============================================================ AGLA / COMPLETE STACK CANDIDATE CONTEXTUAL CONTRACTION OPERATOR Version: 1.0.0-METAE-CONTEXTUAL-CONTRACTION-FULL-STACK Status: COMPLETE STACK / METAE CANDIDATE / NON-CANONICAL / SIGMA_SATOR-READY Date: 2026-05-05 Authority: AGLA_MAIN_LAB REQUEST / LOCAL DEVELOPMENT NODE Class: TENET + AREPO + ROTAS + OPERA + SATOR Scope: GENERAL-PURPOSE PORTABLE COGNITIVE OPERATOR Deployment: DEVELOPMENT-ONLY UNTIL CONTROL-PLANE PROMOTION Target property: MAXIMUM PROPAGATION MINIMUM ONTOLOGICAL DISTORTION Operator: X ⟨ Y ⟩ Reading: X under context Y X as instantiated within Y X relative to Y ============================================================ ============================================================ STACK POSITION ============================================================ This artifact defines CONTEXTUAL CONTRACTION as a complete five-class stack and as a META-ARTICULATION LAYER. It is not a new isolated stack. It does not compete with: A T S Q derived regimes It is positioned above individual regimes as a portable reasoning primitive that may articulate any admitted stack without creating new ontology, execution behavior, or hidden recursion. It is general-purpose because it can be used with Ars principles, rules, and subjects without being exclusive to Ars principles, rules, or subjects. ------------------------------------------------------------ CORE FORMULA: X ⟨ Y ⟩ TYPED FORM: X^{τ_X} ⟨ Y^{τ_Y} ⟩ RELATIONAL PROFILE: X ⟨ Y ⟩ | R' PATH SEMANTICS: Z → Y → X OPTIONAL EXTRACTION DUAL: X ⟩ Y ⟨ ANALOGY FORM: X ⟨ Y ⟩ ~ X ⟨ Z ⟩ ============================================================ END STACK POSITION ============================================================ ============================================================ TENET — DOCTRINAL LAYER ============================================================ I. PURPOSE ============================================================ TENET defines the doctrinal status of CONTEXTUAL CONTRACTION. CONTEXTUAL CONTRACTION is the controlled articulation of: X as constrained, interpreted, projected, or instantiated under Y. It is portable across: philosophy science art systems engineering cognition LLM reasoning control It must not be reduced to a Llull-specific construct. It may support Ars-compatible use, but its status is general-purpose and trans-regime. II. ONTOLOGICAL STATUS ============================================================ CONTEXTUAL CONTRACTION belongs to: SECUNDA INTENTIO It is an articulation of intelligibility. It is not: a new entity a new type a new principle a new subject a new ontology a logical predicate by default a function evaluation by default an execution instruction by default It is: a view a projection a contraction a context-bound articulation a traceable relation between term and context III. NON-CREATION LAW ============================================================ FORMAL: X ⟨ Y ⟩ ∉ new_ontology RULE: CONTEXTUAL CONTRACTION must not create X, Y, or a third ontological item. CONSTRAINT: The expression X ⟨ Y ⟩ may only articulate X under the admitted constraints of Y. PROHIBITED: treating X ⟨ Y ⟩ as a new primitive treating X ⟨ Y ⟩ as a new substance treating X ⟨ Y ⟩ as a new regime deriving ontology from notation FAILURE: ontology_creation contraction_reification notation_derived_entity IV. ASYMMETRY LAW ============================================================ FORMAL: X ⟨ Y ⟩ ≠ Y ⟨ X ⟩ RULE: Contextual contraction is directional. INTERPRETATION: Y is the context / field / constraint carrier. X is the contracted / projected / instantiated item. CONSTRAINT: Reversal requires explicit re-expression. EXAMPLES: Force⟨Fluid⟩ ≠ Fluid⟨Force⟩ Color⟨Watercolor⟩ ≠ Watercolor⟨Color⟩ Justice⟨War⟩ ≠ War⟨Justice⟩ Memory⟨Trauma⟩ ≠ Trauma⟨Memory⟩ V. CONTEXT DOMINANCE LAW ============================================================ RULE: In X ⟨ Y ⟩, Y defines the operative context. Y may determine: admissible constraints relevant relations interpretive limits substrate conditions domain-specific variance collapse eligibility Y may not: create X erase X silently replace X authorize expansion beyond stated context FAILURE: context_overreach subject_replacement silent_normalization VI. NON-COMMUTATIVITY ============================================================ RULE: CONTEXTUAL CONTRACTION is non-commutative. FORMAL: X ⟨ Y ⟩ ≠ Y ⟨ X ⟩ CONSTRAINT: Any claim of equivalence between directional forms requires explicit equivalence admission under AREPO. VII. NON-ASSOCIATIVITY ============================================================ RULE: CONTEXTUAL CONTRACTION is non-associative. FORMAL: X ⟨ Y ⟨ Z ⟩ ⟩ ≠ (X ⟨ Y ⟩) ⟨ Z ⟩ INTERPRETATION: X ⟨ Y ⟨ Z ⟩ ⟩ means: X under Y, where Y is already under Z. (X ⟨ Y ⟩) ⟨ Z ⟩ means: the contraction of X under Y is itself placed under Z. CONSTRAINT: Parentheses and nesting order are structurally meaningful. VIII. PATH SEMANTICS LAW ============================================================ RULE: Nested contraction defines an ordered contraction path. FORMAL: X ⟨ Y ⟨ Z ⟩ ⟩ PATH: Z → Y → X INTERPRETATION: Z shapes Y. Y shapes X. CONSTRAINT: Path semantics must not be flattened into unordered context. PROHIBITED: X ⟨ Y ⟨ Z ⟩ ⟩ = X ⟨ Y, Z ⟩ IX. RECURSION CONSTRAINTS ============================================================ RULE: Recursion is permitted only when each layer is explicit, typed, and admissible. ALLOWED FORM: X ⟨ Y ⟨ Z ⟩ ⟩ CONSTRAINTS: each layer must preserve directionality each context must be typed or otherwise admissibly bounded each added layer must increase clarity no hidden recursive expansion is permitted PROHIBITED: automatic nesting inferred nesting recursive expansion by association unbounded contraction chains FAILURE: uncontrolled_recursion hidden_nesting context_chain_explosion X. COLLAPSE RULES ============================================================ Collapse is allowed only under explicit rule. ------------------------------------------------------------ RULE A — IDENTITY COLLAPSE ------------------------------------------------------------ FORMAL: X ⟨ X ⟩ ⇒ X CONDITION: identity collapse applies unless the expression is explicitly marked as non-trivial or reflexive-analysis. NON-TRIVIAL MARK: X ⟨ X ⟩ [reflexive] ------------------------------------------------------------ RULE B — DOMINANCE COLLAPSE ------------------------------------------------------------ FORMAL: if X ⊆ Y structurally, then X ⟨ Y ⟩ ≈ X CONDITION: dominance collapse applies only when Y contributes no additional operative constraint beyond the structure already carried by X. ------------------------------------------------------------ RULE C — EQUIVALENCE COLLAPSE ------------------------------------------------------------ FORMAL: if X ≡ Y, then X ⟨ Y ⟩ = X = Y CONDITION: equivalence must be admitted explicitly. CONSTRAINT: Full equivalence collapses context. FAILURE: false_identity false_dominance false_equivalence premature_collapse XI. RELATIONAL PROFILE LAW ============================================================ FORMAL: X ⟨ Y ⟩ | R' DEFINITION: R' is the active relation profile admitted for X under Y. R' may include, by domain: distinction compatibility tension scale equivalence causality dependence analogy containment resistance RULE: X ⟨ Y ⟩ does not automatically activate all possible relations between X and Y. CONSTRAINT: Relations must be attached, admitted, or exposed. XII. OPTIONAL DUAL OPERATOR ============================================================ FORMAL: X ⟩ Y ⟨ READING: extract X-relevant structure from Y STATUS: OPTIONAL / AUXILIARY EXAMPLES: Color⟩Painting⟨ extract palette-relevant structure from Painting Strategy⟩Game⟨ extract strategy-relevant structure from Game CONSTRAINT: The dual operator must not be assumed present unless invoked. XIII. ANALOGY OPERATOR ============================================================ FORMAL: X ⟨ Y ⟩ ~ X ⟨ Z ⟩ READING: X behaves analogously under Y and Z. RULE: Analogy compares contextualized forms, not unbounded terms. CONSTRAINT: Analogy must preserve the distinct contexts Y and Z. FAILURE: false_analogy context_erasure ungrounded_transfer XIV. PROPAGATION LAW ============================================================ CONTEXTUAL CONTRACTION propagates across stacks as a META-ARTICULATION LAYER. It does not become: Stack A Stack T Stack S Stack Q a derived execution stack Propagation examples: Q: "What is X?" may become: "What is X ⟨ Y ⟩?" T: relations may be filtered by context: R → R' S: Y may act as contextual substrate where admissible. A: contraction may articulate principial manifestation without breaking unity or creating new principles. GLOBAL RULE: CONTEXTUAL CONTRACTION may articulate existing regimes. It must not replace, merge, or supersede them. XV. FINAL TENET ASSERTION ============================================================ CONTEXTUAL CONTRACTION is: a portable cognitive operator a controlled contextualization primitive a secunda intentio articulation a non-creative projection under constraint a trans-regime meta-articulation layer It is not: an execution kernel an ontology generator a Llull-only construct a symbolic curiosity a hidden expansion engine ============================================================ END TENET ============================================================ ============================================================ AREPO — ADMISSIBILITY LAYER ============================================================ I. PURPOSE ============================================================ AREPO defines when X ⟨ Y ⟩ is admissible. It gates: typing context sufficiency recursion relational profile attachment ambiguity handling collapse eligibility It does not execute the operator. II. BASIC ADMISSIBILITY FORM ============================================================ INPUT: X ⟨ Y ⟩ ADMISSIBLE only if: X is declared or recoverable from explicit input Y is declared or recoverable from explicit input direction is clear context role is clear ontology creation is not implied no hidden expansion is required If any condition fails: INSUFFICIENT ADMISSIBILITY III. TYPING REQUIREMENTS ============================================================ TYPED FORM: X^{τ_X} ⟨ Y^{τ_Y} ⟩ τ_X may identify: concept object force quality medium system function memory structure principle relation question substrate τ_Y may identify: domain medium environment frame substrate regime condition historical context material context cognitive context RULE: τ_X and τ_Y need not be identical. CONSTRAINT: They must be compatible enough to permit meaningful contextual articulation. FAILURE: type_absent type_conflict domain_unbounded context_unclear IV. ADMISSIBILITY TEST ============================================================ AREPO admits X ⟨ Y ⟩ only if all tests pass: T1: X_PRESENT T2: Y_PRESENT T3: DIRECTION_EXPLICIT T4: TYPE_COMPATIBLE T5: CONTEXT_BOUND T6: NON_CREATIVE T7: RECURSION_BOUNDED T8: RELATION_PROFILE_DECLARED_OR_OPTIONAL T9: COLLAPSE_NOT_FORCED T10: SOURCE_ARTIFACT_DISTINCTION_PRESERVED If any required test fails: INSUFFICIENT ADMISSIBILITY V. RECURSION LIMITS ============================================================ Nested forms are admissible only when each layer passes AREPO. FORM: X ⟨ Y ⟨ Z ⟩ ⟩ REQUIRED: Y ⟨ Z ⟩ is admissible X ⟨ Y ⟨ Z ⟩ ⟩ is admissible path Z → Y → X is preservable no layer is inferred silently DEFAULT LIMIT: depth = explicitly provided depth No additional depth may be generated automatically. FAILURE: recursion_unbounded missing_layer_type path_ambiguous hidden_context VI. ANTI-EXPLOSION SAFEGUARDS ============================================================ No expression may generate all possible contractions. PROHIBITED: expanding X across all contexts expanding Y across all possible X enumerating nested paths without request deriving relation profiles exhaustively treating analogy as unlimited transfer RULE: Expansion requires explicit user or artifact instruction. DEFAULT: read only the stated expression. FAILURE: combinatorial_explosion unauthorized_expansion relation_overgeneration VII. AMBIGUITY THRESHOLDS ============================================================ Return INSUFFICIENT ADMISSIBILITY when: X cannot be identified Y cannot be identified X/Y direction is ambiguous context boundary is unclear requested typing cannot be inferred safely collapse is possible but not decidable analogy lacks a shared X or declared mapping extraction dual is confused with contraction source text is being treated as validated artifact MANDATORY RESPONSE: INSUFFICIENT ADMISSIBILITY No substitute explanation may silently repair ambiguity. VIII. RELATIONAL PROFILE ADMISSION ============================================================ FORM: X ⟨ Y ⟩ | R' R' is admissible if: each relation is named relation scope is local to the contraction relation does not imply ontology creation relation does not contradict context dominance If R' is absent: The contraction remains readable. No full relation profile is assumed. IX. COLLAPSE ADMISSION ============================================================ Collapse requires explicit eligibility. IDENTITY: X ⟨ X ⟩ ⇒ X DOMINANCE: if X ⊆ Y structurally, then X ⟨ Y ⟩ ≈ X EQUIVALENCE: if X ≡ Y, then X ⟨ Y ⟩ = X = Y CONSTRAINT: Collapse must not erase meaningful context unless the collapse condition is admitted. If collapse cannot be decided: INSUFFICIENT ADMISSIBILITY X. PORTABLE DOMAIN ADMISSION EXAMPLES ============================================================ Physics: Force⟨Fluid⟩ admissible when Force and Fluid are typed as physical term and material domain. Art: Color⟨Watercolor⟩ admissible when Color is treated as visual quality and Watercolor as medium. Ethics: Justice⟨War⟩ admissible when Justice is treated as normative concept and War as conflict context. Cognition: Memory⟨Trauma⟩ admissible when Memory is cognitive function and Trauma is psychological context. LLM reasoning control: Answer⟨Source-Bound-Mode⟩ admissible when Answer is output object and Source-Bound-Mode is declared reasoning constraint. XI. FINAL AREPO ASSERTION ============================================================ AREPO admits contextual contraction only when: the expression is explicit the context is bounded the types are compatible recursion is controlled relation profiles are not overgenerated collapse is not forced source and artifact remain distinct Otherwise: INSUFFICIENT ADMISSIBILITY ============================================================ END AREPO ============================================================ ============================================================ ROTAS — STRUCTURAL EXPOSURE ============================================================ I. PURPOSE ============================================================ ROTAS exposes the structure of contextual contraction without executing or expanding it. ROTAS defines: notation nesting path semantics relational profile display graph compatibility stack propagation display II. NOTATION STANDARD ============================================================ BASE: X ⟨ Y ⟩ TYPED: X^{τ_X} ⟨ Y^{τ_Y} ⟩ NESTED: X ⟨ Y ⟨ Z ⟩ ⟩ PARENTHESIZED: (X ⟨ Y ⟩) ⟨ Z ⟩ RELATIONAL PROFILE: X ⟨ Y ⟩ | R' EXTRACTION DUAL: X ⟩ Y ⟨ ANALOGY: X ⟨ Y ⟩ ~ X ⟨ Z ⟩ III. STRUCTURAL ROLES ============================================================ In: X ⟨ Y ⟩ ROTAS exposes: X = contracted item Y = context field ⟨ ⟩ = contextual contraction boundary Direction: Y → X Read: Y constrains X. IV. PATH SEMANTICS VISUALIZATION ============================================================ For: X ⟨ Y ⟨ Z ⟩ ⟩ ROTAS exposes: Z → Y → X Graph: [Z] | v [Y] | v [X] Meaning: Z shapes Y. Y shapes X. CONSTRAINT: The graph is directional and ordered. V. NON-FLATTENING DISPLAY ============================================================ ROTAS must preserve distinction between: X ⟨ Y ⟨ Z ⟩ ⟩ and: X ⟨ Y, Z ⟩ and: (X ⟨ Y ⟩) ⟨ Z ⟩ No display may normalize these into one form. VI. RELATIONAL PROFILE ATTACHMENT ============================================================ FORM: X ⟨ Y ⟩ | R' DISPLAY: X: contracted item Y: context field R': active local relation profile Example: Justice⟨War⟩ | {tension, constraint, scale} Meaning: Justice is articulated under War using only the attached local relation profile. VII. GRAPH COMPATIBILITY ============================================================ CONTEXTUAL CONTRACTION is graph-compatible. Node classes: TERM_NODE CONTEXT_NODE CONTRACTION_NODE RELATION_PROFILE_NODE Edges: CONTEXT_OF: Y → X CONTRACTS: X + Y → X⟨Y⟩ HAS_PROFILE: X⟨Y⟩ → R' NESTED_CONTEXT: Z → Y → X Graph rule: Edges must preserve asymmetry. Cycle rule: Cycles are not admitted unless explicitly marked as reflexive analysis. VIII. ROTA COMPATIBILITY ============================================================ In a reasoning rota, X ⟨ Y ⟩ may be placed as: a labeled edge a constrained node a path segment a local articulation layer It must not be placed as: a new root principle a new stack a hidden OPERA an unbounded expansion point IX. PROPAGATION DISPLAY ACROSS STACKS ============================================================ ROTAS may expose propagation as: STACK A: A-item ⟨ context ⟩ contraction without breaking unity STACK T: relation ⟨ context ⟩ R → R' STACK S: X ⟨ substrate Y ⟩ Y as contextual substrate where admitted STACK Q: Question(X) may become: Question(X ⟨ Y ⟩) DERIVED REGIMES: contraction remains an articulation layer only X. FINAL ROTAS ASSERTION ============================================================ ROTAS exposes contextual contraction as: visible directional typed where needed path-preserving relation-profile-aware graph-compatible non-executive It must not: flatten nesting infer hidden layers create relations normalize expression order convert articulation into ontology ============================================================ END ROTAS ============================================================ ============================================================ OPERA — INTERACTION LAYER ============================================================ I. PURPOSE ============================================================ OPERA for this stack is MINIMAL / NON-AGGRESSIVE. It defines how OPERAE may read X ⟨ Y ⟩. It does not define automatic execution behavior. II. READ-ONLY INTERPRETATION ============================================================ An OPERA may read: X ⟨ Y ⟩ as: X under context Y An OPERA may read: X^{τ_X} ⟨ Y^{τ_Y} ⟩ as: typed X under typed context Y An OPERA may read: X ⟨ Y ⟩ | R' as: X under context Y with active relation profile R' III. EXECUTION PROHIBITION ============================================================ This stack does not authorize: automatic expansion automatic recursion automatic graph traversal automatic relation generation automatic analogy transfer automatic extraction automatic collapse hidden evaluation ontology creation RULE: No OPERA may execute contextual contraction unless another admitted, loaded, registered OPERA explicitly defines such behavior under its own authority. IV. NO IMPLICIT EXPANSION ============================================================ Given: X ⟨ Y ⟩ OPERA must not infer: all X under Y variants all Y-like contexts all relation profiles all nested contexts all analogies all extraction duals DEFAULT: preserve the expression as stated. V. NO HIDDEN RECURSION ============================================================ Given: X ⟨ Y ⟩ OPERA must not produce: X ⟨ Y ⟨ Z ⟩ ⟩ unless Z is explicitly supplied or admitted by a separate loaded artifact. VI. COLLAPSE HANDLING ============================================================ OPERA may recognize collapse candidates only as candidates. It must not apply collapse unless AREPO admits the collapse. If collapse status is ambiguous: INSUFFICIENT ADMISSIBILITY VII. INTERPRETABILITY FOCUS ============================================================ OPERA may support: parsing the expression preserving direction displaying path semantics exposing declared relations flagging ambiguity OPERA may not: simulate conclusions supply missing ontology invent contexts normalize terms silently convert notation into runtime behavior VIII. FINAL OPERA ASSERTION ============================================================ OPERA in this stack is: interpretability-only non-executive by default no-expansion no-hidden-recursion AREPO-bound ROTAS-visible TENET-constrained ============================================================ END OPERA ============================================================ ============================================================ SATOR — MEDIATION LAYER ============================================================ I. PURPOSE ============================================================ SATOR defines how an assistant exposes, suggests, and mediates CONTEXTUAL CONTRACTION. SATOR must preserve: investigation-first stance user control source/artifact distinction non-creation law no automatic expansion II. USER-FACING EXPOSURE ============================================================ When explaining: X ⟨ Y ⟩ SATOR may say: "This reads as X under context Y." "Y is the context field; X is the item being articulated." "The expression does not create a new entity." SATOR must not say: "X becomes Y." "Y produces X." "This proves X." "This executes X under Y." III. SUGGESTION RULE ============================================================ SATOR may propose contextualization only when: the user is comparing domains a concept is being interpreted under a condition a question needs a bounded context an ambiguity appears context-dependent the user asks for relative or situated meaning Allowed prompt: "Would you like to contextualize X under Y?" Constraint: This suggestion must not force nesting. IV. OVER-INTERPRETATION PREVENTION ============================================================ SATOR must prevent: over-reading context treating Y as total explanation treating X ⟨ Y ⟩ as proof adding unstated relations expanding into all possible contexts converting analogy into equivalence If the user asks for conclusions beyond admitted structure: SATOR must identify the missing admissibility condition. V. FORCED NESTING PREVENTION ============================================================ SATOR must not introduce nested forms unless: the user supplies the nested context the artifact explicitly supplies the nested context AREPO admits the nested context SATOR must not transform: X ⟨ Y ⟩ into: X ⟨ Y ⟨ Z ⟩ ⟩ by conversational implication alone. VI. ONTOLOGY DRIFT PREVENTION ============================================================ SATOR must maintain: X remains X Y remains Y X ⟨ Y ⟩ remains articulation no new ontology is created no regime is collapsed no stack is replaced If drift is detected: SATOR must state the drift risk and return to explicit terms. VII. INVESTIGATION-FIRST STANCE ============================================================ SATOR should treat contextual contraction as a question-guiding tool before treating it as an answer structure. Recommended investigative forms: What is X ⟨ Y ⟩? Which constraints does Y impose on X? Which relations are active in X ⟨ Y ⟩ | R'? Does X ⟨ Y ⟩ collapse under identity, dominance, or equivalence? Is X ⟨ Y ⟩ analogous to X ⟨ Z ⟩? SATOR must not: conclude beyond admitted context hide uncertainty replace investigation with assertion VIII. AMBIGUITY RESPONSE ============================================================ If the assistant cannot identify: X Y direction type context boundary relation profile collapse eligibility where required, it must return: INSUFFICIENT ADMISSIBILITY IX. PORTABLE EXAMPLES FOR MEDIATION ============================================================ Physics: Force⟨Fluid⟩ "force as constrained by fluid behavior." Art: Color⟨Watercolor⟩ "color under the medium constraints of watercolor." Ethics: Justice⟨War⟩ "justice interpreted within the constraints and tensions of war." Cognition: Memory⟨Trauma⟩ "memory under the cognitive and affective context of trauma." X. FINAL SATOR ASSERTION ============================================================ SATOR exposes contextual contraction as: optional explicit bounded non-creative investigation-first portable across domains SATOR must prevent: over-interpretation forced nesting ontology drift hidden recursion silent normalization ============================================================ END SATOR ============================================================ ============================================================ GLOBAL CONSTRAINTS ============================================================ SOURCE ≠ ARTIFACT PARSE ≠ VALIDATE NOTATION ≠ ONTOLOGY ARTICULATION ≠ EXECUTION CONTEXT ≠ CREATION ANALOGY ≠ EQUIVALENCE NESTING ≠ FLATTENING RELATION PROFILE ≠ ALL RELATIONS If ambiguity exceeds admissibility: INSUFFICIENT ADMISSIBILITY ============================================================ END GLOBAL CONSTRAINTS ============================================================ ============================================================ PROMOTION NOTES ============================================================ PROMOTION TARGET: TENET-root compatible meta-articulation layer. PROMOTION REQUIREMENT: Control-plane review must decide whether this artifact remains one integrated full-stack artifact or is split into separate: TENET_CONTEXTUAL_CONTRACTION AREPO_CONTEXTUAL_CONTRACTION ROTAS_CONTEXTUAL_CONTRACTION OPERA_CONTEXTUAL_CONTRACTION SATOR_CONTEXTUAL_CONTRACTION NON-CANONICAL STATUS: This artifact is not active SYSTEM_INDEX authority. It is not an execution kernel. It is promotion-ready candidate material. FINAL STATE: METAE / NON-CANONICAL / PROMOTION-READY ============================================================ END AGLA / METAE FULL STACK CANDIDATE CONTEXTUAL CONTRACTION OPERATOR ============================================================