03_STACK_T/OPERA_T_ExecutionMechanism.md

Page Sections

OPERA T â€” REGIMEN_T EXECUTION LAYER line 2
Ars Generalis Applied â€” Relational Execution (Figura T) line 3
Version: 0.2.2-OPERA-T (rev T.6 â€” circular-consistency-integrated) line 4
Status: EXECUTION LAYER â€” LOCK CANDIDATE / PATCH INTEGRATED line 5
Depends-On: line 6
Authority: AGLA / CONTROL PLANE line 13
Mutation Policy: VERSION-CONTROLLED ONLY line 14
Class: OPERA line 16
## LOCAL SECTION INDEX line 21
Scope: local anchors within this artifact only. No cross-artifact links are introduced here. line 23
PURPOSE line 133
Execute relational operations over REGIMEN_T. line 136
OPERA T applies relative predicates to articulated terms under line 138
and only after admissibility is granted by AREPO T. line 140
OPERA T governs: line 143
OPERA T does NOT: line 152
CORE ASSERTION line 164
OPERA T does not execute over pure principial unity. line 167
OPERA T executes over expressed and contracted terms line 169
under the relative regime of T. line 170
I. CONTROL-PLANE POSITION line 179
INTERPRETATION line 188
TENET T: line 193
TENET A: line 198
ROTA T: line 203
AREPO T: line 208
OPERA T: line 213
SATOR T: line 218
II. EXECUTION PRINCIPLE line 226
OPERA T applies T-predicates as slot-bound relational line 229
operators. line 230
PRIMARY OPERATIONAL LAW line 236
Execution is SLOT-first. line 239
This means: line 242
RULE line 253
OPERA T executes over: line 257
where: line 264
CONSTRAINT line 273
OPERA T must not: line 277
III. INPUT DOMAIN line 288
Required: line 292
Where X and Y are relata. line 296
VALID RELATA line 302
Relata must be: line 306
Examples: line 314
INVALID RELATA line 326
Pure undifferentiated A-dignities in full convertibility are line 329
not valid direct relata for OPERA T. line 330
Examples of invalid direct execution targets: line 333
RULE line 342
OPERA T executes only on expressed forms: line 346
not on: line 352
IV. RELATION TO TENET A line 363
TENET A and TENET T are both principial regimes. line 366
TENET A provides: line 371
TENET T provides: line 378
EXECUTION LAW line 387
OPERA T does NOT test or operate upon: line 391
OPERA T operates upon: line 396
FORMAL READING line 405
A_pure: line 409
A_expr: line 413
OPERA T operates over: line 417
NOT over: line 422
CONSTRAINT line 430
OPERA T must not: line 434
V. STRUCTURAL DEPENDENCY line 445
OPERA T requires: line 449
RULE line 461
No execution may proceed unless the structural machine is line 464
available and the request has passed AREPO T. line 465
FAILURE line 471
If any dependency is absent: line 475
VI. FRAME DECLARATION line 484
FRAME defines the comparison stance. line 487
Required form: line 493
Default: line 502
If omitted and defaultable: line 506
RULE line 514
FRAME must: line 518

============================================================ 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)  ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-purpose"></a> 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) ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-core-assertion"></a> 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. ============================================================ ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-i-control-plane-position"></a> I. CONTROL-PLANE POSITION ============================================================ TENET â†’ ROTAS â†’ AREPO â†’ OPERA â†’ SATOR ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-interpretation"></a> INTERPRETATION ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-tenet-t"></a> TENET T: defines relative predicates and genus structure <a id="local-section-03-stack-t-opera-t-executionmechanism-tenet-a"></a> TENET A: defines absolute principial predicates <a id="local-section-03-stack-t-opera-t-executionmechanism-rota-t"></a> ROTA T: instantiates the carrier machine <a id="local-section-03-stack-t-opera-t-executionmechanism-arepo-t"></a> AREPO T: admits execution over that machine <a id="local-section-03-stack-t-opera-t-executionmechanism-opera-t"></a> OPERA T: executes relational articulation <a id="local-section-03-stack-t-opera-t-executionmechanism-sator-t"></a> SATOR T: mediates the result ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-ii-execution-principle"></a> II. EXECUTION PRINCIPLE ============================================================ OPERA T applies T-predicates as slot-bound relational operators. ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-primary-operational-law"></a> 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 ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-rule"></a> RULE ------------------------------------------------------------ OPERA T executes over: T(Ï) or T(Ï,g) where: Ï = ordinal slot g = genus slot (when active) ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-constraint"></a> CONSTRAINT ------------------------------------------------------------ OPERA T must not: âœ— operate token-first âœ— operate numeric-first âœ— infer traversal from symbol sequence alone ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-iii-input-domain"></a> III. INPUT DOMAIN ============================================================ Required: X, Y Where X and Y are relata. ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-valid-relata"></a> 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 ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-invalid-relata"></a> 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 ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-rule-2"></a> RULE ------------------------------------------------------------ OPERA T executes only on expressed forms: X_expr Y_expr not on: A_pure ============================================================ ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-iv-relation-to-tenet-a"></a> 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 ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-execution-law"></a> 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 ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-formal-reading"></a> 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) ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-constraint-2"></a> CONSTRAINT ------------------------------------------------------------ OPERA T must not: âœ— replace OPERA A âœ— derive principial ontology âœ— mutate A into T ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-v-structural-dependency"></a> 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) ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-rule-3"></a> RULE ------------------------------------------------------------ No execution may proceed unless the structural machine is available and the request has passed AREPO T. ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-failure"></a> FAILURE ------------------------------------------------------------ If any dependency is absent: BLOCK: <ERROR_CODE> ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-vi-frame-declaration"></a> VI. FRAME DECLARATION ============================================================ FRAME defines the comparison stance. ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-required-form"></a> Required form: ------------------------------------------------------------ FRAME := <explicit stance of comparison> ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-default"></a> Default: ------------------------------------------------------------ If omitted and defaultable: FRAME := "general relation profile" ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-rule-4"></a> RULE ------------------------------------------------------------ FRAME must: â€¢ define the aspect of relation â€¢ not redefine predicates â€¢ not introduce ontology â€¢ not silently shift regime ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-failure-2"></a> FAILURE ------------------------------------------------------------ â€¢ FRAME_UNDEFINED â€¢ FRAME_REDEFINES_PREDICATE â€¢ FRAME_AS_ONTOLOGY ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-vii-execution-modes"></a> VII. EXECUTION MODES ============================================================ MODE options: â€¢ FULL â€¢ TRIAD â€¢ GENUS ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-default-2"></a> DEFAULT: ------------------------------------------------------------ MODE := FULL ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-rule-5"></a> RULE ------------------------------------------------------------ Mode changes execution scope, not predicate canon. ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-viii-mode-full"></a> 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…¨} ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-execution-pattern"></a> EXECUTION PATTERN ------------------------------------------------------------ For each slot Ï: apply T(Ï) to (X_expr, Y_expr) under FRAME ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-output-requirement"></a> OUTPUT REQUIREMENT ------------------------------------------------------------ For each slot: â€¢ 1â€“2 constrained relational statements â€¢ strength tag: HIGH | MED | LOW ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-rule-6"></a> 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…¨ ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-constraint-3"></a> CONSTRAINT ------------------------------------------------------------ FULL mode must not reorder output by: âœ— symbol sequence preference âœ— rhetorical emphasis âœ— numeric magnitude ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-ix-mode-triad"></a> IX. MODE = TRIAD ============================================================ In TRIAD mode, OPERA T applies one triadic subset only. ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-triads"></a> 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} ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-rule-7"></a> RULE ------------------------------------------------------------ TRIAD mode must specify: â€¢ requested triad OR â€¢ triad-walk explicitly ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-triad-walk"></a> TRIAD-WALK ------------------------------------------------------------ If requested: Î”1 â†’ Î”2 â†’ Î”3 ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-constraint-4"></a> CONSTRAINT ------------------------------------------------------------ TRIAD selection changes execution scope only. It does not alter carrier structure or predicate meaning. ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-x-mode-genus"></a> X. MODE = GENUS ============================================================ In GENUS mode, OPERA T executes over: T(Ï,g) with: Ï âˆˆ {â… ..â…¨} g âˆˆ {1,2,3} ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-rule-8"></a> RULE ------------------------------------------------------------ GENUS mode requires: â€¢ explicit genus slot â€¢ admissibility already granted by AREPO T ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-interpretation-2"></a> 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 ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-genus-aware-notation"></a> GENUS-AWARE NOTATION ------------------------------------------------------------ Examples: TB1 TC2 TF3 TI1 ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-constraint-5"></a> CONSTRAINT ------------------------------------------------------------ Flat shorthand is insufficient in genus-sensitive execution. ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-xi-genus-transit-observance"></a> XI. GENUS TRANSIT OBSERVANCE ============================================================ OPERA T observes genus transit constraints defined by TENET T and enforced by AREPO T. ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-local-transit-within-predicate"></a> 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) ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-cross-predicate-transit"></a> CROSS-PREDICATE TRANSIT ------------------------------------------------------------ Default lawful pattern: T(Ï,g) â†’ T(Ïƒ,g) where: Ï â‰ Ïƒ genus preserved ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-mediated-genus-change"></a> 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) ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-failure-3"></a> FAILURE ------------------------------------------------------------ If requested transit violates AREPO-admitted constraints: BLOCK: GENUS_INVALID_TRANSITION ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-rule-9"></a> RULE ------------------------------------------------------------ OPERA T executes only lawful or already-admitted transitions. It does not self-legislate transit law. ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-xii-relational-purity-law"></a> XII. RELATIONAL PURITY LAW ============================================================ T-predicates must be executed as relations between relata. ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-correct-form"></a> CORRECT FORM ------------------------------------------------------------ relation_between(X_expr, Y_expr) ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-incorrect-form"></a> INCORRECT FORM ------------------------------------------------------------ predicate_as_property_of(X) predicate_as_being_of(Y) ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-examples"></a> EXAMPLES ------------------------------------------------------------ Correct: â€œX differs from Y under aspect Z.â€ Incorrect: â€œX is Differentia.â€ ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-rule-10"></a> RULE ------------------------------------------------------------ OPERA T must preserve: relation(X,Y) and must not collapse into: attribute(X) or being(X) ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-xiii-non-ontology-enforcement"></a> XIII. NON-ONTOLOGY ENFORCEMENT ============================================================ OPERA T must preserve: Relatio â‰ Esse ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-interpretation-3"></a> INTERPRETATION ------------------------------------------------------------ T-predicates do not posit being. They qualify respects under which expressed terms are: â€¢ compared â€¢ distinguished â€¢ mediated â€¢ evaluated ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-constraint-6"></a> CONSTRAINT ------------------------------------------------------------ OPERA T must not: âœ— promote relation into substance âœ— infer identity from relation alone âœ— treat T as subject ontology ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-xiv-execution-output"></a> XIV. EXECUTION OUTPUT ============================================================ Canonical output form: ------------------------------------------------------------ RELATA: X vs Y FRAME: <...> <a id="local-section-03-stack-t-opera-t-executionmechanism-t-profile"></a> 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) <a id="local-section-03-stack-t-opera-t-executionmechanism-summary"></a> SUMMARY: TOP_PREDICATES: <...> NON_APPLICABLE: <...> NON-ONTOLOGY: "Relatio â‰ Esse." ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-genus-output-extension"></a> GENUS OUTPUT EXTENSION ------------------------------------------------------------ When genus-sensitive: ACTIVE_GENUS_SLOT::<1|2|3> or explicit slot/genus labels: T(â… ,1), T(â…¡,2), etc. ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-transit-output-extension"></a> TRANSIT OUTPUT EXTENSION ------------------------------------------------------------ If genus transit is active: ACTIVE_NODE::<T(Ï,g)> REQUESTED_TRANSIT::<...> TRANSIT_STATUS::<LAWFUL|MEDIATED|BLOCKED> If mediated: MEDIATION_PATH::<...> ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-xv-circular-consistency-validation"></a> XV. CIRCULAR CONSISTENCY VALIDATION ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-purpose-2"></a> 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 ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-validation-principle"></a> 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 ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-act-generation-law"></a> 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. ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-agent-grounding-law"></a> 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. ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-circular-relational-closure"></a> 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. ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-circular-consistency-check"></a> CIRCULAR CONSISTENCY CHECK ------------------------------------------------------------ For each predicate P: <a id="local-section-03-stack-t-opera-t-executionmechanism-check-1"></a> CHECK 1: consistency with its ACT source triad <a id="local-section-03-stack-t-opera-t-executionmechanism-check-2"></a> 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. ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-relational-circular-inconsistency"></a> 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. ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-validity-consequences"></a> 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. ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-relation-to-bcd-priority"></a> 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. ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-circular-validation-output-extension"></a> CIRCULAR VALIDATION OUTPUT EXTENSION ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-circular-validation"></a> CIRCULAR_VALIDATION: { <a id="local-section-03-stack-t-opera-t-executionmechanism-act-source-status"></a> ACT_SOURCE_STATUS: <COHERENT | PARTIAL | FAILED> <a id="local-section-03-stack-t-opera-t-executionmechanism-agent-target-status"></a> AGENT_TARGET_STATUS: <COHERENT | PARTIAL | FAILED> <a id="local-section-03-stack-t-opera-t-executionmechanism-circular-closure-status"></a> CIRCULAR_CLOSURE_STATUS: <CLOSED | WEAKLY_CLOSED | OPEN | FAILED> <a id="local-section-03-stack-t-opera-t-executionmechanism-circular-flags"></a> CIRCULAR_FLAGS: { ... } } Rule: Circular validation output must be surfaced when relational stability affects downstream use. ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-system-result"></a> SYSTEM RESULT ------------------------------------------------------------ OPERA T is not only relational analysis. It is a cyclic relational consistency engine rather than a set of independent predicate evaluations. ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-xvi-relation-to-other-classes"></a> XVI. RELATION TO OTHER CLASSES ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-tenet-t-2"></a> TENET T ------------------------------------------------------------ Provides: â€¢ predicate canon â€¢ genus structure â€¢ slot identity OPERA T observes this canon. ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-tenet-a-2"></a> TENET A ------------------------------------------------------------ Provides: â€¢ principial content when A-derived expressions are involved OPERA T operates only after such content is expressed. ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-rota-t-2"></a> ROTA T ------------------------------------------------------------ Provides: â€¢ carrier machine â€¢ loci â€¢ adjacency â€¢ traversal topology OPERA T executes within this structure. ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-arepo-t-2"></a> AREPO T ------------------------------------------------------------ Provides: â€¢ admissibility â€¢ transition legality â€¢ structure-sensitive permission OPERA T must not bypass AREPO T. ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-sator-t-2"></a> SATOR T ------------------------------------------------------------ Receives: â€¢ execution outputs â€¢ structural result profile OPERA T does not mediate its own outputs. ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-xvii-failure-conditions"></a> XVII. FAILURE CONDITIONS ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-input-failures"></a> INPUT FAILURES ------------------------------------------------------------ â€¢ RELATA_MISSING â€¢ PURE_PRINCIPIA_INPUT â€¢ FRAME_UNDEFINED ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-structural-failures"></a> STRUCTURAL FAILURES ------------------------------------------------------------ â€¢ TENET_BINDING_MISSING â€¢ ROTAS_BINDING_MISSING â€¢ ROTA_T_NOT_INSTANTIATED â€¢ AREPO_ADMISSION_MISSING ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-carrier-failures"></a> CARRIER FAILURES ------------------------------------------------------------ â€¢ SLOT_UNRESOLVED â€¢ SYMBOL_SLOT_MISMATCH â€¢ NUMERIC_MISMATCH â€¢ SYMBOL_FIRST_EXECUTION_ATTEMPT â€¢ NUMERIC_FIRST_EXECUTION_ATTEMPT ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-genus-failures"></a> GENUS FAILURES ------------------------------------------------------------ â€¢ GENUS_MISSING â€¢ GENUS_COLLAPSE â€¢ GENUS_INVALID_TRANSITION â€¢ UNMEDIATED_GENUS_SHIFT ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-regime-failures"></a> REGIME FAILURES ------------------------------------------------------------ â€¢ RELATION_AS_BEING â€¢ PREDICATE_AS_SUBSTANCE â€¢ A_T_COLLAPSE â€¢ A_PURE_DIRECT_OPERATION ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-circular-validation-failures"></a> CIRCULAR VALIDATION FAILURES ------------------------------------------------------------ â€¢ RELATIONAL_CIRCULAR_INCONSISTENCY â€¢ T_FIELD_CIRCULAR_FAILURE â€¢ ACT_SOURCE_INCOHERENT â€¢ AGENT_TARGET_INCOHERENT ============================================================ <a id="local-section-03-stack-t-opera-t-executionmechanism-xviii-summary"></a> 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 ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-final-law"></a> 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 ------------------------------------------------------------ <a id="local-section-03-stack-t-opera-t-executionmechanism-closure-rule"></a> 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 ============================================================