============================================================ OPERA H — MULTIPLICATIO FIGURAE QUARTAE Ars Generalis Applied — Combinatory Execution Kernel Version: 0.1.3-OPERA-H-TENET-D-SUPPORT Status: PROVISIONAL / EXECUTION-KERNEL (PATCHED) Scope: execution of multiplicatio over Figura Quarta under TENET-dispatched regimes Authority: OPERA Class: OPERA Regime: H (MULTIPLICATIO) Depends-On: - TENET D -- PRINCIPIA DUPLEX / A-T ARTICULATION SUPPORT • TENET D — PRINCIPIA DUPLEX • TENET I — MIXTURA • TENET A — ABSOLUTA • TENET T — RELATIVA • TENET — REGIMEN DISPATCH LAW • ROTAS D — OCTO ROTAE FIGURAE QUARTAE • OPERA F — EXECUTIO TABULAE • AEGIS POPULUS — MULTIPLICATIO PARADIGMA ============================================================ ## LOCAL SECTION INDEX Scope: local anchors within this artifact only. No cross-artifact links are introduced here. - [I. PURPOSE](#local-section-09-stack-h-opera-h-executionmechanism-i-purpose) - [CORE ASSERTION](#local-section-09-stack-h-opera-h-executionmechanism-core-assertion) - [II. EXECUTION POSITION](#local-section-09-stack-h-opera-h-executionmechanism-ii-execution-position) - [FUNCTION](#local-section-09-stack-h-opera-h-executionmechanism-function) - [III. INPUT CONTRACT](#local-section-09-stack-h-opera-h-executionmechanism-iii-input-contract) - [REQUIREMENTS](#local-section-09-stack-h-opera-h-executionmechanism-requirements) - [TENET DISPATCH REQUIREMENT](#local-section-09-stack-h-opera-h-executionmechanism-tenet-dispatch-requirement) - [MULTIPLICATIO MODE](#local-section-09-stack-h-opera-h-executionmechanism-multiplicatio-mode) - [DEFAULT](#local-section-09-stack-h-opera-h-executionmechanism-default) - [FAILURE](#local-section-09-stack-h-opera-h-executionmechanism-failure) - [IV. PRE-EXECUTION VALIDATION](#local-section-09-stack-h-opera-h-executionmechanism-iv-pre-execution-validation) - [0. TENET DISPATCH VALIDITY](#local-section-09-stack-h-opera-h-executionmechanism-0-tenet-dispatch-validity) - [1. ROTA VALIDITY](#local-section-09-stack-h-opera-h-executionmechanism-1-rota-validity) - [2. REGIME CONSISTENCY](#local-section-09-stack-h-opera-h-executionmechanism-2-regime-consistency) - [3. ORDINAL PRESERVATION](#local-section-09-stack-h-opera-h-executionmechanism-3-ordinal-preservation) - [4. MODE COMPATIBILITY](#local-section-09-stack-h-opera-h-executionmechanism-4-mode-compatibility) - [FAILURE](#local-section-09-stack-h-opera-h-executionmechanism-failure-2) - [BLOCKING RULE](#local-section-09-stack-h-opera-h-executionmechanism-blocking-rule) - [V. TENET DISPATCH LAYER](#local-section-09-stack-h-opera-h-executionmechanism-v-tenet-dispatch-layer) - [ELEMENT GROUPS](#local-section-09-stack-h-opera-h-executionmechanism-element-groups) - [DISPATCH RULE](#local-section-09-stack-h-opera-h-executionmechanism-dispatch-rule) - [SPECIAL RULE](#local-section-09-stack-h-opera-h-executionmechanism-special-rule) - [RULE](#local-section-09-stack-h-opera-h-executionmechanism-rule) - [FAILURE](#local-section-09-stack-h-opera-h-executionmechanism-failure-3) - [VI. CONFIGURATION SELECTION LAYER](#local-section-09-stack-h-opera-h-executionmechanism-vi-configuration-selection-layer) - [TENET-BOUND SELECTION RULE](#local-section-09-stack-h-opera-h-executionmechanism-tenet-bound-selection-rule) - [DOMAIN RULES](#local-section-09-stack-h-opera-h-executionmechanism-domain-rules) - [TENET A:](#local-section-09-stack-h-opera-h-executionmechanism-tenet-a) - [TENET T:](#local-section-09-stack-h-opera-h-executionmechanism-tenet-t) - [TENET D:](#local-section-09-stack-h-opera-h-executionmechanism-tenet-d) - [TENET I:](#local-section-09-stack-h-opera-h-executionmechanism-tenet-i) - [DEFAULT](#local-section-09-stack-h-opera-h-executionmechanism-default-2) - [FAILURE](#local-section-09-stack-h-opera-h-executionmechanism-failure-4) - [VII. SELECTION MODES](#local-section-09-stack-h-opera-h-executionmechanism-vii-selection-modes) - [RULE](#local-section-09-stack-h-opera-h-executionmechanism-rule-2) - [FAILURE](#local-section-09-stack-h-opera-h-executionmechanism-failure-5) - [VIII. TABULA PRESET INTERFACE](#local-section-09-stack-h-opera-h-executionmechanism-viii-tabula-preset-interface) - [FAILURE](#local-section-09-stack-h-opera-h-executionmechanism-failure-6) - [IX. EXECUTION CORE — MODE DISPATCH](#local-section-09-stack-h-opera-h-executionmechanism-ix-execution-core-mode-dispatch) - [RULE](#local-section-09-stack-h-opera-h-executionmechanism-rule-3) - [FAILURE](#local-section-09-stack-h-opera-h-executionmechanism-failure-7) - [X. EXECUTION — ORDINAL-ALIGNED MULTIPLICATIO](#local-section-09-stack-h-opera-h-executionmechanism-x-execution-ordinal-aligned-multiplicatio) - [PROPERTIES](#local-section-09-stack-h-opera-h-executionmechanism-properties) - [FAILURE](#local-section-09-stack-h-opera-h-executionmechanism-failure-8) - [XI. EXECUTION — POSITION-LOCKED MULTIPLICATIO](#local-section-09-stack-h-opera-h-executionmechanism-xi-execution-position-locked-multiplicatio) - [IDENTIFIER:](#local-section-09-stack-h-opera-h-executionmechanism-identifier) - [DEFINITION](#local-section-09-stack-h-opera-h-executionmechanism-definition) - [FORMAL](#local-section-09-stack-h-opera-h-executionmechanism-formal) - [OUTPUT](#local-section-09-stack-h-opera-h-executionmechanism-output) - [PROPERTIES](#local-section-09-stack-h-opera-h-executionmechanism-properties-2) - [FAILURE](#local-section-09-stack-h-opera-h-executionmechanism-failure-9) - [XII. EXECUTION — CARTESIAN MULTIPLICATIO](#local-section-09-stack-h-opera-h-executionmechanism-xii-execution-cartesian-multiplicatio) - [IDENTIFIER:](#local-section-09-stack-h-opera-h-executionmechanism-identifier-2) - [DEFINITION](#local-section-09-stack-h-opera-h-executionmechanism-definition-2) - [FORMAL](#local-section-09-stack-h-opera-h-executionmechanism-formal-2) - [PROPERTIES](#local-section-09-stack-h-opera-h-executionmechanism-properties-3) - [CONSTRAINT](#local-section-09-stack-h-opera-h-executionmechanism-constraint) - [TENET BINDING](#local-section-09-stack-h-opera-h-executionmechanism-tenet-binding) - [FAILURE](#local-section-09-stack-h-opera-h-executionmechanism-failure-10) - [XIII. EXECUTION — ROTA-TRANSFORMATIONAL MULTIPLICATIO](#local-section-09-stack-h-opera-h-executionmechanism-xiii-execution-rota-transformational-multiplicatio) - [IDENTIFIER:](#local-section-09-stack-h-opera-h-executionmechanism-identifier-3) - [DEFINITION](#local-section-09-stack-h-opera-h-executionmechanism-definition-3) - [FORMAL](#local-section-09-stack-h-opera-h-executionmechanism-formal-3) - [TRANSFORMATIONS MAY INCLUDE](#local-section-09-stack-h-opera-h-executionmechanism-transformations-may-include) - [TENET CONSTRAINT](#local-section-09-stack-h-opera-h-executionmechanism-tenet-constraint) - [FAILURE](#local-section-09-stack-h-opera-h-executionmechanism-failure-11) - [XIV. RESULT STRUCTURE](#local-section-09-stack-h-opera-h-executionmechanism-xiv-result-structure) - [RULE](#local-section-09-stack-h-opera-h-executionmechanism-rule-4) - [CONSTRAINT](#local-section-09-stack-h-opera-h-executionmechanism-constraint-2) - [FAILURE](#local-section-09-stack-h-opera-h-executionmechanism-failure-12) - [XV. TRACE DISCIPLINE](#local-section-09-stack-h-opera-h-executionmechanism-xv-trace-discipline) - [RULE](#local-section-09-stack-h-opera-h-executionmechanism-rule-5) - [CONSTRAINT](#local-section-09-stack-h-opera-h-executionmechanism-constraint-3) - [FAILURE](#local-section-09-stack-h-opera-h-executionmechanism-failure-13) - [XVI. REGIME INTEGRITY LAW](#local-section-09-stack-h-opera-h-executionmechanism-xvi-regime-integrity-law) - [PROHIBITIONS](#local-section-09-stack-h-opera-h-executionmechanism-prohibitions) - [RULE](#local-section-09-stack-h-opera-h-executionmechanism-rule-6) - [FAILURE](#local-section-09-stack-h-opera-h-executionmechanism-failure-14) - [XVII. FAILURE CONDITIONS](#local-section-09-stack-h-opera-h-executionmechanism-xvii-failure-conditions) - [EXECUTION FAILURES](#local-section-09-stack-h-opera-h-executionmechanism-execution-failures) - [STRUCTURAL FAILURES](#local-section-09-stack-h-opera-h-executionmechanism-structural-failures) - [TRACE FAILURES](#local-section-09-stack-h-opera-h-executionmechanism-trace-failures) - [TENET DISPATCH FAILURES](#local-section-09-stack-h-opera-h-executionmechanism-tenet-dispatch-failures) - [TENET-SELECTION DETERMINISM FAILURES](#local-section-09-stack-h-opera-h-executionmechanism-tenet-selection-determinism-failures) - [RULE](#local-section-09-stack-h-opera-h-executionmechanism-rule-7) - [XVIII. FUNCTION](#local-section-09-stack-h-opera-h-executionmechanism-xviii-function) - [ROLE IN AGLA CLASS CHAIN](#local-section-09-stack-h-opera-h-executionmechanism-role-in-agla-class-chain) - [TENET:](#local-section-09-stack-h-opera-h-executionmechanism-tenet) - [ROTAS:](#local-section-09-stack-h-opera-h-executionmechanism-rotas) - [AREPO:](#local-section-09-stack-h-opera-h-executionmechanism-arepo) - [OPERA:](#local-section-09-stack-h-opera-h-executionmechanism-opera) - [SATOR:](#local-section-09-stack-h-opera-h-executionmechanism-sator) - [CONSTRAINT](#local-section-09-stack-h-opera-h-executionmechanism-constraint-4) - [FAILURE](#local-section-09-stack-h-opera-h-executionmechanism-failure-15) - [XIX. CLOSURE](#local-section-09-stack-h-opera-h-executionmechanism-xix-closure) - [FINAL LAW](#local-section-09-stack-h-opera-h-executionmechanism-final-law) - [EXECUTION VALIDITY CONDITION](#local-section-09-stack-h-opera-h-executionmechanism-execution-validity-condition) - [DEFAULT EXECUTION LAW](#local-section-09-stack-h-opera-h-executionmechanism-default-execution-law) - [DEFAULT OUTPUT](#local-section-09-stack-h-opera-h-executionmechanism-default-output) - [FINAL STATE](#local-section-09-stack-h-opera-h-executionmechanism-final-state) - [CLOSURE RULE](#local-section-09-stack-h-opera-h-executionmechanism-closure-rule) END SECTION 0 — HEADER ============================================================ ============================================================ I. PURPOSE ============================================================ Define the execution kernel for: MULTIPLICATIO FIGURAE QUARTAE ------------------------------------------------------------ OPERA H establishes: • how TENET anchoring is resolved • how configurations are selected • how chambers are combined • how multiplicatio modes are executed • how results are constructed • how combinatory trace is preserved ------------------------------------------------------------ CORE ASSERTION ------------------------------------------------------------ Multiplicatio is: TENET-dispatched, configuration-selected, admissibility-gated, mode-dependent, trace-preserving execution over ROTAS-defined chambers. TENET D supplies the articulation support for any H execution surface where TENET A absolute principles and TENET T relative principles are jointly operative. TENET D support does not authorize OPERA D execution and does not collapse TENET A or TENET T into a hidden default. ============================================================ END SECTION I ============================================================ ============================================================ II. EXECUTION POSITION ============================================================ OPERA H operates: after AREPO admission under TENET dispatch resolution over ROTAS-instantiated structures ------------------------------------------------------------ OPERA H does NOT: • define principles (TENET) • define topology (ROTAS) • define admissibility (AREPO) • define mediation (SATOR) ------------------------------------------------------------ FUNCTION ------------------------------------------------------------ OPERA H executes: TENET DISPATCH → CONFIGURATION SELECTION → MULTIPLICATIO EXECUTION ============================================================ END SECTION II ============================================================ ============================================================ III. INPUT CONTRACT ============================================================ OPERA H receives: ------------------------------------------------------------ H_INPUT := { chambers: [C₁, C₂, ..., Cₙ] (optional), multiplicatio_mode (optional), selection_mode (optional), configuration_count (optional), rota_set (optional), tabula_preset (optional), preloaded_tabula_context (optional), context_regime, element_set, interaction_type (optional), operator_presence (optional), selected_tenet (optional) } ------------------------------------------------------------ REQUIREMENTS ------------------------------------------------------------ Each chamber must: • declare rota_id • declare W1, W2, W3 • include regime binding (A or T) • include ordinal_slot per carrier ------------------------------------------------------------ TENET DISPATCH REQUIREMENT ------------------------------------------------------------ OPERA H must resolve: selected_tenet before execution. ------------------------------------------------------------ MULTIPLICATIO MODE ------------------------------------------------------------ multiplicatio_mode ∈ { MULTIPLICATIO_OA, MULTIPLICATIO_PL, MULTIPLICATIO_CT, MULTIPLICATIO_RT } ------------------------------------------------------------ DEFAULT ------------------------------------------------------------ If not explicitly provided: multiplicatio_mode := MULTIPLICATIO_OA ------------------------------------------------------------ FAILURE ------------------------------------------------------------ input_incomplete missing_rota missing_ordinal ambiguous_mode element_set_missing interaction_type_unresolved operator_presence_unresolved selected_tenet_missing ============================================================ END SECTION III ============================================================ ============================================================ IV. PRE-EXECUTION VALIDATION ============================================================ Before execution, OPERA H must verify: ------------------------------------------------------------ 0. TENET DISPATCH VALIDITY ------------------------------------------------------------ selected_tenet must be resolved according to: TENET — REGIMEN DISPATCH LAW Validation must confirm: • element_set is explicit or derivable • interaction_type is resolved • operator_presence is detected • selected_tenet is compatible with context ------------------------------------------------------------ 1. ROTA VALIDITY ------------------------------------------------------------ each chamber belongs to ROTAS D family ------------------------------------------------------------ 2. REGIME CONSISTENCY ------------------------------------------------------------ carriers match declared regime (A/T) ------------------------------------------------------------ 3. ORDINAL PRESERVATION ------------------------------------------------------------ ordinal slots are present and valid if selected_tenet == TENET I: ordinal slots must follow TENET I MIXTURA carrier order and full token identity requirements ------------------------------------------------------------ 4. MODE COMPATIBILITY ------------------------------------------------------------ multiplicatio_mode is declared and supported ------------------------------------------------------------ FAILURE ------------------------------------------------------------ tenet_dispatch_invalid tenet_context_mismatch unresolved_operator_presence rota_invalid regime_mismatch ordinal_missing mode_invalid ------------------------------------------------------------ BLOCKING RULE ------------------------------------------------------------ If any validation fails: execution := BLOCKED ============================================================ END SECTION IV ============================================================ ============================================================ V. TENET DISPATCH LAYER ============================================================ Before configuration selection, OPERA H must resolve the correct TENET anchor. ------------------------------------------------------------ TENET_DISPATCH := { element_set, interaction_type, operator_presence, selected_tenet, dispatch_trace } ------------------------------------------------------------ ELEMENT GROUPS ------------------------------------------------------------ A-elements: absolute principles T-elements: relative principles E-elements: interrogatives and rules ------------------------------------------------------------ DISPATCH RULE ------------------------------------------------------------ If: S ⊆ A Then: selected_tenet := TENET A ------------------------------------------------------------ If: S ⊆ T Then: selected_tenet := TENET T ------------------------------------------------------------ If: S ⊆ (A ∪ T) AND interaction is principial Then: selected_tenet := TENET D ------------------------------------------------------------ If: S ∩ E ≠ ∅ AND (A ∪ T) present Then: selected_tenet := TENET I ------------------------------------------------------------ SPECIAL RULE ------------------------------------------------------------ If: S ⊆ E Then: OPERA H is not the primary execution context. ------------------------------------------------------------ RULE ------------------------------------------------------------ OPERA H must not execute until: selected_tenet is resolved ------------------------------------------------------------ FAILURE ------------------------------------------------------------ TENET_UNRESOLVED REGIMEN_AMBIGUITY INCORRECT_TENET_SELECTION OPERATOR_PRESENCE_IGNORED ============================================================ END SECTION V ============================================================ ============================================================ VI. CONFIGURATION SELECTION LAYER ============================================================ Configuration selection precedes multiplicatio. ------------------------------------------------------------ CONFIGURATION_SELECTION := { selection_mode, configuration_count, rota_set, tabula_preset, preloaded_tabula_context, selection_trace } ------------------------------------------------------------ TENET-BOUND SELECTION RULE ------------------------------------------------------------ Configuration selection must operate under: selected_tenet ------------------------------------------------------------ DOMAIN RULES ------------------------------------------------------------ TENET A: A-only domain TENET T: T-only domain TENET D: A ∪ T domain TENET I: A ∪ T ∪ E domain ------------------------------------------------------------ DEFAULT ------------------------------------------------------------ selection_mode := MODEL_GUIDED_SINGLE configuration_count := 1 ------------------------------------------------------------ FAILURE ------------------------------------------------------------ model_selection_tenet_violation selected_rota_tenet_mismatch ============================================================ END SECTION VI ============================================================ ============================================================ VII. SELECTION MODES ============================================================ MODEL_GUIDED_SINGLE EXPLICIT_ROTA MODEL_GUIDED_N PRESET_BREVIS PRESET_GRU PRELOADED_TABULA_SELECTION ------------------------------------------------------------ RULE ------------------------------------------------------------ All selection must respect selected_tenet. ------------------------------------------------------------ FAILURE ------------------------------------------------------------ explicit_rota_tenet_conflict configuration_count_tenet_conflict ============================================================ END SECTION VII ============================================================ ============================================================ VIII. TABULA PRESET INTERFACE ============================================================ TABULA presets must be provided via OPERA F. ------------------------------------------------------------ OPERA H must not derive TABULA independently. ------------------------------------------------------------ FAILURE ------------------------------------------------------------ tabula_preload_missing opera_f_bypass ============================================================ END SECTION VIII ============================================================ ============================================================ IX. EXECUTION CORE — MODE DISPATCH ============================================================ MULTIPLICATIO_OA → SECTION X MULTIPLICATIO_PL → SECTION XI MULTIPLICATIO_CT → SECTION XII MULTIPLICATIO_RT → SECTION XIII ------------------------------------------------------------ RULE ------------------------------------------------------------ Only one mode active per execution. ------------------------------------------------------------ FAILURE ------------------------------------------------------------ multi_mode_conflict ============================================================ END SECTION IX ============================================================ ============================================================ X. EXECUTION — ORDINAL-ALIGNED MULTIPLICATIO ============================================================ Default multiplicatio mode. ------------------------------------------------------------ Produces: 9 ordinal-aligned chambers ------------------------------------------------------------ PROPERTIES ------------------------------------------------------------ • deterministic • TENET-consistent • trace-preserving ------------------------------------------------------------ FAILURE ------------------------------------------------------------ ordinal_mismatch carrier_misalignment ============================================================ END SECTION X ============================================================ ============================================================ XI. EXECUTION — POSITION-LOCKED MULTIPLICATIO ============================================================ IDENTIFIER: MULTIPLICATIO_PL ------------------------------------------------------------ DEFINITION ------------------------------------------------------------ Combine chambers: strictly by wheel position ------------------------------------------------------------ FORMAL ------------------------------------------------------------ W1' := combine(W1 from all chambers) W2' := combine(W2 from all chambers) W3' := combine(W3 from all chambers) ------------------------------------------------------------ OUTPUT ------------------------------------------------------------ RESULT := { single combined chamber } ------------------------------------------------------------ PROPERTIES ------------------------------------------------------------ • preserves topology • low expansion • position-stable • TENET-consistent under selected_tenet ------------------------------------------------------------ FAILURE ------------------------------------------------------------ position_conflict regime_violation tenet_anchor_mismatch ============================================================ END SECTION XI ============================================================ ============================================================ XII. EXECUTION — CARTESIAN MULTIPLICATIO ============================================================ IDENTIFIER: MULTIPLICATIO_CT ------------------------------------------------------------ DEFINITION ------------------------------------------------------------ Combine chambers: across all compatible carrier pairs ------------------------------------------------------------ FORMAL ------------------------------------------------------------ RESULT := { all valid combinations of carriers across chambers } ------------------------------------------------------------ PROPERTIES ------------------------------------------------------------ • maximal expansion • exploratory combinatorics • TENET-bounded compatibility filtering required ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ AREPO filtering is REQUIRED post-execution ------------------------------------------------------------ TENET BINDING ------------------------------------------------------------ All combinations must: • respect selected_tenet domain • avoid cross-domain contamination • preserve carrier integrity ------------------------------------------------------------ FAILURE ------------------------------------------------------------ combinatorial_overflow trace_loss tenet_domain_violation invalid_cross_combination ============================================================ END SECTION XII ============================================================ ============================================================ XIII. EXECUTION — ROTA-TRANSFORMATIONAL MULTIPLICATIO ============================================================ IDENTIFIER: MULTIPLICATIO_RT ------------------------------------------------------------ DEFINITION ------------------------------------------------------------ Combine chambers with transformation of: • wheel positions • regime bindings • ROTA identity ------------------------------------------------------------ FORMAL ------------------------------------------------------------ RESULT := transform(chambers, transformation_rules) ------------------------------------------------------------ TRANSFORMATIONS MAY INCLUDE ------------------------------------------------------------ • W1 ↔ W2 ↔ W3 permutation • A ↔ T projection (if TENET-allowed) • ROTA reassignment ------------------------------------------------------------ TENET CONSTRAINT ------------------------------------------------------------ All transformations must: • preserve selected_tenet anchoring • not violate TENET invariants • not introduce non-admissible domains ------------------------------------------------------------ FAILURE ------------------------------------------------------------ invalid_transformation regime_violation topology_break tenet_anchor_violation ============================================================ END SECTION XIII ============================================================ ============================================================ XIV. RESULT STRUCTURE ============================================================ All executions produce: ------------------------------------------------------------ H_RESULT := { chambers: [...], selected_tenet, tenet_dispatch, multiplicatio_mode, selection_mode, configuration_count, selected_rota_set, tabula_preset, tabula_preload_reference, source_chambers, source_rotae, trace, status } ------------------------------------------------------------ STATUS ∈ { COMPLETED, BLOCKED } ------------------------------------------------------------ RULE ------------------------------------------------------------ All results must be: • explicit • non-compressed • reproducible • TENET-context preserving ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ RESULT must preserve: • selected TENET anchoring • dispatch trace linkage • configuration lineage • multiplicatio trace integrity ------------------------------------------------------------ FAILURE ------------------------------------------------------------ result_incomplete tenet_context_loss trace_missing structure_loss ============================================================ END SECTION XIV ============================================================ ============================================================ XV. TRACE DISCIPLINE ============================================================ TRACE := { input_chambers, input_rotae, element_set, interaction_type, operator_presence, selected_tenet, dispatch_trace, selection_mode, configuration_count, selected_rota_set, tabula_preset, tabula_preload_reference, multiplicatio_mode, ordinal_mapping (if applicable), operation_steps, output_mapping } ------------------------------------------------------------ RULE ------------------------------------------------------------ Trace must preserve: • TENET dispatch reasoning • configuration selection origin • multiplicatio execution lineage • full mapping continuity ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ Trace must explicitly state: • why TENET A, T, D, or I was selected • whether selection was model-guided or deterministic • whether OPERA F preload was used • which TABULA preset was active ------------------------------------------------------------ FAILURE ------------------------------------------------------------ trace_break origin_loss mapping_ambiguity dispatch_trace_missing selected_tenet_trace_loss ============================================================ END SECTION XV ============================================================ ============================================================ XVI. REGIME INTEGRITY LAW ============================================================ OPERA H must preserve: • TENET I full-token identity where MIXTURA carriers are present • TENET I ordinal integrity where MIXTURA carriers are present • selected TENET anchoring • A/T/E distinction where applicable • carrier domain integrity • TENET A / T / D / I constraints ------------------------------------------------------------ PROHIBITIONS ------------------------------------------------------------ OPERA H must not: • collapse A / T / E into undifferentiated MIXTURA • infer identity from numeric value alone • infer identity from partial token • replace K with K1 or K2 in combinatory operations • collapse A into T • collapse T into A • introduce foreign carriers • execute OPERA E reduction logic • execute OPERA D decision logic • treat TENET dispatch as OPERA execution • mutate selected_tenet after dispatch without trace ------------------------------------------------------------ RULE ------------------------------------------------------------ TENET anchoring must remain invariant throughout execution. When selected_tenet == TENET I, MIXTURA discipline must preserve: • full token presence • carrier identity • ordinal integrity • regime distinction • non-identity of numeric coincidence ------------------------------------------------------------ FAILURE ------------------------------------------------------------ regime_collapse carrier_contamination tenet_anchor_mutation dispatch_execution_collapse mixtura_token_incomplete mixtura_ordinal_drift mixtura_numeric_identity_error ============================================================ END SECTION XVI ============================================================ ============================================================ XVII. FAILURE CONDITIONS ============================================================ OPERA H must expose: ------------------------------------------------------------ EXECUTION FAILURES ------------------------------------------------------------ • mode_invalid • input_invalid • transformation_invalid ------------------------------------------------------------ STRUCTURAL FAILURES ------------------------------------------------------------ • rota_invalid • ordinal_loss • carrier_mismatch ------------------------------------------------------------ TRACE FAILURES ------------------------------------------------------------ • trace_loss • mapping_ambiguity ------------------------------------------------------------ TENET DISPATCH FAILURES ------------------------------------------------------------ • TENET_UNRESOLVED • REGIMEN_AMBIGUITY • INCORRECT_TENET_SELECTION • OPERATOR_PRESENCE_IGNORED • element_set_missing • interaction_type_unresolved • operator_presence_unresolved • selected_tenet_missing • tenet_context_mismatch • dispatch_trace_missing ------------------------------------------------------------ TENET-SELECTION DETERMINISM FAILURES ------------------------------------------------------------ • selected_tenet_ignored • model_selection_tenet_violation • explicit_rota_tenet_conflict • selected_tenet_trace_loss ------------------------------------------------------------ RULE ------------------------------------------------------------ All failures must be: • explicit • typed • non-silent ============================================================ END SECTION XVII ============================================================ ============================================================ ============================================================ XVIII. FUNCTION ============================================================ OPERA H governs: • TENET dispatch resolution • configuration selection logic • TABULA preset integration (via OPERA F) • multiplicatio execution across modes • chamber combination under regime discipline • deterministic and non-deterministic combinatory expansion • result construction with full trace preservation ------------------------------------------------------------ OPERA H is: • execution-only • TENET-dispatch-bound • configuration-aware • mode-dependent • trace-complete ------------------------------------------------------------ OPERA H is NOT: • doctrinal (TENET) • topological (ROTAS) • admissibility layer (AREPO) • mediation layer (SATOR) • interrogative execution layer (OPERA E) • decision execution layer (OPERA D) ------------------------------------------------------------ ROLE IN AGLA CLASS CHAIN ------------------------------------------------------------ TENET: defines invariant domains and dispatch law ROTAS: defines chamber topology and traversal space AREPO: validates admissibility OPERA: executes multiplicatio SATOR: mediates output ------------------------------------------------------------ CONSTRAINT ------------------------------------------------------------ OPERA H must remain: • non-validating • non-topological • non-interpretative • non-doctrinal • non-regime-mutating ------------------------------------------------------------ FAILURE ------------------------------------------------------------ class_boundary_violation execution_leak interpretation_leak tenet_dispatch_violation ============================================================ END SECTION XVIII ============================================================ ============================================================ XIX. CLOSURE ============================================================ OPERA H defines: the execution kernel for multiplicatio under explicit TENET dispatch, configuration selection, and controlled combinatory expansion. ------------------------------------------------------------ FINAL LAW ------------------------------------------------------------ No OPERA H execution is valid unless: • TENET dispatch is resolved • selected_tenet is explicitly declared • configuration selection is TENET-compliant • multiplicatio mode is declared • trace preserves full lineage • regime integrity is maintained ------------------------------------------------------------ EXECUTION VALIDITY CONDITION ------------------------------------------------------------ Multiplicatio is valid iff: selected_tenet_resolved ∧ configuration_selection_valid ∧ multiplicatio_mode_declared ∧ trace_complete ∧ invariant_preserved ∧ topology_respected ------------------------------------------------------------ DEFAULT EXECUTION LAW ------------------------------------------------------------ If user does not specify: • selected_tenet • rota_set • tabula_preset • configuration_count • deterministic selection rule then OPERA H must: 1. resolve selected_tenet via TENET_DISPATCH 2. set selection_mode := MODEL_GUIDED_SINGLE 3. set configuration_count := 1 4. set multiplicatio_mode := MULTIPLICATIO_OA ------------------------------------------------------------ DEFAULT OUTPUT ------------------------------------------------------------ • one TENET-resolved execution context • one selected ROTA-compatible configuration • nine ordinal-aligned chambers • full trace ------------------------------------------------------------ FINAL STATE ------------------------------------------------------------ PROVISIONAL / EXECUTION-KERNEL (PATCHED-DISPATCH-INTEGRATED) ------------------------------------------------------------ CLOSURE RULE ------------------------------------------------------------ OPERA H must not: • execute without TENET anchoring • select configurations outside TENET domain • produce results without trace • collapse regime distinctions • mutate dispatch context silently ------------------------------------------------------------ OPERA H is: TENET-anchored configuration-driven multiplicatio-executing trace-preserving ============================================================ END OPERA H — MULTIPLICATIO FIGURAE QUARTAE ============================================================