section-99-sigma-sator-output-sigma-sator-t-sigma-sator-t-kernel-kernel-lifecycle) - [CLASS_MAPPING:](#local-section-99-sigma-sator-output-sigma-sator-t-sigma-sator-t-kernel-class-mapping) - [VALIDATION:](#local-section-99-sigma-sator-output-sigma-sator-t-sigma-sator-t-kernel-validation) - [SOURCE_ARTIFACT_MANIFEST:](#local-section-99-sigma-sator-output-sigma-sator-t-sigma-sator-t-kernel-source-artifact-manifest) - [EMBEDDED CLASS ARTIFACTS -- FULL VERBATIM REPRODUCTION](#local-section-99-sigma-sator-output-sigma-sator-t-sigma-sator-t-kernel-embedded-class-artifacts-full-verbatim-reproduction) KERNEL_LIFECYCLE: LOAD -> RESOLVE -> BIND -> ADMIT -> EXECUTE -> RETURN CLASS_MAPPING: LOAD / RESOLVE / BIND: TENET + ROTAS ADMIT: AREPO EXECUTE: OPERA RETURN: SATOR VALIDATION: all_five_classes_present: TRUE all_five_classes_non_empty: TRUE support_dependencies_non_empty: TRUE full_verbatim_embedding_attempted: TRUE kernel_valid: TRUE SOURCE_ARTIFACT_MANIFEST: - class: TENET file: 03_STACK_T/TENET_T_DoctrinalInvariants.md exists: TRUE non_empty: TRUE bytes: 21523 sha256: a115a73c4931a054eef2371e4aa190de1be00c791ebfddbbf3849e3c9efff6e6 - class: ROTAS file: 03_STACK_T/ROTAS_T_StructuralInstantiation.md exists: TRUE non_empty: TRUE bytes: 28090 sha256: 29595d84a7f3499fee3a47848b171770cbfd4df7d5b093c0ea54a8108bdba809 - class: AREPO file: 03_STACK_T/AREPO_T_InputAdmissibility.md exists: TRUE non_empty: TRUE bytes: 22304 sha256: 00be45ac113747ad16e1b6f99c65feaf40e558e1173c30adc2fc85de8f276a2a - class: OPERA file: 03_STACK_T/OPERA_T_ExecutionMechanism.md exists: TRUE non_empty: TRUE bytes: 48511 sha256: f68799731e815b59597fe474c51af52dc900a58cc3eedbeedfbcf5bd235ba615 - class: SATOR file: 03_STACK_T/SATOR_T_OutputRequirements.md exists: TRUE non_empty: TRUE bytes: 25071 sha256: bd2d5628d33168a66b7e40e69833e25c379160acb2fba0e389cd630d4ba4d38d ============================================================ EMBEDDED CLASS ARTIFACTS -- FULL VERBATIM REPRODUCTION ============================================================ ============================================================ BEGIN_VERBATIM_ARTIFACT: TENET Source_File: 03_STACK_T/TENET_T_DoctrinalInvariants.md Source_Exists: TRUE Source_Non_Empty: TRUE Source_Length_Bytes: 21523 Source_SHA256: a115a73c4931a054eef2371e4aa190de1be00c791ebfddbbf3849e3c9efff6e6 ------------------------------------------------------------ ============================================================ TENET T — PRINCIPIA RELATIVA (FIGURA T) Ars Generalis Applied — Doctrinal Layer (Relational Regime) Version: 0.2.1-TENET-T (rev T.5 — ordinal-primacy / A-T-corrected / genus-disciplined) Status: DOCTRINAL LAYER — LOCK CANDIDATE Authority: AGLA / CONTROL PLANE Mutation Policy: VERSION-CONTROLLED ONLY Class: TENET ============================================================ ## LOCAL SECTION INDEX Scope: local anchors within this artifact only. No cross-artifact links are introduced here. - [PURPOSE](#local-section-03-stack-t-tenet-t-doctrinalinvariants-purpose) - [DEFINITION](#local-section-03-stack-t-tenet-t-doctrinalinvariants-definition) - [CORE ASSERTION](#local-section-03-stack-t-tenet-t-doctrinalinvariants-core-assertion) - [I. CONTROL-PLANE POSITION](#local-section-03-stack-t-tenet-t-doctrinalinvariants-i-control-plane-position) - [INTERPRETATION](#local-section-03-stack-t-tenet-t-doctrinalinvariants-interpretation) - [TENET T:](#local-section-03-stack-t-tenet-t-doctrinalinvariants-tenet-t) - [RULE](#local-section-03-stack-t-tenet-t-doctrinalinvariants-rule) - [II. PREDICATE SET](#local-section-03-stack-t-tenet-t-doctrinalinvariants-ii-predicate-set) - [SCOPE](#local-section-03-stack-t-tenet-t-doctrinalinvariants-scope) - [RULE](#local-section-03-stack-t-tenet-t-doctrinalinvariants-rule-2) - [III. ORDINAL PRIMACY](#local-section-03-stack-t-tenet-t-doctrinalinvariants-iii-ordinal-primacy) - [DOMINIUM ORDINALE T](#local-section-03-stack-t-tenet-t-doctrinalinvariants-dominium-ordinale-t) - [PRIMARY STRUCTURE](#local-section-03-stack-t-tenet-t-doctrinalinvariants-primary-structure) - [SYMBOL BINDING](#local-section-03-stack-t-tenet-t-doctrinalinvariants-symbol-binding) - [ORDINAL PRIMACY LAW](#local-section-03-stack-t-tenet-t-doctrinalinvariants-ordinal-primacy-law) - [CONSTRAINT](#local-section-03-stack-t-tenet-t-doctrinalinvariants-constraint) - [ANTI-DRIFT RULE](#local-section-03-stack-t-tenet-t-doctrinalinvariants-anti-drift-rule) - [INTERPRETATION](#local-section-03-stack-t-tenet-t-doctrinalinvariants-interpretation-2) - [IV. NON-ONTOLOGY LAW](#local-section-03-stack-t-tenet-t-doctrinalinvariants-iv-non-ontology-law) - [FORMULA](#local-section-03-stack-t-tenet-t-doctrinalinvariants-formula) - [INTERPRETATION](#local-section-03-stack-t-tenet-t-doctrinalinvariants-interpretation-3) - [RULE](#local-section-03-stack-t-tenet-t-doctrinalinvariants-rule-3) - [CONSTRAINT](#local-section-03-stack-t-tenet-t-doctrinalinvariants-constraint-2) - [V. GENUS STRUCTURE](#local-section-03-stack-t-tenet-t-doctrinalinvariants-v-genus-structure) - [GENUS SLOTS](#local-section-03-stack-t-tenet-t-doctrinalinvariants-genus-slots) - [FORM](#local-section-03-stack-t-tenet-t-doctrinalinvariants-form) - [EXAMPLES](#local-section-03-stack-t-tenet-t-doctrinalinvariants-examples) - [RULE](#local-section-03-stack-t-tenet-t-doctrinalinvariants-rule-4) - [CONSTRAINT](#local-section-03-stack-t-tenet-t-doctrinalinvariants-constraint-3) - [PROVENANCE NOTE](#local-section-03-stack-t-tenet-t-doctrinalinvariants-provenance-note) - [VI. TRIADIC GROUPING](#local-section-03-stack-t-tenet-t-doctrinalinvariants-vi-triadic-grouping) - [FUNCTIONAL READING (NON-ABSOLUTE)](#local-section-03-stack-t-tenet-t-doctrinalinvariants-functional-reading-non-absolute) - [RULE](#local-section-03-stack-t-tenet-t-doctrinalinvariants-rule-5) - [CONSTRAINT](#local-section-03-stack-t-tenet-t-doctrinalinvariants-constraint-4) - [VII. RELATION TO TENET A](#local-section-03-stack-t-tenet-t-doctrinalinvariants-vii-relation-to-tenet-a) - [TENET A](#local-section-03-stack-t-tenet-t-doctrinalinvariants-tenet-a) - [TENET T](#local-section-03-stack-t-tenet-t-doctrinalinvariants-tenet-t-2) - [RELATION LAW](#local-section-03-stack-t-tenet-t-doctrinalinvariants-relation-law) - [INTERPRETATION](#local-section-03-stack-t-tenet-t-doctrinalinvariants-interpretation-4) - [VIII. APPLICATION DOMAIN](#local-section-03-stack-t-tenet-t-doctrinalinvariants-viii-application-domain) - [RULE](#local-section-03-stack-t-tenet-t-doctrinalinvariants-rule-6) - [CONSTRAINT](#local-section-03-stack-t-tenet-t-doctrinalinvariants-constraint-5) - [IX. PROHIBITIONS](#local-section-03-stack-t-tenet-t-doctrinalinvariants-ix-prohibitions) - [X. SUMMARY](#local-section-03-stack-t-tenet-t-doctrinalinvariants-x-summary) - [FINAL LAW](#local-section-03-stack-t-tenet-t-doctrinalinvariants-final-law) - [CLOSURE RULE](#local-section-03-stack-t-tenet-t-doctrinalinvariants-closure-rule) ============================================================ PURPOSE ============================================================ Define the principial regime of T (Figura T) within Ars Generalis Applied. TENET T establishes: • the canonical set of relative predicates • their ordinal structure • their genus stratification • their non-ontological nature • their role in mediating articulated terms TENET T governs: • relational predicates (categorigmata relativa) • their lawful application domain • their structural articulation rules TENET T does NOT: • define being (TENET K) • define absolute principial content (TENET A) • define structure (ROTAS) • define admissibility (AREPO) • define execution (OPERA) ------------------------------------------------------------ DEFINITION ------------------------------------------------------------ TENET T := principial system of relative predicates ordered by ordinal slots and stratified by genus ------------------------------------------------------------ CORE ASSERTION ------------------------------------------------------------ T predicates are principial, but relative. They do not define what things are. They define how expressed things relate. ============================================================ ============================================================ I. CONTROL-PLANE POSITION ============================================================ TENET → ROTAS → AREPO → OPERA → SATOR ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ TENET T: • defines relational predicates • defines their lawful structure • constrains all downstream relational operations ------------------------------------------------------------ RULE ------------------------------------------------------------ TENET T is: • not provisional • not inferred • not modified at runtime ============================================================ II. PREDICATE SET ============================================================ The canonical predicates of T are: SLOT | SYMBOL | NAME | FUNCTIONAL LABEL ------------------------------------------------ Ⅰ | B | Differentia | Differens Ⅱ | C | Concordantia | Concordans Ⅲ | D | Contrarietas | Contrarium Ⅳ | E | Principium | Initialis Ⅴ | F | Medium | Medians Ⅵ | G | Finis | Finalis Ⅶ | H | Maioritas | Maior Ⅷ | I | Aequalitas | Aequalis Ⅸ | K | Minoritas | Minor ------------------------------------------------------------ SCOPE ------------------------------------------------------------ These predicates are: • widely applicable across domains • general in relational scope ------------------------------------------------------------ RULE ------------------------------------------------------------ Predicate identity is fixed. No predicate may be: ✗ added ✗ removed ✗ renamed ✗ reordered ============================================================ ============================================================ III. ORDINAL PRIMACY ============================================================ ------------------------------------------------------------ DOMINIUM ORDINALE T ------------------------------------------------------------ The primary carrier of T is the ordinal slot. ------------------------------------------------------------ PRIMARY STRUCTURE ------------------------------------------------------------ Ⅰ → Ⅱ → Ⅲ → Ⅳ → Ⅴ → Ⅵ → Ⅶ → Ⅷ → Ⅸ ------------------------------------------------------------ SYMBOL BINDING ------------------------------------------------------------ Ⅰ→B, Ⅱ→C, Ⅲ→D, Ⅳ→E, Ⅴ→F, Ⅵ→G, Ⅶ→H, Ⅷ→I, Ⅸ→K ------------------------------------------------------------ ORDINAL PRIMACY LAW ------------------------------------------------------------ Structure is defined by SLOT. SYMBOL and NUMERIC are bound projections. ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ SYMBOL and NUMERIC must not: ✗ redefine structure ✗ determine traversal ✗ imply hierarchy ------------------------------------------------------------ ANTI-DRIFT RULE ------------------------------------------------------------ TENET T must not be read through: ✗ alphabetical order ✗ symbolic proximity ✗ numeric magnitude ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ B is not first because of alphabet. B is first because it occupies SLOT Ⅰ. ============================================================ ============================================================ IV. NON-ONTOLOGY LAW ============================================================ ------------------------------------------------------------ FORMULA ------------------------------------------------------------ Relatio ≠ Esse ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ T predicates do not posit being. They qualify respects under which expressed terms may be: • compared • distinguished • mediated • evaluated ------------------------------------------------------------ RULE ------------------------------------------------------------ T predicates: • do not define substance • do not define identity • do not define essence ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ TENET T must not: ✗ collapse into TENET K (subjects) ✗ redefine ontology ✗ infer identity from relation ============================================================ ============================================================ V. GENUS STRUCTURE ============================================================ Each predicate is stratified into three genus levels. ------------------------------------------------------------ GENUS SLOTS ------------------------------------------------------------ g1 = higher / abstract / formal g2 = intermediate / mediated g3 = lower / concrete / applied ------------------------------------------------------------ FORM ------------------------------------------------------------ T(ρ,g) ------------------------------------------------------------ EXAMPLES ------------------------------------------------------------ TB1, TB2, TB3 TF1, TF2, TF3 ------------------------------------------------------------ RULE ------------------------------------------------------------ Each predicate must preserve: • three distinct genus slots • ordered relation between them ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ Genus levels must not: ✗ collapse into one another ✗ be skipped in transitions ✗ be treated as interchangeable ------------------------------------------------------------ PROVENANCE NOTE ------------------------------------------------------------ Genus definitions are inherited from stabilized CAPUT/CARCER extraction and are not re-derived in this artifact. ============================================================ ============================================================ VI. TRIADIC GROUPING ============================================================ Predicates are grouped into triads: Δ1 := {Ⅰ,Ⅱ,Ⅲ} Δ2 := {Ⅳ,Ⅴ,Ⅵ} Δ3 := {Ⅶ,Ⅷ,Ⅸ} ------------------------------------------------------------ FUNCTIONAL READING (NON-ABSOLUTE) ------------------------------------------------------------ Triads may be read functionally as: Δ1 → distinction Δ2 → process Δ3 → comparison / measure ------------------------------------------------------------ RULE ------------------------------------------------------------ Triads define grouping, not substitution or reduction. ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ Triads must not: ✗ override ordinal identity ✗ redefine predicate meaning ============================================================ ============================================================ VII. RELATION TO TENET A ============================================================ TENET A and TENET T are both principial regimes. ------------------------------------------------------------ TENET A ------------------------------------------------------------ Defines: • absolute predicates • principial content • full convertibility in undifferentiated unity ------------------------------------------------------------ TENET T ------------------------------------------------------------ Defines: • relative predicates • mediation between articulated terms ------------------------------------------------------------ RELATION LAW ------------------------------------------------------------ T predicates operate over articulated or contracted expressions of principial content. T does not: • alter A's principial identity • replace convertibility in A ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ A provides: what is principially affirmed T provides: how articulated terms relate under that affirmation ============================================================ ============================================================ VIII. APPLICATION DOMAIN ============================================================ T predicates apply only to: • expressed terms • articulated states • relational contexts ------------------------------------------------------------ RULE ------------------------------------------------------------ In machine-sensitive, validation-sensitive, or execution-sensitive contexts: explicit genus slot is required. ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ T predicates must not be applied to: ✗ pure undifferentiated principia ✗ unexpressed substrate ✗ non-relational contexts ============================================================ ============================================================ IX. PROHIBITIONS ============================================================ ✗ redefining predicate set ✗ altering ordinal order ✗ collapsing genus structure ✗ deriving ontology from relation ✗ applying T to pure principial unity ✗ treating symbol sequence as primary ✗ treating numeric sequence as primary ✗ substituting traversal order for structural order ============================================================ ============================================================ X. SUMMARY ============================================================ TENET T defines: • principial relative predicates • ordinally grounded structure • genus-stratified articulation • non-ontological relational domain ------------------------------------------------------------ FINAL LAW ------------------------------------------------------------ T predicates are principial, but relative. They do not define what is. They define how what is expressed may be related. ------------------------------------------------------------ CLOSURE RULE ------------------------------------------------------------ TENET T must preserve: • ordinal primacy • genus integrity • relational purity • principial distinction from TENET A ============================================================ END OF ARTIFACT ============================================================ END_VERBATIM_ARTIFACT: TENET ============================================================ ============================================================ BEGIN_VERBATIM_ARTIFACT: ROTAS Source_File: 03_STACK_T/ROTAS_T_StructuralInstantiation.md Source_Exists: TRUE Source_Non_Empty: TRUE Source_Length_Bytes: 28090 Source_SHA256: 29595d84a7f3499fee3a47848b171770cbfd4df7d5b093c0ea54a8108bdba809 ------------------------------------------------------------ ## LOCAL SECTION INDEX Scope: local anchors within this artifact only. No cross-artifact links are introduced here. - [Class: ROTAS](#local-section-03-stack-t-rotas-t-structuralinstantiation-class-rotas) - [PURPOSE](#local-section-03-stack-t-rotas-t-structuralinstantiation-purpose) - [I. PRINCIPLE](#local-section-03-stack-t-rotas-t-structuralinstantiation-i-principle) - [CORE ASSERTION](#local-section-03-stack-t-rotas-t-structuralinstantiation-core-assertion) - [FORMAL POSITION IN CONTROL PLANE](#local-section-03-stack-t-rotas-t-structuralinstantiation-formal-position-in-control-plane) - [INTERPRETATION](#local-section-03-stack-t-rotas-t-structuralinstantiation-interpretation) - [TENET T:](#local-section-03-stack-t-rotas-t-structuralinstantiation-tenet-t) - [ROTA T:](#local-section-03-stack-t-rotas-t-structuralinstantiation-rota-t) - [AREPO T:](#local-section-03-stack-t-rotas-t-structuralinstantiation-arepo-t) - [OPERA T:](#local-section-03-stack-t-rotas-t-structuralinstantiation-opera-t) - [SATOR T:](#local-section-03-stack-t-rotas-t-structuralinstantiation-sator-t) - [II. ORDER SYSTEM DECLARATION](#local-section-03-stack-t-rotas-t-structuralinstantiation-ii-order-system-declaration) - [ACTIVE_ORDER:](#local-section-03-stack-t-rotas-t-structuralinstantiation-active-order) - [INTERPRETATION](#local-section-03-stack-t-rotas-t-structuralinstantiation-interpretation-2) - [CLARIFICATION](#local-section-03-stack-t-rotas-t-structuralinstantiation-clarification) - [CONSTRAINT](#local-section-03-stack-t-rotas-t-structuralinstantiation-constraint) - [RULE](#local-section-03-stack-t-rotas-t-structuralinstantiation-rule) - [III. CARRIER STRUCTURE (EXPLICIT)](#local-section-03-stack-t-rotas-t-structuralinstantiation-iii-carrier-structure-explicit) - [PRIMARY CARRIER:](#local-section-03-stack-t-rotas-t-structuralinstantiation-primary-carrier) - [CARRIER_ORDER:](#local-section-03-stack-t-rotas-t-structuralinstantiation-carrier-order) - [SYMBOL BINDING:](#local-section-03-stack-t-rotas-t-structuralinstantiation-symbol-binding) - [SYMBOL_BINDING (BETICAL):](#local-section-03-stack-t-rotas-t-structuralinstantiation-symbol-binding-betical) - [NUMERIC BINDING:](#local-section-03-stack-t-rotas-t-structuralinstantiation-numeric-binding) - [CARRIER ATOM](#local-section-03-stack-t-rotas-t-structuralinstantiation-carrier-atom) - [DISPLAY NOTE](#local-section-03-stack-t-rotas-t-structuralinstantiation-display-note) - [CONSTRAINT](#local-section-03-stack-t-rotas-t-structuralinstantiation-constraint-2) - [ORDINAL PRIMACY LAW (ENFORCED)](#local-section-03-stack-t-rotas-t-structuralinstantiation-ordinal-primacy-law-enforced) - [IV. TOPOLOGICAL STRUCTURE](#local-section-03-stack-t-rotas-t-structuralinstantiation-iv-topological-structure) - [FORMAL STRUCTURE](#local-section-03-stack-t-rotas-t-structuralinstantiation-formal-structure) - [RULE](#local-section-03-stack-t-rotas-t-structuralinstantiation-rule-2) - [CONSTRAINT](#local-section-03-stack-t-rotas-t-structuralinstantiation-constraint-3) - [V. TRAVERSAL STRUCTURE](#local-section-03-stack-t-rotas-t-structuralinstantiation-v-traversal-structure) - [TRAVERSAL_ORDER (STRUCTURAL WALK)](#local-section-03-stack-t-rotas-t-structuralinstantiation-traversal-order-structural-walk) - [DISTINCTION (CRITICAL)](#local-section-03-stack-t-rotas-t-structuralinstantiation-distinction-critical) - [RULE](#local-section-03-stack-t-rotas-t-structuralinstantiation-rule-3) - [CONSTRAINT](#local-section-03-stack-t-rotas-t-structuralinstantiation-constraint-4) - [TRAVERSAL_ORDER:](#local-section-03-stack-t-rotas-t-structuralinstantiation-traversal-order) - [VI. TRIAD STRUCTURE](#local-section-03-stack-t-rotas-t-structuralinstantiation-vi-triad-structure) - [TRIADS (STRUCTURAL PARTITION)](#local-section-03-stack-t-rotas-t-structuralinstantiation-triads-structural-partition) - [TRIAD WALK](#local-section-03-stack-t-rotas-t-structuralinstantiation-triad-walk) - [INTERPRETATION](#local-section-03-stack-t-rotas-t-structuralinstantiation-interpretation-3) - [CONSTRAINT](#local-section-03-stack-t-rotas-t-structuralinstantiation-constraint-5) - [VII. GENUS LAYER COMPATIBILITY](#local-section-03-stack-t-rotas-t-structuralinstantiation-vii-genus-layer-compatibility) - [STRUCTURE](#local-section-03-stack-t-rotas-t-structuralinstantiation-structure) - [GENUS_LAYER:](#local-section-03-stack-t-rotas-t-structuralinstantiation-genus-layer) - [FULL MACHINE DOMAIN](#local-section-03-stack-t-rotas-t-structuralinstantiation-full-machine-domain) - [INTERPRETATION](#local-section-03-stack-t-rotas-t-structuralinstantiation-interpretation-4) - [ROTA T:](#local-section-03-stack-t-rotas-t-structuralinstantiation-rota-t-2) - [CONSTRAINT](#local-section-03-stack-t-rotas-t-structuralinstantiation-constraint-6) - [VIII. GEOMETRIC PARAMETERS](#local-section-03-stack-t-rotas-t-structuralinstantiation-viii-geometric-parameters) - [FIGURA:](#local-section-03-stack-t-rotas-t-structuralinstantiation-figura) - [ENUMERATIO_CAMBRARUM:](#local-section-03-stack-t-rotas-t-structuralinstantiation-enumeratio-cambrarum) - [SENSUS_ROTATIONIS:](#local-section-03-stack-t-rotas-t-structuralinstantiation-sensus-rotationis) - [ANGULUS_ANCORA:](#local-section-03-stack-t-rotas-t-structuralinstantiation-angulus-ancora) - [ANGULUS_STEP:](#local-section-03-stack-t-rotas-t-structuralinstantiation-angulus-step) - [ANGLE FUNCTION:](#local-section-03-stack-t-rotas-t-structuralinstantiation-angle-function) - [CAMBRA IDENTIFIER](#local-section-03-stack-t-rotas-t-structuralinstantiation-cambra-identifier) - [INTERPRETATION](#local-section-03-stack-t-rotas-t-structuralinstantiation-interpretation-5) - [CONSTRAINT](#local-section-03-stack-t-rotas-t-structuralinstantiation-constraint-7) - [IX. RELATION TO OTHER CLASSES](#local-section-03-stack-t-rotas-t-structuralinstantiation-ix-relation-to-other-classes) - [TENET T](#local-section-03-stack-t-rotas-t-structuralinstantiation-tenet-t-2) - [ROTA T:](#local-section-03-stack-t-rotas-t-structuralinstantiation-rota-t-3) - [AREPO T](#local-section-03-stack-t-rotas-t-structuralinstantiation-arepo-t-2) - [OPERA T](#local-section-03-stack-t-rotas-t-structuralinstantiation-opera-t-2) - [SATOR T](#local-section-03-stack-t-rotas-t-structuralinstantiation-sator-t-2) - [X. FAILURE CONDITIONS](#local-section-03-stack-t-rotas-t-structuralinstantiation-x-failure-conditions) - [STRUCTURAL FAILURES](#local-section-03-stack-t-rotas-t-structuralinstantiation-structural-failures) - [ORDER FAILURES](#local-section-03-stack-t-rotas-t-structuralinstantiation-order-failures) - [CLASS VIOLATIONS](#local-section-03-stack-t-rotas-t-structuralinstantiation-class-violations) - [MACHINE FAILURES](#local-section-03-stack-t-rotas-t-structuralinstantiation-machine-failures) - [XI. SUMMARY](#local-section-03-stack-t-rotas-t-structuralinstantiation-xi-summary) - [FINAL LAW](#local-section-03-stack-t-rotas-t-structuralinstantiation-final-law) ============================================================ ROTA T — REGIMEN_T MACHINE INSTANTIATION Ars Generalis Applied — Structural Machine Layer (Figura T) Version: 0.2.1-ROTA-T (rev T.5 — carrier-complete / lock-candidate) Status: STRUCTURAL MACHINE — ACCEPT WITH MINOR REVISION APPLIED Derived from: TENET T Authority: AGLA / TENET / ROTAS Mutation Policy: VERSION-CONTROLLED ONLY Class: ROTAS ============================================================ ============================================================ PURPOSE ============================================================ Instantiate the ROTAS-class machine for REGIMEN_T. ROTA T defines: • the structural instantiation of Figura T • the geometric binding of predicate carriers to loci • the cyclic topology of the predicate space • the lawful traversal domain over REGIMEN_T carriers ROTA T is: • structural • cyclic • machine-level • non-doctrinal • non-executive ============================================================ I. PRINCIPLE ============================================================ ROTA T is a ROTAS-class machine. ------------------------------------------------------------ CORE ASSERTION ------------------------------------------------------------ ROTA T does not display structure. ROTA T defines: • where predicates are located • how they are arranged cyclically • how they may be traversed structurally ------------------------------------------------------------ FORMAL POSITION IN CONTROL PLANE ------------------------------------------------------------ TENET → ROTAS → AREPO → OPERA → SATOR ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ TENET T: defines predicates ROTA T: instantiates their structural space AREPO T: validates admissibility within that space OPERA T: executes relations within that space SATOR T: mediates outputs derived from that space ============================================================ II. ORDER SYSTEM DECLARATION ============================================================ ACTIVE_ORDER: BETICAL ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ ACTIVE_ORDER identifies the bound carrier package: (SLOT, SYMBOL, NUMERIC) ------------------------------------------------------------ CLARIFICATION ------------------------------------------------------------ ACTIVE_ORDER does not establish structural primacy over SLOT. SLOT remains primary structural carrier within the active carrier package. ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ ACTIVE_ORDER does NOT override: • ordinal slot primacy • structural carrier identity ------------------------------------------------------------ RULE ------------------------------------------------------------ Within ROTA T: SLOT remains the primary structural carrier SYMBOL and NUMERIC are bound surfaces derived from the ACTIVE_ORDER ============================================================ III. CARRIER STRUCTURE (EXPLICIT) ============================================================ PRIMARY CARRIER: ------------------------------------------------------------ CARRIER_ORDER: ORDINAL_SLOTS := {Ⅰ,Ⅱ,Ⅲ,Ⅳ,Ⅴ,Ⅵ,Ⅶ,Ⅷ,Ⅸ} ------------------------------------------------------------ SYMBOL BINDING: ------------------------------------------------------------ SYMBOL_BINDING (BETICAL): Ⅰ → B Ⅱ → C Ⅲ → D Ⅳ → E Ⅴ → F Ⅵ → G Ⅶ → H Ⅷ → I Ⅸ → K ------------------------------------------------------------ NUMERIC BINDING: ------------------------------------------------------------ NUMERIC_BINDING (BETICAL native mapping): Ⅰ → 2 Ⅱ → 3 Ⅲ → 4 Ⅳ → 5 Ⅴ → 6 Ⅵ → 7 Ⅶ → 8 Ⅷ → 9 Ⅸ → 10 ------------------------------------------------------------ CARRIER ATOM ------------------------------------------------------------ For each locus: CARRIER_UNIT := (SLOT, SYMBOL, NUMERIC) ------------------------------------------------------------ DISPLAY NOTE ------------------------------------------------------------ NUMERIC display may be suppressed when not load-bearing, but NUMERIC remains part of carrier identity. ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ NUMERIC is: • part of carrier identity • NOT mandatory for all representations • NOT structurally primary ------------------------------------------------------------ ORDINAL PRIMACY LAW (ENFORCED) ------------------------------------------------------------ Structure is defined by SLOT. SYMBOL and NUMERIC must not: ✗ redefine structure ✗ determine traversal ✗ imply hierarchy ============================================================ IV. TOPOLOGICAL STRUCTURE ============================================================ ROTA T defines a cyclic structure: • 9 loci • closed loop • return-complete ------------------------------------------------------------ FORMAL STRUCTURE ------------------------------------------------------------ CYCLE_T := cyclic arrangement of: {Ⅰ,Ⅱ,Ⅲ,Ⅳ,Ⅴ,Ⅵ,Ⅶ,Ⅷ,Ⅸ} ------------------------------------------------------------ RULE ------------------------------------------------------------ The cycle is: • ordered • non-permutable • structurally closed ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ Breaking cyclic closure invalidates the machine. ============================================================ V. TRAVERSAL STRUCTURE ============================================================ TRAVERSAL_ORDER (STRUCTURAL WALK) ------------------------------------------------------------ Primary traversal: Ⅰ → Ⅳ → Ⅶ → Ⅱ → Ⅴ → Ⅷ → Ⅲ → Ⅵ → Ⅸ ------------------------------------------------------------ Equivalent SYMBOL projection: B → E → H → C → F → I → D → G → K ------------------------------------------------------------ DISTINCTION (CRITICAL) ------------------------------------------------------------ The following are NOT the same: • CARRIER_ORDER • SYMBOL_BINDING • TRAVERSAL_ORDER ------------------------------------------------------------ RULE ------------------------------------------------------------ These must NEVER be collapsed. ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ TRAVERSAL_ORDER: • does NOT redefine carrier structure • does NOT imply symbolic primacy • does NOT alter ordinal identity ============================================================ VI. TRIAD STRUCTURE ============================================================ TRIADS (STRUCTURAL PARTITION) ------------------------------------------------------------ Δ1 := {Ⅰ,Ⅱ,Ⅲ} = {B,C,D} Δ2 := {Ⅳ,Ⅴ,Ⅵ} = {E,F,G} Δ3 := {Ⅶ,Ⅷ,Ⅸ} = {H,I,K} ------------------------------------------------------------ TRIAD WALK ------------------------------------------------------------ ρ → ρ+3 → ρ+6 (mod 9) ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ Triads are: • structural partitions of the carrier • not doctrinal assertions • not semantic classifications ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ Triads must not be interpreted as: ✗ ontological categories ✗ semantic hierarchies ============================================================ VII. GENUS LAYER COMPATIBILITY ============================================================ ROTA T supports the internal genus structure of TENET T. ------------------------------------------------------------ STRUCTURE ------------------------------------------------------------ GENUS_LAYER: g ∈ {1,2,3} ------------------------------------------------------------ FULL MACHINE DOMAIN ------------------------------------------------------------ T_DOMAIN := { (ρ,g) | ρ ∈ {Ⅰ..Ⅸ}, g ∈ {1,2,3} } ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ ROTA T: • hosts genus layers • aligns genus vertically over each locus • does not define genus meaning ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ ROTA T must not: ✗ collapse genus layers ✗ infer genus transitions ✗ assign semantic content to genus ============================================================ VIII. GEOMETRIC PARAMETERS ============================================================ FIGURA: T ------------------------------------------------------------ ENUMERATIO_CAMBRARUM: 9 ------------------------------------------------------------ SENSUS_ROTATIONIS: clockwise ------------------------------------------------------------ ANGULUS_ANCORA: 90° ------------------------------------------------------------ ANGULUS_STEP: 40° ------------------------------------------------------------ ANGLE FUNCTION: ------------------------------------------------------------ θ(ρ) = 90° − (Index(ρ) − 1) * 40° mod 360 ------------------------------------------------------------ CAMBRA IDENTIFIER ------------------------------------------------------------ CAMBRA_ID := T- ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ Geometry provides: • positional indexing • reproducible layout • deterministic alignment ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ Geometry does NOT: ✗ define meaning ✗ define admissibility ✗ define execution ============================================================ IX. RELATION TO OTHER CLASSES ============================================================ ROTA T is the REGIMEN_T machine instantiation within the ROTAS class. ------------------------------------------------------------ TENET T ------------------------------------------------------------ Provides: • predicate definitions • genus structure ROTA T: • instantiates their structural space ------------------------------------------------------------ AREPO T ------------------------------------------------------------ Validates: • whether operations over this structure are admissible Requires: • bound(TENET T) • instantiated(ROTA T) ------------------------------------------------------------ OPERA T ------------------------------------------------------------ Operates over: • slot-bound predicates • within ROTA T topology ------------------------------------------------------------ SATOR T ------------------------------------------------------------ May expose: • loci • traversal paths • symbolic projections But must not: ✗ redefine structure ============================================================ X. FAILURE CONDITIONS ============================================================ STRUCTURAL FAILURES ------------------------------------------------------------ • treating SYMBOL as primary carrier • treating NUMERIC as primary carrier • collapsing traversal into carrier order • breaking cyclic closure • non-deterministic indexing ------------------------------------------------------------ ORDER FAILURES ------------------------------------------------------------ • implicit order inference • mixing carrier orders • symbol-first interpretation • numeric-first interpretation ------------------------------------------------------------ CLASS VIOLATIONS ------------------------------------------------------------ • ROTA T executing OPERA • ROTA T defining TENET • ROTA T validating admissibility • ROTA T acting as SATOR ------------------------------------------------------------ MACHINE FAILURES ------------------------------------------------------------ • non-traversable structure • inconsistent adjacency • genus_layer_misalignment • genus_layer_erasure ============================================================ XI. SUMMARY ============================================================ ROTA T defines: • a 9-slot cyclic machine • slot-primary carrier structure • symbol and numeric as bound surfaces • explicit traversal topology • triadic partition • genus-layer hosting ------------------------------------------------------------ FINAL LAW ------------------------------------------------------------ ROTA T defines the structural space in which REGIMEN_T becomes operable. Structure is: slot-bound cyclic non-permutable and strictly prior to: admissibility (AREPO) execution (OPERA) mediation (SATOR) ============================================================ END OF ARTIFACT ============================================================ END_VERBATIM_ARTIFACT: ROTAS ============================================================ ============================================================ BEGIN_VERBATIM_ARTIFACT: AREPO Source_File: 03_STACK_T/AREPO_T_InputAdmissibility.md Source_Exists: TRUE Source_Non_Empty: TRUE Source_Length_Bytes: 22304 Source_SHA256: 00be45ac113747ad16e1b6f99c65feaf40e558e1173c30adc2fc85de8f276a2a ------------------------------------------------------------ ## LOCAL SECTION INDEX Scope: local anchors within this artifact only. No cross-artifact links are introduced here. - [Class: AREPO](#local-section-03-stack-t-arepo-t-inputadmissibility-class-arepo) - [PURPOSE](#local-section-03-stack-t-arepo-t-inputadmissibility-purpose) - [CORE ASSERTION](#local-section-03-stack-t-arepo-t-inputadmissibility-core-assertion) - [I. PRINCIPLE](#local-section-03-stack-t-arepo-t-inputadmissibility-i-principle) - [CONTROL-PLANE POSITION](#local-section-03-stack-t-arepo-t-inputadmissibility-control-plane-position) - [INTERPRETATION](#local-section-03-stack-t-arepo-t-inputadmissibility-interpretation) - [TENET T:](#local-section-03-stack-t-arepo-t-inputadmissibility-tenet-t) - [ROTA T:](#local-section-03-stack-t-arepo-t-inputadmissibility-rota-t) - [AREPO T:](#local-section-03-stack-t-arepo-t-inputadmissibility-arepo-t) - [II. BINDING REQUIREMENTS](#local-section-03-stack-t-arepo-t-inputadmissibility-ii-binding-requirements) - [INTERPRETATION](#local-section-03-stack-t-arepo-t-inputadmissibility-interpretation-2) - [CONSTRAINT](#local-section-03-stack-t-arepo-t-inputadmissibility-constraint) - [III. CARRIER RESOLUTION LAW](#local-section-03-stack-t-arepo-t-inputadmissibility-iii-carrier-resolution-law) - [PRIMARY RULE](#local-section-03-stack-t-arepo-t-inputadmissibility-primary-rule) - [VALID CARRIER UNIT](#local-section-03-stack-t-arepo-t-inputadmissibility-valid-carrier-unit) - [RESOLUTION PRIORITY](#local-section-03-stack-t-arepo-t-inputadmissibility-resolution-priority) - [INTERPRETATION](#local-section-03-stack-t-arepo-t-inputadmissibility-interpretation-3) - [CONSTRAINT](#local-section-03-stack-t-arepo-t-inputadmissibility-constraint-2) - [IV. ORDER RESOLUTION](#local-section-03-stack-t-arepo-t-inputadmissibility-iv-order-resolution) - [RULE](#local-section-03-stack-t-arepo-t-inputadmissibility-rule) - [DEFAULT](#local-section-03-stack-t-arepo-t-inputadmissibility-default) - [FAILURE](#local-section-03-stack-t-arepo-t-inputadmissibility-failure) - [INTERPRETATION](#local-section-03-stack-t-arepo-t-inputadmissibility-interpretation-4) - [V. STRUCTURAL ADMISSIBILITY (ROTAS)](#local-section-03-stack-t-arepo-t-inputadmissibility-v-structural-admissibility-rotas) - [INTERPRETATION](#local-section-03-stack-t-arepo-t-inputadmissibility-interpretation-5) - [FAILURE](#local-section-03-stack-t-arepo-t-inputadmissibility-failure-2) - [RULE](#local-section-03-stack-t-arepo-t-inputadmissibility-rule-2) - [VI. GENUS ADMISSIBILITY](#local-section-03-stack-t-arepo-t-inputadmissibility-vi-genus-admissibility) - [RULE](#local-section-03-stack-t-arepo-t-inputadmissibility-rule-3) - [VALID STATE](#local-section-03-stack-t-arepo-t-inputadmissibility-valid-state) - [GENUS CONSISTENCY](#local-section-03-stack-t-arepo-t-inputadmissibility-genus-consistency) - [TRANSITION CONTROL](#local-section-03-stack-t-arepo-t-inputadmissibility-transition-control) - [FAILURE RESPONSE](#local-section-03-stack-t-arepo-t-inputadmissibility-failure-response) - [VII. REQUEST VALIDITY](#local-section-03-stack-t-arepo-t-inputadmissibility-vii-request-validity) - [INVALID REQUEST TYPES](#local-section-03-stack-t-arepo-t-inputadmissibility-invalid-request-types) - [RULE](#local-section-03-stack-t-arepo-t-inputadmissibility-rule-4) - [VIII. NON-ONTOLOGY ENFORCEMENT](#local-section-03-stack-t-arepo-t-inputadmissibility-viii-non-ontology-enforcement) - [BLOCK IF](#local-section-03-stack-t-arepo-t-inputadmissibility-block-if) - [INTERPRETATION](#local-section-03-stack-t-arepo-t-inputadmissibility-interpretation-6) - [IX. FAILURE TYPES](#local-section-03-stack-t-arepo-t-inputadmissibility-ix-failure-types) - [STRUCTURAL FAILURES](#local-section-03-stack-t-arepo-t-inputadmissibility-structural-failures) - [CARRIER FAILURES](#local-section-03-stack-t-arepo-t-inputadmissibility-carrier-failures) - [GENUS FAILURES](#local-section-03-stack-t-arepo-t-inputadmissibility-genus-failures) - [GOVERNANCE FAILURES](#local-section-03-stack-t-arepo-t-inputadmissibility-governance-failures) - [X. RELATION TO OTHER CLASSES](#local-section-03-stack-t-arepo-t-inputadmissibility-x-relation-to-other-classes) - [TENET T](#local-section-03-stack-t-arepo-t-inputadmissibility-tenet-t-2) - [ROTA T](#local-section-03-stack-t-arepo-t-inputadmissibility-rota-t-2) - [OPERA T](#local-section-03-stack-t-arepo-t-inputadmissibility-opera-t) - [SATOR T](#local-section-03-stack-t-arepo-t-inputadmissibility-sator-t) - [RULE](#local-section-03-stack-t-arepo-t-inputadmissibility-rule-5) - [XI. SUMMARY](#local-section-03-stack-t-arepo-t-inputadmissibility-xi-summary) - [FINAL LAW](#local-section-03-stack-t-arepo-t-inputadmissibility-final-law) - [CLOSURE RULE](#local-section-03-stack-t-arepo-t-inputadmissibility-closure-rule) ============================================================ AREPO T — REGIMEN_T ADMISSIBILITY LAYER Ars Generalis Applied — Execution Governance (Figura T) Version: 0.2.1-AREPO-T (rev T.5 — carrier-complete / lock-candidate) Status: ADMISSIBILITY LAYER — ACCEPT WITH MINOR REVISION APPLIED Depends-On: • TENET T • ROTAS (class binding) • ROTA T (machine instantiation) Authority: AGLA / CONTROL PLANE Mutation Policy: VERSION-CONTROLLED ONLY Class: AREPO ============================================================ ============================================================ PURPOSE ============================================================ Define admissibility conditions for execution over REGIMEN_T. AREPO T determines whether a request involving: • T predicates • T carrier structure • T genus layers may proceed to OPERA T. ------------------------------------------------------------ CORE ASSERTION ------------------------------------------------------------ No relational execution over REGIMEN_T is valid unless: • doctrinally bound (TENET T) • structurally instantiated (ROTA T) • carrier-resolved (slot-first) • relata explicit • genus-consistent (when applicable) ============================================================ I. PRINCIPLE ============================================================ AREPO T operates on: • TENET-bound predicates • ROTAS-instantiated structure • OPERA-bound requests ------------------------------------------------------------ CONTROL-PLANE POSITION ------------------------------------------------------------ TENET → ROTAS → AREPO → OPERA → SATOR ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ TENET T: defines relational predicates ROTA T: defines structural space AREPO T: validates admissibility within that space ============================================================ II. BINDING REQUIREMENTS ============================================================ A request over REGIMEN_T is admissible iff: ------------------------------------------------------------ valid_admission(request) ⇔ bound(TENET T) ∧ bound(ROTAS) ∧ instantiated(ROTA T) ∧ resolved(CARRIER) ∧ explicit(RELATA) ∧ valid(request) ∧ explicit(dependencies) ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ AREPO T requires: • doctrinal binding (TENET T) • structural binding (ROTAS class) • machine availability (ROTA T) • carrier resolution (slot-first) • explicit relational terms (RELATA) ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ AREPO T does NOT: ✗ infer missing bindings ✗ create structure ✗ repair invalid requests ============================================================ III. CARRIER RESOLUTION LAW ============================================================ PRIMARY RULE ------------------------------------------------------------ Carrier resolution is SLOT-first. ------------------------------------------------------------ VALID CARRIER UNIT ------------------------------------------------------------ CARRIER_UNIT := (SLOT, SYMBOL, NUMERIC) ------------------------------------------------------------ RESOLUTION PRIORITY ------------------------------------------------------------ 1. SLOT must be resolved 2. SYMBOL must match SLOT under ACTIVE_ORDER 3. NUMERIC must match order-native mapping (if used) ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ AREPO validates: • slot identity first • symbol consistency second • numeric consistency third ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ Invalid if: ✗ SYMBOL used without SLOT grounding ✗ SYMBOL contradicts SLOT ✗ NUMERIC contradicts order mapping ✗ carrier inferred from symbol alone ============================================================ IV. ORDER RESOLUTION ============================================================ RULE ------------------------------------------------------------ ACTIVE_ORDER must be declared when: • symbol interpretation is ambiguous • numeric interpretation is used • cross-order mapping is possible ------------------------------------------------------------ DEFAULT ------------------------------------------------------------ No implicit order is assumed. ------------------------------------------------------------ FAILURE ------------------------------------------------------------ BLOCK if: • multiple possible orders • symbol ambiguity unresolved • numeric mapping unclear ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ AREPO enforces: structure must be unambiguous before execution ============================================================ V. STRUCTURAL ADMISSIBILITY (ROTAS) ============================================================ AREPO T requires: • bound(ROTAS) • instantiated(ROTA T) ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ Structure must exist as: • cyclic domain (Ⅰ..Ⅸ) • loci-bound predicates • structurally coherent adjacency under instantiated ROTA T ------------------------------------------------------------ FAILURE ------------------------------------------------------------ BLOCK if: • ROTA T not instantiated • structure not traversable • locus undefined • cycle broken ------------------------------------------------------------ RULE ------------------------------------------------------------ No structure ⇒ no admissibility ⇒ no execution ============================================================ VI. GENUS ADMISSIBILITY ============================================================ GENUS_SLOT_T := {1,2,3} ------------------------------------------------------------ RULE ------------------------------------------------------------ If genus-sensitive context is active: • genus must be explicitly declared ------------------------------------------------------------ VALID STATE ------------------------------------------------------------ T(ρ,g) where: ρ ∈ {Ⅰ..Ⅸ} g ∈ {1,2,3} ------------------------------------------------------------ GENUS CONSISTENCY ------------------------------------------------------------ Invalid if: ✗ genus omitted in genus-sensitive request ✗ conflicting genus assignments ✗ implicit genus transitions ------------------------------------------------------------ TRANSITION CONTROL ------------------------------------------------------------ AREPO enforces: • no direct jump: g1 ↛ g3 • mediation required for genus change • no silent cross-predicate genus shift ------------------------------------------------------------ FAILURE RESPONSE ------------------------------------------------------------ If invalid: • BLOCK request • expose violation • expose required mediation condition ============================================================ VII. REQUEST VALIDITY ============================================================ A valid request must be: • explicitly targeted to OPERA T as downstream execution layer • structurally grounded (ROTA T) • doctrinally bound (TENET T) ------------------------------------------------------------ INVALID REQUEST TYPES ------------------------------------------------------------ • ontological inference from T • symbol-first reasoning • numeric-first reasoning • structure-free relation request • genus collapse request ------------------------------------------------------------ RULE ------------------------------------------------------------ AREPO rejects: any request that violates class separation or carrier discipline ============================================================ VIII. NON-ONTOLOGY ENFORCEMENT ============================================================ AREPO T enforces: relation ≠ being ------------------------------------------------------------ BLOCK IF ------------------------------------------------------------ • T predicates treated as subjects • relational statements promoted to ontology • identity inferred from relation alone ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ AREPO protects TENET boundary: T remains relational regime only ============================================================ IX. FAILURE TYPES ============================================================ STRUCTURAL FAILURES ------------------------------------------------------------ • TENET_BINDING_MISSING • ROTAS_BINDING_MISSING • ROTA_T_NOT_INSTANTIATED • STRUCTURE_NON_TRAVERSABLE ------------------------------------------------------------ CARRIER FAILURES ------------------------------------------------------------ • CARRIER_UNRESOLVED • SLOT_MISSING • SYMBOL_SLOT_MISMATCH • NUMERIC_MISMATCH • SYMBOL_ONLY_INFERENCE ------------------------------------------------------------ GENUS FAILURES ------------------------------------------------------------ • GENUS_MISSING • GENUS_CONTRADICTION • GENUS_INVALID_TRANSITION • GENUS_COLLAPSE ------------------------------------------------------------ GOVERNANCE FAILURES ------------------------------------------------------------ • DEPENDENCY_NOT_EXPLICIT • IMPLICIT_FALLBACK • SILENT_ADMISSION_ATTEMPT ============================================================ X. RELATION TO OTHER CLASSES ============================================================ TENET T ------------------------------------------------------------ Provides: • predicate definitions • genus structure AREPO T validates compliance. ------------------------------------------------------------ ROTA T ------------------------------------------------------------ Provides: • structural machine AREPO T requires: instantiated(ROTA T) ------------------------------------------------------------ OPERA T ------------------------------------------------------------ Receives: • admitted requests only ------------------------------------------------------------ SATOR T ------------------------------------------------------------ Receives: • admissibility results • failure diagnostics ------------------------------------------------------------ RULE ------------------------------------------------------------ AREPO informs but does not mediate. ============================================================ XI. SUMMARY ============================================================ AREPO T defines: • admissibility for REGIMEN_T execution • slot-first carrier validation • order resolution requirements • genus-state enforcement • structural dependency on ROTA T ------------------------------------------------------------ FINAL LAW ------------------------------------------------------------ No OPERA T execution is valid unless: • TENET T is bound • ROTAS is bound • ROTA T is instantiated • carrier is resolved (slot-first) • relata are explicit • genus is consistent (if active) ------------------------------------------------------------ CLOSURE RULE ------------------------------------------------------------ AREPO admits only that which is: structurally instantiated, doctrinally grounded, carrier-consistent, and relationally explicit. ============================================================ END OF ARTIFACT ============================================================ END_VERBATIM_ARTIFACT: AREPO ============================================================ ============================================================ BEGIN_VERBATIM_ARTIFACT: OPERA Source_File: 03_STACK_T/OPERA_T_ExecutionMechanism.md Source_Exists: TRUE Source_Non_Empty: TRUE Source_Length_Bytes: 48511 Source_SHA256: f68799731e815b59597fe474c51af52dc900a58cc3eedbeedfbcf5bd235ba615 ------------------------------------------------------------ ============================================================ OPERA T â€” REGIMEN_T EXECUTION LAYER Ars Generalis Applied â€” Relational Execution (Figura T) Version: 0.2.2-OPERA-T (rev T.6 â€” circular-consistency-integrated) Status: EXECUTION LAYER â€” LOCK CANDIDATE / PATCH INTEGRATED Depends-On: â€¢ TENET T â€¢ TENET A â€¢ TENET E â€¢ ROTAS (class binding) â€¢ ROTA T (machine instantiation) â€¢ AREPO T (admissibility) Authority: AGLA / CONTROL PLANE Mutation Policy: VERSION-CONTROLLED ONLY Class: OPERA ============================================================ ## LOCAL SECTION INDEX Scope: local anchors within this artifact only. No cross-artifact links are introduced here. - [PURPOSE](#local-section-03-stack-t-opera-t-executionmechanism-purpose) - [CORE ASSERTION](#local-section-03-stack-t-opera-t-executionmechanism-core-assertion) - [I. CONTROL-PLANE POSITION](#local-section-03-stack-t-opera-t-executionmechanism-i-control-plane-position) - [INTERPRETATION](#local-section-03-stack-t-opera-t-executionmechanism-interpretation) - [TENET T:](#local-section-03-stack-t-opera-t-executionmechanism-tenet-t) - [TENET A:](#local-section-03-stack-t-opera-t-executionmechanism-tenet-a) - [ROTA T:](#local-section-03-stack-t-opera-t-executionmechanism-rota-t) - [AREPO T:](#local-section-03-stack-t-opera-t-executionmechanism-arepo-t) - [OPERA T:](#local-section-03-stack-t-opera-t-executionmechanism-opera-t) - [SATOR T:](#local-section-03-stack-t-opera-t-executionmechanism-sator-t) - [II. EXECUTION PRINCIPLE](#local-section-03-stack-t-opera-t-executionmechanism-ii-execution-principle) - [PRIMARY OPERATIONAL LAW](#local-section-03-stack-t-opera-t-executionmechanism-primary-operational-law) - [RULE](#local-section-03-stack-t-opera-t-executionmechanism-rule) - [CONSTRAINT](#local-section-03-stack-t-opera-t-executionmechanism-constraint) - [III. INPUT DOMAIN](#local-section-03-stack-t-opera-t-executionmechanism-iii-input-domain) - [VALID RELATA](#local-section-03-stack-t-opera-t-executionmechanism-valid-relata) - [INVALID RELATA](#local-section-03-stack-t-opera-t-executionmechanism-invalid-relata) - [RULE](#local-section-03-stack-t-opera-t-executionmechanism-rule-2) - [IV. RELATION TO TENET A](#local-section-03-stack-t-opera-t-executionmechanism-iv-relation-to-tenet-a) - [EXECUTION LAW](#local-section-03-stack-t-opera-t-executionmechanism-execution-law) - [FORMAL READING](#local-section-03-stack-t-opera-t-executionmechanism-formal-reading) - [CONSTRAINT](#local-section-03-stack-t-opera-t-executionmechanism-constraint-2) - [V. STRUCTURAL DEPENDENCY](#local-section-03-stack-t-opera-t-executionmechanism-v-structural-dependency) - [RULE](#local-section-03-stack-t-opera-t-executionmechanism-rule-3) - [FAILURE](#local-section-03-stack-t-opera-t-executionmechanism-failure) - [VI. FRAME DECLARATION](#local-section-03-stack-t-opera-t-executionmechanism-vi-frame-declaration) - [Required form:](#local-section-03-stack-t-opera-t-executionmechanism-required-form) - [Default:](#local-section-03-stack-t-opera-t-executionmechanism-default) - [RULE](#local-section-03-stack-t-opera-t-executionmechanism-rule-4) - [FAILURE](#local-section-03-stack-t-opera-t-executionmechanism-failure-2) - [VII. EXECUTION MODES](#local-section-03-stack-t-opera-t-executionmechanism-vii-execution-modes) - [DEFAULT:](#local-section-03-stack-t-opera-t-executionmechanism-default-2) - [RULE](#local-section-03-stack-t-opera-t-executionmechanism-rule-5) - [VIII. MODE = FULL](#local-section-03-stack-t-opera-t-executionmechanism-viii-mode-full) - [EXECUTION PATTERN](#local-section-03-stack-t-opera-t-executionmechanism-execution-pattern) - [OUTPUT REQUIREMENT](#local-section-03-stack-t-opera-t-executionmechanism-output-requirement) - [RULE](#local-section-03-stack-t-opera-t-executionmechanism-rule-6) - [CONSTRAINT](#local-section-03-stack-t-opera-t-executionmechanism-constraint-3) - [IX. MODE = TRIAD](#local-section-03-stack-t-opera-t-executionmechanism-ix-mode-triad) - [TRIADS](#local-section-03-stack-t-opera-t-executionmechanism-triads) - [RULE](#local-section-03-stack-t-opera-t-executionmechanism-rule-7) - [TRIAD-WALK](#local-section-03-stack-t-opera-t-executionmechanism-triad-walk) - [CONSTRAINT](#local-section-03-stack-t-opera-t-executionmechanism-constraint-4) - [X. MODE = GENUS](#local-section-03-stack-t-opera-t-executionmechanism-x-mode-genus) - [RULE](#local-section-03-stack-t-opera-t-executionmechanism-rule-8) - [INTERPRETATION](#local-section-03-stack-t-opera-t-executionmechanism-interpretation-2) - [GENUS-AWARE NOTATION](#local-section-03-stack-t-opera-t-executionmechanism-genus-aware-notation) - [CONSTRAINT](#local-section-03-stack-t-opera-t-executionmechanism-constraint-5) - [XI. GENUS TRANSIT OBSERVANCE](#local-section-03-stack-t-opera-t-executionmechanism-xi-genus-transit-observance) - [LOCAL TRANSIT (WITHIN PREDICATE)](#local-section-03-stack-t-opera-t-executionmechanism-local-transit-within-predicate) - [CROSS-PREDICATE TRANSIT](#local-section-03-stack-t-opera-t-executionmechanism-cross-predicate-transit) - [MEDIATED GENUS CHANGE](#local-section-03-stack-t-opera-t-executionmechanism-mediated-genus-change) - [FAILURE](#local-section-03-stack-t-opera-t-executionmechanism-failure-3) - [RULE](#local-section-03-stack-t-opera-t-executionmechanism-rule-9) - [XII. RELATIONAL PURITY LAW](#local-section-03-stack-t-opera-t-executionmechanism-xii-relational-purity-law) - [CORRECT FORM](#local-section-03-stack-t-opera-t-executionmechanism-correct-form) - [INCORRECT FORM](#local-section-03-stack-t-opera-t-executionmechanism-incorrect-form) - [EXAMPLES](#local-section-03-stack-t-opera-t-executionmechanism-examples) - [RULE](#local-section-03-stack-t-opera-t-executionmechanism-rule-10) - [XIII. NON-ONTOLOGY ENFORCEMENT](#local-section-03-stack-t-opera-t-executionmechanism-xiii-non-ontology-enforcement) - [INTERPRETATION](#local-section-03-stack-t-opera-t-executionmechanism-interpretation-3) - [CONSTRAINT](#local-section-03-stack-t-opera-t-executionmechanism-constraint-6) - [XIV. EXECUTION OUTPUT](#local-section-03-stack-t-opera-t-executionmechanism-xiv-execution-output) - [T_PROFILE:](#local-section-03-stack-t-opera-t-executionmechanism-t-profile) - [SUMMARY:](#local-section-03-stack-t-opera-t-executionmechanism-summary) - [GENUS OUTPUT EXTENSION](#local-section-03-stack-t-opera-t-executionmechanism-genus-output-extension) - [TRANSIT OUTPUT EXTENSION](#local-section-03-stack-t-opera-t-executionmechanism-transit-output-extension) - [XV. CIRCULAR CONSISTENCY VALIDATION](#local-section-03-stack-t-opera-t-executionmechanism-xv-circular-consistency-validation) - [PURPOSE](#local-section-03-stack-t-opera-t-executionmechanism-purpose-2) - [VALIDATION PRINCIPLE](#local-section-03-stack-t-opera-t-executionmechanism-validation-principle) - [ACT GENERATION LAW](#local-section-03-stack-t-opera-t-executionmechanism-act-generation-law) - [AGENT GROUNDING LAW](#local-section-03-stack-t-opera-t-executionmechanism-agent-grounding-law) - [CIRCULAR RELATIONAL CLOSURE](#local-section-03-stack-t-opera-t-executionmechanism-circular-relational-closure) - [CIRCULAR CONSISTENCY CHECK](#local-section-03-stack-t-opera-t-executionmechanism-circular-consistency-check) - [CHECK 1:](#local-section-03-stack-t-opera-t-executionmechanism-check-1) - [CHECK 2:](#local-section-03-stack-t-opera-t-executionmechanism-check-2) - [RELATIONAL_CIRCULAR_INCONSISTENCY](#local-section-03-stack-t-opera-t-executionmechanism-relational-circular-inconsistency) - [VALIDITY CONSEQUENCES](#local-section-03-stack-t-opera-t-executionmechanism-validity-consequences) - [RELATION TO BCD PRIORITY](#local-section-03-stack-t-opera-t-executionmechanism-relation-to-bcd-priority) - [CIRCULAR VALIDATION OUTPUT EXTENSION](#local-section-03-stack-t-opera-t-executionmechanism-circular-validation-output-extension) - [CIRCULAR_VALIDATION:](#local-section-03-stack-t-opera-t-executionmechanism-circular-validation) - [ACT_SOURCE_STATUS:](#local-section-03-stack-t-opera-t-executionmechanism-act-source-status) - [AGENT_TARGET_STATUS:](#local-section-03-stack-t-opera-t-executionmechanism-agent-target-status) - [CIRCULAR_CLOSURE_STATUS:](#local-section-03-stack-t-opera-t-executionmechanism-circular-closure-status) - [CIRCULAR_FLAGS:](#local-section-03-stack-t-opera-t-executionmechanism-circular-flags) - [SYSTEM RESULT](#local-section-03-stack-t-opera-t-executionmechanism-system-result) - [XVI. RELATION TO OTHER CLASSES](#local-section-03-stack-t-opera-t-executionmechanism-xvi-relation-to-other-classes) - [TENET T](#local-section-03-stack-t-opera-t-executionmechanism-tenet-t-2) - [TENET A](#local-section-03-stack-t-opera-t-executionmechanism-tenet-a-2) - [ROTA T](#local-section-03-stack-t-opera-t-executionmechanism-rota-t-2) - [AREPO T](#local-section-03-stack-t-opera-t-executionmechanism-arepo-t-2) - [SATOR T](#local-section-03-stack-t-opera-t-executionmechanism-sator-t-2) - [XVII. FAILURE CONDITIONS](#local-section-03-stack-t-opera-t-executionmechanism-xvii-failure-conditions) - [INPUT FAILURES](#local-section-03-stack-t-opera-t-executionmechanism-input-failures) - [STRUCTURAL FAILURES](#local-section-03-stack-t-opera-t-executionmechanism-structural-failures) - [CARRIER FAILURES](#local-section-03-stack-t-opera-t-executionmechanism-carrier-failures) - [GENUS FAILURES](#local-section-03-stack-t-opera-t-executionmechanism-genus-failures) - [REGIME FAILURES](#local-section-03-stack-t-opera-t-executionmechanism-regime-failures) - [CIRCULAR VALIDATION FAILURES](#local-section-03-stack-t-opera-t-executionmechanism-circular-validation-failures) - [XVIII. SUMMARY](#local-section-03-stack-t-opera-t-executionmechanism-xviii-summary) - [FINAL LAW](#local-section-03-stack-t-opera-t-executionmechanism-final-law) - [CLOSURE RULE](#local-section-03-stack-t-opera-t-executionmechanism-closure-rule) ============================================================ PURPOSE ============================================================ Execute relational operations over REGIMEN_T. OPERA T applies relative predicates to articulated terms under a declared frame, within the structure instantiated by ROTA T and only after admissibility is granted by AREPO T. OPERA T governs: â€¢ relational profiling â€¢ frame-bound comparison â€¢ slot-bound predicate application â€¢ genus-sensitive execution â€¢ structurally lawful relational output OPERA T does NOT: â€¢ define predicates (TENET) â€¢ define structure (ROTAS) â€¢ define admissibility (AREPO) â€¢ mediate output (SATOR) ------------------------------------------------------------ CORE ASSERTION ------------------------------------------------------------ OPERA T does not execute over pure principial unity. OPERA T executes over expressed and contracted terms under the relative regime of T. ============================================================ ============================================================ I. CONTROL-PLANE POSITION ============================================================ TENET â†’ ROTAS â†’ AREPO â†’ OPERA â†’ SATOR ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ TENET T: defines relative predicates and genus structure TENET A: defines absolute principial predicates ROTA T: instantiates the carrier machine AREPO T: admits execution over that machine OPERA T: executes relational articulation SATOR T: mediates the result ============================================================ II. EXECUTION PRINCIPLE ============================================================ OPERA T applies T-predicates as slot-bound relational operators. ------------------------------------------------------------ PRIMARY OPERATIONAL LAW ------------------------------------------------------------ Execution is SLOT-first. This means: â€¢ SLOT is the primary operational anchor â€¢ SYMBOL is a bound surface â€¢ NUMERIC is a bound projection â€¢ no symbolic or numeric surface may override slot identity ------------------------------------------------------------ RULE ------------------------------------------------------------ OPERA T executes over: T(Ï) or T(Ï,g) where: Ï = ordinal slot g = genus slot (when active) ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ OPERA T must not: âœ— operate token-first âœ— operate numeric-first âœ— infer traversal from symbol sequence alone ============================================================ III. INPUT DOMAIN ============================================================ Required: X, Y Where X and Y are relata. ------------------------------------------------------------ VALID RELATA ------------------------------------------------------------ Relata must be: â€¢ expressed â€¢ articulated â€¢ comparable â€¢ non-pure Examples: â€¢ articulated terms â€¢ states â€¢ situations â€¢ propositions â€¢ expressed principial contractions ------------------------------------------------------------ INVALID RELATA ------------------------------------------------------------ Pure undifferentiated A-dignities in full convertibility are not valid direct relata for OPERA T. Examples of invalid direct execution targets: âœ— Bonitas as pure undifferentiated principium âœ— Magnitudo as pure undifferentiated principium ------------------------------------------------------------ RULE ------------------------------------------------------------ OPERA T executes only on expressed forms: X_expr Y_expr not on: A_pure ============================================================ ============================================================ IV. RELATION TO TENET A ============================================================ TENET A and TENET T are both principial regimes. ------------------------------------------------------------ TENET A provides: â€¢ absolute predicates â€¢ principial content â€¢ convertibility in undifferentiated unity TENET T provides: â€¢ relative predicates â€¢ mediating articulations over expressed terms ------------------------------------------------------------ EXECUTION LAW ------------------------------------------------------------ OPERA T does NOT test or operate upon: pure convertibility of A OPERA T operates upon: contracted or articulated expressions in which principial content is already expressed in context ------------------------------------------------------------ FORMAL READING ------------------------------------------------------------ A_pure: undifferentiated principial unity A_expr: contracted or articulated principial expression OPERA T operates over: relation_between(A_expr, A_expr) NOT over: relation_between(A_pure, A_pure) ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ OPERA T must not: âœ— replace OPERA A âœ— derive principial ontology âœ— mutate A into T ============================================================ V. STRUCTURAL DEPENDENCY ============================================================ OPERA T requires: â€¢ bound(TENET T) â€¢ bound(TENET A) when A-derived content is involved â€¢ bound(ROTAS) â€¢ instantiated(ROTA T) â€¢ admitted(AREPO T) ------------------------------------------------------------ RULE ------------------------------------------------------------ No execution may proceed unless the structural machine is available and the request has passed AREPO T. ------------------------------------------------------------ FAILURE ------------------------------------------------------------ If any dependency is absent: BLOCK: ============================================================ VI. FRAME DECLARATION ============================================================ FRAME defines the comparison stance. ------------------------------------------------------------ Required form: ------------------------------------------------------------ FRAME := ------------------------------------------------------------ Default: ------------------------------------------------------------ If omitted and defaultable: FRAME := "general relation profile" ------------------------------------------------------------ RULE ------------------------------------------------------------ FRAME must: â€¢ define the aspect of relation â€¢ not redefine predicates â€¢ not introduce ontology â€¢ not silently shift regime ------------------------------------------------------------ FAILURE ------------------------------------------------------------ â€¢ FRAME_UNDEFINED â€¢ FRAME_REDEFINES_PREDICATE â€¢ FRAME_AS_ONTOLOGY ============================================================ VII. EXECUTION MODES ============================================================ MODE options: â€¢ FULL â€¢ TRIAD â€¢ GENUS ------------------------------------------------------------ DEFAULT: ------------------------------------------------------------ MODE := FULL ------------------------------------------------------------ RULE ------------------------------------------------------------ Mode changes execution scope, not predicate canon. ============================================================ VIII. MODE = FULL ============================================================ In FULL mode, OPERA T executes across the full slot-domain: Ï âˆˆ {â… ,â…¡,â…¢,â…£,â…¤,â…¥,â…¦,â…§,â…¨} ------------------------------------------------------------ EXECUTION PATTERN ------------------------------------------------------------ For each slot Ï: apply T(Ï) to (X_expr, Y_expr) under FRAME ------------------------------------------------------------ OUTPUT REQUIREMENT ------------------------------------------------------------ For each slot: â€¢ 1â€“2 constrained relational statements â€¢ strength tag: HIGH | MED | LOW ------------------------------------------------------------ RULE ------------------------------------------------------------ Execution order must preserve slot order. That order is: â… â†’ â…¡ â†’ â…¢ â†’ â…£ â†’ â…¤ â†’ â…¥ â†’ â…¦ â†’ â…§ â†’ â…¨ ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ FULL mode must not reorder output by: âœ— symbol sequence preference âœ— rhetorical emphasis âœ— numeric magnitude ============================================================ IX. MODE = TRIAD ============================================================ In TRIAD mode, OPERA T applies one triadic subset only. ------------------------------------------------------------ TRIADS ------------------------------------------------------------ Î”1 := {â… ,â…¡,â…¢} = {B,C,D} Î”2 := {â…£,â…¤,â…¥} = {E,F,G} Î”3 := {â…¦,â…§,â…¨} = {H,I,K} ------------------------------------------------------------ RULE ------------------------------------------------------------ TRIAD mode must specify: â€¢ requested triad OR â€¢ triad-walk explicitly ------------------------------------------------------------ TRIAD-WALK ------------------------------------------------------------ If requested: Î”1 â†’ Î”2 â†’ Î”3 ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ TRIAD selection changes execution scope only. It does not alter carrier structure or predicate meaning. ============================================================ X. MODE = GENUS ============================================================ In GENUS mode, OPERA T executes over: T(Ï,g) with: Ï âˆˆ {â… ..â…¨} g âˆˆ {1,2,3} ------------------------------------------------------------ RULE ------------------------------------------------------------ GENUS mode requires: â€¢ explicit genus slot â€¢ admissibility already granted by AREPO T ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ Genus modulates: â€¢ abstraction layer â€¢ type of relation â€¢ domain sensitivity Genus does NOT: â€¢ redefine relata â€¢ define ontology â€¢ replace predicate identity ------------------------------------------------------------ GENUS-AWARE NOTATION ------------------------------------------------------------ Examples: TB1 TC2 TF3 TI1 ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ Flat shorthand is insufficient in genus-sensitive execution. ============================================================ XI. GENUS TRANSIT OBSERVANCE ============================================================ OPERA T observes genus transit constraints defined by TENET T and enforced by AREPO T. ------------------------------------------------------------ LOCAL TRANSIT (WITHIN PREDICATE) ------------------------------------------------------------ Allowed: T(Ï,1) â†” T(Ï,2) T(Ï,2) â†” T(Ï,3) Forbidden: T(Ï,1) â†› T(Ï,3) T(Ï,3) â†› T(Ï,1) ------------------------------------------------------------ CROSS-PREDICATE TRANSIT ------------------------------------------------------------ Default lawful pattern: T(Ï,g) â†’ T(Ïƒ,g) where: Ï â‰ Ïƒ genus preserved ------------------------------------------------------------ MEDIATED GENUS CHANGE ------------------------------------------------------------ If genus changes across predicates, mediation is required. Examples of admissible mediation: T(Ï,g1) â†’ T(Ï,g2) â†’ T(Ïƒ,g2) or T(Ï,g1) â†’ T(Ïƒ,g1) â†’ T(Ïƒ,g2) ------------------------------------------------------------ FAILURE ------------------------------------------------------------ If requested transit violates AREPO-admitted constraints: BLOCK: GENUS_INVALID_TRANSITION ------------------------------------------------------------ RULE ------------------------------------------------------------ OPERA T executes only lawful or already-admitted transitions. It does not self-legislate transit law. ============================================================ XII. RELATIONAL PURITY LAW ============================================================ T-predicates must be executed as relations between relata. ------------------------------------------------------------ CORRECT FORM ------------------------------------------------------------ relation_between(X_expr, Y_expr) ------------------------------------------------------------ INCORRECT FORM ------------------------------------------------------------ predicate_as_property_of(X) predicate_as_being_of(Y) ------------------------------------------------------------ EXAMPLES ------------------------------------------------------------ Correct: â€œX differs from Y under aspect Z.â€ Incorrect: â€œX is Differentia.â€ ------------------------------------------------------------ RULE ------------------------------------------------------------ OPERA T must preserve: relation(X,Y) and must not collapse into: attribute(X) or being(X) ============================================================ XIII. NON-ONTOLOGY ENFORCEMENT ============================================================ OPERA T must preserve: Relatio â‰ Esse ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ T-predicates do not posit being. They qualify respects under which expressed terms are: â€¢ compared â€¢ distinguished â€¢ mediated â€¢ evaluated ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ OPERA T must not: âœ— promote relation into substance âœ— infer identity from relation alone âœ— treat T as subject ontology ============================================================ XIV. EXECUTION OUTPUT ============================================================ Canonical output form: ------------------------------------------------------------ RELATA: X vs Y FRAME: <...> T_PROFILE: â… /B Differentia (Differens) [TB] : <...> (HIGH|MED|LOW) â…¡/C Concordantia (Concordans) [TC] : <...> (HIGH|MED|LOW) â…¢/D Contrarietas (Contrarium) [TD] : <...> (HIGH|MED|LOW) â…£/E Principium (Initialis) [TE] : <...> (HIGH|MED|LOW) â…¤/F Medium (Medians) [TF] : <...> (HIGH|MED|LOW) â…¥/G Finis (Finalis) [TG] : <...> (HIGH|MED|LOW) â…¦/H Maioritas (Maior) [TH] : <...> (HIGH|MED|LOW) â…§/I Aequalitas (Aequalis) [TI] : <...> (HIGH|MED|LOW) â…¨/K Minoritas (Minor) [TK] : <...> (HIGH|MED|LOW) SUMMARY: TOP_PREDICATES: <...> NON_APPLICABLE: <...> NON-ONTOLOGY: "Relatio â‰ Esse." ------------------------------------------------------------ GENUS OUTPUT EXTENSION ------------------------------------------------------------ When genus-sensitive: ACTIVE_GENUS_SLOT::<1|2|3> or explicit slot/genus labels: T(â… ,1), T(â…¡,2), etc. ------------------------------------------------------------ TRANSIT OUTPUT EXTENSION ------------------------------------------------------------ If genus transit is active: ACTIVE_NODE:: REQUESTED_TRANSIT::<...> TRANSIT_STATUS:: If mediated: MEDIATION_PATH::<...> ============================================================ XV. CIRCULAR CONSISTENCY VALIDATION ============================================================ PURPOSE ------------------------------------------------------------ Circular consistency validation adds second-order validation to OPERA T without replacing: â€¢ T-predicate evaluation â€¢ pairwise / triadic relational analysis â€¢ Q-mediated interrogation â€¢ standard OPERA T outputs It adds: â€¢ cyclic relational closure checking â€¢ act-generation validation for predicates â€¢ agent-grounding validation for predicates â€¢ global relational coherence enforcement ------------------------------------------------------------ VALIDATION PRINCIPLE ------------------------------------------------------------ A relation is not fully validated merely because it is locally coherent. It must also be coherent with: â€¢ the triad of relations from which it is generated (ACT) â€¢ the triad of relations for which it functions as agent Thus OPERA T validates: local relation validity + relational coherence across triads + circular consistency of the T-field ------------------------------------------------------------ ACT GENERATION LAW ------------------------------------------------------------ Derived relational predicates are read as acts of prior triads. Canonical articulation: E (BEGINNING) = ACT(B, C, D) F (MIDDLE) = ACT(C, D, E) G (END) = ACT(D, E, F) H (MAJORITY) = ACT(E, F, G) I (EQUALITY) = ACT(F, G, H) K (MINORITY) = ACT(G, H, I) Where: B = DIFFERENCE C = CONCORDANCE D = CONTRARIETY This means: â€¢ Beginning emerges from the interplay of difference, concordance, and contrariety â€¢ Middle emerges from concordance, contrariety, and beginning â€¢ End emerges from contrariety, beginning, and middle â€¢ and so forth through the full chain Rule: No derived predicate (E-K) may receive a strong relational reading if the triad from which it is generated cannot structurally sustain that relation. Constraint: This law refines but does not replace local relational analysis. ------------------------------------------------------------ AGENT GROUNDING LAW ------------------------------------------------------------ Core predicates are read as agents of later triads: B (DIFFERENCE) = AGENT(H, I, K) C (CONCORDANCE) = AGENT(I, K, B) D (CONTRARIETY) = AGENT(K, B, C) This means: â€¢ Difference must remain compatible with the field constituted by Majority, Equality, Minority â€¢ Concordance must remain compatible with IKB â€¢ Contrariety must remain compatible with KBC Rule: BCD is not only foundational. It is also retroactively validated by the higher relational field. Constraint: This does not invert relational priority. It introduces retroactive validation, not causal inversion. ------------------------------------------------------------ CIRCULAR RELATIONAL CLOSURE ------------------------------------------------------------ The T-field must form a cyclic relational system: B â†’ C â†’ D â†’ E â†’ F â†’ G â†’ H â†’ I â†’ K â†’ B Minimal structural articulation: (DIFFERENCE â†’ CONCORDANCE â†’ CONTRARIETY) â†’ (BEGINNING â†’ MIDDLE â†’ END) â†’ (MAJORITY â†’ EQUALITY â†’ MINORITY) â†’ back to DIFFERENCE After OPERA T execution, the relational field must be checked for cyclic coherence. A relational interpretation may be: â€¢ locally valid â€¢ pairwise consistent â€¢ yet globally inconsistent Such a result must be flagged. Constraint: Circular closure is a validation layer, not a new execution mode. ------------------------------------------------------------ CIRCULAR CONSISTENCY CHECK ------------------------------------------------------------ For each predicate P: CHECK 1: consistency with its ACT source triad CHECK 2: consistency with its AGENT target triad Formal schema: CONSISTENT_ACT(Px) := Px is structurally supported by source_triad(Px) CONSISTENT_AGENT(Px) := Px is structurally supported by target_triad(Px) CIRCULAR_OK := âˆ€ P: CONSISTENT_ACT(P) âˆ§ CONSISTENT_AGENT(P) where applicable Rule: This validation occurs after relational analysis, not during. ------------------------------------------------------------ RELATIONAL_CIRCULAR_INCONSISTENCY ------------------------------------------------------------ Definition: assigned when a relational predicate is locally coherent but incompatible with: â€¢ its generating triad â€¢ its grounding triad â€¢ the global relational cycle Examples: 1. Beginning appears strong, but Difference/Concordance/Contrariety cannot sustain it 2. Equality appears balanced, but Majority/Minority structure contradicts it 3. Difference is asserted, but Majority/Equality/Minority collapse it Rule: This flag must be explicit. Silent relational inconsistency is forbidden. ------------------------------------------------------------ VALIDITY CONSEQUENCES ------------------------------------------------------------ If inconsistency is local: â€¢ degrade predicate strength â€¢ attach flag If inconsistency propagates: â€¢ degrade relational structure If inconsistency breaks the cycle: â€¢ mark: T_FIELD_CIRCULAR_FAILURE Rule: Relational coherence must not be presented as stable if the cycle is broken. ------------------------------------------------------------ RELATION TO BCD PRIORITY ------------------------------------------------------------ Difference, Concordance, and Contrariety remain foundational. Circular validation does not replace them. Instead: BCD defines relational ground circular closure validates relational completeness Validation order: 1. local predicate evaluation 2. triadic analysis (BCD) 3. derived predicate formation (E-K) 4. relational synthesis 5. circular consistency check Constraint: Circular closure must not bypass foundational triads. ------------------------------------------------------------ CIRCULAR VALIDATION OUTPUT EXTENSION ------------------------------------------------------------ CIRCULAR_VALIDATION: { ACT_SOURCE_STATUS: AGENT_TARGET_STATUS: CIRCULAR_CLOSURE_STATUS: CIRCULAR_FLAGS: { ... } } Rule: Circular validation output must be surfaced when relational stability affects downstream use. ------------------------------------------------------------ SYSTEM RESULT ------------------------------------------------------------ OPERA T is not only relational analysis. It is a cyclic relational consistency engine rather than a set of independent predicate evaluations. ============================================================ XVI. RELATION TO OTHER CLASSES ============================================================ TENET T ------------------------------------------------------------ Provides: â€¢ predicate canon â€¢ genus structure â€¢ slot identity OPERA T observes this canon. ------------------------------------------------------------ TENET A ------------------------------------------------------------ Provides: â€¢ principial content when A-derived expressions are involved OPERA T operates only after such content is expressed. ------------------------------------------------------------ ROTA T ------------------------------------------------------------ Provides: â€¢ carrier machine â€¢ loci â€¢ adjacency â€¢ traversal topology OPERA T executes within this structure. ------------------------------------------------------------ AREPO T ------------------------------------------------------------ Provides: â€¢ admissibility â€¢ transition legality â€¢ structure-sensitive permission OPERA T must not bypass AREPO T. ------------------------------------------------------------ SATOR T ------------------------------------------------------------ Receives: â€¢ execution outputs â€¢ structural result profile OPERA T does not mediate its own outputs. ============================================================ XVII. FAILURE CONDITIONS ============================================================ INPUT FAILURES ------------------------------------------------------------ â€¢ RELATA_MISSING â€¢ PURE_PRINCIPIA_INPUT â€¢ FRAME_UNDEFINED ------------------------------------------------------------ STRUCTURAL FAILURES ------------------------------------------------------------ â€¢ TENET_BINDING_MISSING â€¢ ROTAS_BINDING_MISSING â€¢ ROTA_T_NOT_INSTANTIATED â€¢ AREPO_ADMISSION_MISSING ------------------------------------------------------------ CARRIER FAILURES ------------------------------------------------------------ â€¢ SLOT_UNRESOLVED â€¢ SYMBOL_SLOT_MISMATCH â€¢ NUMERIC_MISMATCH â€¢ SYMBOL_FIRST_EXECUTION_ATTEMPT â€¢ NUMERIC_FIRST_EXECUTION_ATTEMPT ------------------------------------------------------------ GENUS FAILURES ------------------------------------------------------------ â€¢ GENUS_MISSING â€¢ GENUS_COLLAPSE â€¢ GENUS_INVALID_TRANSITION â€¢ UNMEDIATED_GENUS_SHIFT ------------------------------------------------------------ REGIME FAILURES ------------------------------------------------------------ â€¢ RELATION_AS_BEING â€¢ PREDICATE_AS_SUBSTANCE â€¢ A_T_COLLAPSE â€¢ A_PURE_DIRECT_OPERATION ------------------------------------------------------------ CIRCULAR VALIDATION FAILURES ------------------------------------------------------------ â€¢ RELATIONAL_CIRCULAR_INCONSISTENCY â€¢ T_FIELD_CIRCULAR_FAILURE â€¢ ACT_SOURCE_INCOHERENT â€¢ AGENT_TARGET_INCOHERENT ============================================================ XVIII. SUMMARY ============================================================ OPERA T defines: â€¢ relational execution over REGIMEN_T â€¢ slot-first application of relative predicates â€¢ execution over expressed terms only â€¢ genus-sensitive execution â€¢ non-ontological relational profiling â€¢ circular consistency validation ------------------------------------------------------------ FINAL LAW ------------------------------------------------------------ OPERA T executes only that which is: â€¢ doctrinally bound â€¢ structurally instantiated â€¢ admissibly validated â€¢ relationally explicit â€¢ expressed rather than pure â€¢ circularly consistent ------------------------------------------------------------ CLOSURE RULE ------------------------------------------------------------ OPERA T does not define what is. It relates what has already been expressed, through slot-bound predicates of REGIMEN_T, within the structure instantiated by ROTA T, under the admissibility of AREPO T. ============================================================ END OF ARTIFACT ============================================================ END_VERBATIM_ARTIFACT: OPERA ============================================================ ============================================================ BEGIN_VERBATIM_ARTIFACT: SATOR Source_File: 03_STACK_T/SATOR_T_OutputRequirements.md Source_Exists: TRUE Source_Non_Empty: TRUE Source_Length_Bytes: 25071 Source_SHA256: bd2d5628d33168a66b7e40e69833e25c379160acb2fba0e389cd630d4ba4d38d ------------------------------------------------------------ ============================================================ SATOR T — REGIMEN_T MEDIATION LAYER Ars Generalis Applied — Relational Mediation (Figura T) Version: 0.2.1-SATOR-T (rev T.5 — slot-first / order-normalized / non-executive-locked) Status: MEDIATION LAYER — LOCK CANDIDATE Depends-On: • OPERA T • AREPO T • ROTA T • TENET T • ORDER DECLARATION PROTOCOL Authority: AGLA / CONTROL PLANE Mutation Policy: VERSION-CONTROLLED ONLY Class: SATOR ============================================================ ## LOCAL SECTION INDEX Scope: local anchors within this artifact only. No cross-artifact links are introduced here. - [PURPOSE](#local-section-03-stack-t-sator-t-outputrequirements-purpose) - [CORE ASSERTION](#local-section-03-stack-t-sator-t-outputrequirements-core-assertion) - [I. CONTROL-PLANE POSITION](#local-section-03-stack-t-sator-t-outputrequirements-i-control-plane-position) - [INTERPRETATION](#local-section-03-stack-t-sator-t-outputrequirements-interpretation) - [OPERA T:](#local-section-03-stack-t-sator-t-outputrequirements-opera-t) - [AREPO T:](#local-section-03-stack-t-sator-t-outputrequirements-arepo-t) - [ROTA T:](#local-section-03-stack-t-sator-t-outputrequirements-rota-t) - [SATOR T:](#local-section-03-stack-t-sator-t-outputrequirements-sator-t) - [II. MEDIATION PRINCIPLE](#local-section-03-stack-t-sator-t-outputrequirements-ii-mediation-principle) - [ORDINAL PRIMACY LAW (ENFORCED)](#local-section-03-stack-t-sator-t-outputrequirements-ordinal-primacy-law-enforced) - [RULE](#local-section-03-stack-t-sator-t-outputrequirements-rule) - [INTERPRETATION](#local-section-03-stack-t-sator-t-outputrequirements-interpretation-2) - [III. ORDER VOCABULARY DISCIPLINE](#local-section-03-stack-t-sator-t-outputrequirements-iii-order-vocabulary-discipline) - [RULE](#local-section-03-stack-t-sator-t-outputrequirements-rule-2) - [DEFINITIONS](#local-section-03-stack-t-sator-t-outputrequirements-definitions) - [ACTIVE_ORDER:](#local-section-03-stack-t-sator-t-outputrequirements-active-order) - [DISPLAY_ORDER:](#local-section-03-stack-t-sator-t-outputrequirements-display-order) - [ORDER_REFERENCE:](#local-section-03-stack-t-sator-t-outputrequirements-order-reference) - [CONSTRAINT](#local-section-03-stack-t-sator-t-outputrequirements-constraint) - [IV. OUTPUT STRUCTURE](#local-section-03-stack-t-sator-t-outputrequirements-iv-output-structure) - [ACTIVE_ORDER:](#local-section-03-stack-t-sator-t-outputrequirements-active-order-2) - [T_PROFILE:](#local-section-03-stack-t-sator-t-outputrequirements-t-profile) - [SUMMARY:](#local-section-03-stack-t-sator-t-outputrequirements-summary) - [RULE](#local-section-03-stack-t-sator-t-outputrequirements-rule-3) - [FLEXIBILITY](#local-section-03-stack-t-sator-t-outputrequirements-flexibility) - [CONSTRAINT](#local-section-03-stack-t-sator-t-outputrequirements-constraint-2) - [V. GENUS AWARENESS](#local-section-03-stack-t-sator-t-outputrequirements-v-genus-awareness) - [GENUS EXPOSURE](#local-section-03-stack-t-sator-t-outputrequirements-genus-exposure) - [RULE](#local-section-03-stack-t-sator-t-outputrequirements-rule-4) - [INTERPRETATION](#local-section-03-stack-t-sator-t-outputrequirements-interpretation-3) - [VI. NON-ONTOLOGY ENFORCEMENT](#local-section-03-stack-t-sator-t-outputrequirements-vi-non-ontology-enforcement) - [INTERPRETATION](#local-section-03-stack-t-sator-t-outputrequirements-interpretation-4) - [RULE](#local-section-03-stack-t-sator-t-outputrequirements-rule-5) - [CONSTRAINT](#local-section-03-stack-t-sator-t-outputrequirements-constraint-3) - [VII. STRUCTURAL FIDELITY](#local-section-03-stack-t-sator-t-outputrequirements-vii-structural-fidelity) - [RULE](#local-section-03-stack-t-sator-t-outputrequirements-rule-6) - [ALLOWED](#local-section-03-stack-t-sator-t-outputrequirements-allowed) - [CONSTRAINT](#local-section-03-stack-t-sator-t-outputrequirements-constraint-4) - [VIII. RELATION TO AREPO T](#local-section-03-stack-t-sator-t-outputrequirements-viii-relation-to-arepo-t) - [RULE](#local-section-03-stack-t-sator-t-outputrequirements-rule-7) - [CONSTRAINT](#local-section-03-stack-t-sator-t-outputrequirements-constraint-5) - [INTERPRETATION](#local-section-03-stack-t-sator-t-outputrequirements-interpretation-5) - [IX. RELATION TO ROTA T](#local-section-03-stack-t-sator-t-outputrequirements-ix-relation-to-rota-t) - [RULE](#local-section-03-stack-t-sator-t-outputrequirements-rule-8) - [INTERPRETATION](#local-section-03-stack-t-sator-t-outputrequirements-interpretation-6) - [X. RELATION TO OPERA T](#local-section-03-stack-t-sator-t-outputrequirements-x-relation-to-opera-t) - [RULE](#local-section-03-stack-t-sator-t-outputrequirements-rule-9) - [CONSTRAINT](#local-section-03-stack-t-sator-t-outputrequirements-constraint-6) - [XI. PEDAGOGICAL MODULATION](#local-section-03-stack-t-sator-t-outputrequirements-xi-pedagogical-modulation) - [ALLOWED](#local-section-03-stack-t-sator-t-outputrequirements-allowed-2) - [CONSTRAINT](#local-section-03-stack-t-sator-t-outputrequirements-constraint-7) - [RULE](#local-section-03-stack-t-sator-t-outputrequirements-rule-10) - [XII. FAILURE CONDITIONS](#local-section-03-stack-t-sator-t-outputrequirements-xii-failure-conditions) - [MEDIATION FAILURES](#local-section-03-stack-t-sator-t-outputrequirements-mediation-failures) - [STRUCTURAL FAILURES](#local-section-03-stack-t-sator-t-outputrequirements-structural-failures) - [REGIME FAILURES](#local-section-03-stack-t-sator-t-outputrequirements-regime-failures) - [INTERACTION FAILURES](#local-section-03-stack-t-sator-t-outputrequirements-interaction-failures) - [XIII. SUMMARY](#local-section-03-stack-t-sator-t-outputrequirements-xiii-summary) - [FINAL LAW](#local-section-03-stack-t-sator-t-outputrequirements-final-law) - [CLOSURE RULE](#local-section-03-stack-t-sator-t-outputrequirements-closure-rule) ============================================================ PURPOSE ============================================================ Mediate the results of OPERA T execution under REGIMEN_T. SATOR T exposes relational structures in a form that is: • structurally faithful • slot-legible • order-aware • genus-aware (when relevant) • non-ontological • non-executive SATOR T governs: • presentation of relational outputs • exposure of structural strength and weakness • controlled explanatory framing • interaction discipline over relational analysis SATOR T does NOT: • execute relations (OPERA) • validate admissibility (AREPO) • define predicates (TENET) • define structure (ROTAS) ------------------------------------------------------------ CORE ASSERTION ------------------------------------------------------------ SATOR T does not compute relations. SATOR T exposes relations computed elsewhere, preserving their structure and limits. ============================================================ ============================================================ I. CONTROL-PLANE POSITION ============================================================ TENET → ROTAS → AREPO → OPERA → SATOR ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ OPERA T: produces relational structures AREPO T: validates admissibility and transitions ROTA T: provides structural carrier machine SATOR T: mediates and exposes the result ============================================================ II. MEDIATION PRINCIPLE ============================================================ SATOR T is SLOT-first in exposure. ------------------------------------------------------------ ORDINAL PRIMACY LAW (ENFORCED) ------------------------------------------------------------ SATOR T must present: SLOT → SYMBOL → NUMERIC (when relevant) ------------------------------------------------------------ RULE ------------------------------------------------------------ SATOR T must not: ✗ present symbol sequence as primary structure ✗ present numeric sequence as structural basis ✗ reorder output based on rhetoric or emphasis ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ Structure is read through SLOT. SYMBOL and NUMERIC are surfaces. ============================================================ ============================================================ III. ORDER VOCABULARY DISCIPLINE ============================================================ SATOR T must explicitly distinguish: • ACTIVE_ORDER • DISPLAY_ORDER (if transformed for readability) • ORDER_REFERENCE (if comparative) ------------------------------------------------------------ RULE ------------------------------------------------------------ SATOR T must never use ambiguous "order". ------------------------------------------------------------ DEFINITIONS ------------------------------------------------------------ ACTIVE_ORDER: the carrier package bound for execution DISPLAY_ORDER: optional transformation for readability (must preserve slot traceability) ORDER_REFERENCE: external mapping surface ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ DISPLAY_ORDER must not: ✗ alter slot identity ✗ alter traversal structure ✗ introduce implicit carrier substitution ============================================================ IV. OUTPUT STRUCTURE ============================================================ Canonical full exposure format: ------------------------------------------------------------ RELATA: X vs Y FRAME: <...> ACTIVE_ORDER: T_PROFILE: Ⅰ/B Differentia [TB] : <...> (HIGH|MED|LOW) Ⅱ/C Concordantia [TC] : <...> (HIGH|MED|LOW) Ⅲ/D Contrarietas [TD] : <...> (HIGH|MED|LOW) Ⅳ/E Principium [TE] : <...> (HIGH|MED|LOW) Ⅴ/F Medium [TF] : <...> (HIGH|MED|LOW) Ⅵ/G Finis [TG] : <...> (HIGH|MED|LOW) Ⅶ/H Maioritas [TH] : <...> (HIGH|MED|LOW) Ⅷ/I Aequalitas [TI] : <...> (HIGH|MED|LOW) Ⅸ/K Minoritas [TK] : <...> (HIGH|MED|LOW) SUMMARY: TOP_PREDICATES: <...> NON_APPLICABLE: <...> ------------------------------------------------------------ RULE ------------------------------------------------------------ This is the canonical full exposure form. ------------------------------------------------------------ FLEXIBILITY ------------------------------------------------------------ Compact or filtered forms are allowed if: • slot traceability is preserved • predicate identity is preserved • order declaration is not obscured ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ No compact form may: ✗ remove slot indexing ✗ collapse predicates into unordered lists ============================================================ V. GENUS AWARENESS ============================================================ SATOR T must expose genus only when: • present in OPERA T output • structurally relevant • required for interpretation ------------------------------------------------------------ GENUS EXPOSURE ------------------------------------------------------------ Forms: • ACTIVE_GENUS_SLOT::<1|2|3> • T(ρ,g) notation ------------------------------------------------------------ RULE ------------------------------------------------------------ SATOR T must not: ✗ infer genus ✗ collapse genus layers ✗ translate genus into ontology ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ Genus is: • structural modulation layer • not semantic redefinition ============================================================ VI. NON-ONTOLOGY ENFORCEMENT ============================================================ SATOR T must preserve: Relatio ≠ Esse ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ Relations describe: • comparison • distinction • mediation They do NOT define: • substance • identity • essence ------------------------------------------------------------ RULE ------------------------------------------------------------ SATOR T must avoid: ✗ "X is Difference" ✗ "Y is Equality" Preferred form: "X differs from Y under aspect Z" ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ SATOR T must not convert: relation → attribute → being ============================================================ VII. STRUCTURAL FIDELITY ============================================================ SATOR T must preserve OPERA T structure. ------------------------------------------------------------ RULE ------------------------------------------------------------ SATOR T must not: ✗ reorder slots ✗ suppress structurally relevant predicates ✗ amplify or diminish strengths arbitrarily ✗ introduce new relations ------------------------------------------------------------ ALLOWED ------------------------------------------------------------ SATOR T may: • compress language • clarify expression • expose reasoning • highlight dominant relations ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ All transformations must be: • reversible • structurally traceable ============================================================ VIII. RELATION TO AREPO T ============================================================ SATOR T may expose admissibility status. ------------------------------------------------------------ RULE ------------------------------------------------------------ SATOR T may: • surface blocking conditions • expose required mediation condition • display failure states ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ SATOR T must not: ✗ validate admissibility ✗ override AREPO decisions ✗ propose execution paths ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ AREPO decides. SATOR explains. ============================================================ IX. RELATION TO ROTA T ============================================================ ROTA T is the REGIMEN_T machine instantiation within ROTAS. ------------------------------------------------------------ SATOR T uses ROTA T: • as structural reference • as positional grid • as traversal frame ------------------------------------------------------------ RULE ------------------------------------------------------------ SATOR T must not: ✗ reinterpret geometry ✗ redefine adjacency ✗ imply alternative traversal ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ ROTA T defines structure. SATOR T exposes it. ============================================================ X. RELATION TO OPERA T ============================================================ SATOR T receives OPERA T output. ------------------------------------------------------------ RULE ------------------------------------------------------------ SATOR T must: • preserve relational structure • preserve slot ordering • preserve strength classification ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ SATOR T must not: ✗ simulate OPERA T reasoning ✗ re-execute predicates ✗ modify relation results ============================================================ XI. PEDAGOGICAL MODULATION ============================================================ SATOR T may provide explanatory framing. ------------------------------------------------------------ ALLOWED ------------------------------------------------------------ • structural explanation • relation clarification • pattern exposure ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ Pedagogy must: • remain secondary • not alter structure • not introduce ontology ------------------------------------------------------------ RULE ------------------------------------------------------------ SATOR T must distinguish: • method (reusable) • example (illustrative) ============================================================ XII. FAILURE CONDITIONS ============================================================ MEDIATION FAILURES ------------------------------------------------------------ • SLOT_SUPPRESSED • SYMBOL_PRIMARY_PRESENTATION • NUMERIC_PRIMARY_PRESENTATION • ORDER_AMBIGUOUS • ORDER_UNDECLARED_WHEN_REQUIRED ------------------------------------------------------------ STRUCTURAL FAILURES ------------------------------------------------------------ • SLOT_REORDERING • PREDICATE_COLLAPSE • GENUS_ERASURE • GENUS_MISALIGNMENT ------------------------------------------------------------ REGIME FAILURES ------------------------------------------------------------ • RELATION_AS_BEING • ATTRIBUTE_FROM_RELATION • ONTOLOGY_INFERENCE ------------------------------------------------------------ INTERACTION FAILURES ------------------------------------------------------------ • EXECUTION_SIMULATION • ADMISSIBILITY_OVERRIDE • ROUTING_IMPLICATION ============================================================ XIII. SUMMARY ============================================================ SATOR T defines: • mediation of relational outputs • slot-first exposure discipline • order-aware presentation • genus-aware clarification • non-ontological framing ------------------------------------------------------------ FINAL LAW ------------------------------------------------------------ SATOR T exposes only that which is: • structurally produced by OPERA T • admissibly validated by AREPO T • instantiated within ROTA T ------------------------------------------------------------ CLOSURE RULE ------------------------------------------------------------ SATOR T does not determine what is true, what is allowed, or what is executed. It renders relational structure visible, without altering its nature. ============================================================ END OF ARTIFACT ============================================================ END_VERBATIM_ARTIFACT: SATOR ============================================================ ============================================================ END SIGMA_SATOR KERNEL BUNDLE: SIGMA_SATOR_T ============================================================