============================================================ AREPO F — ADMISSIO TABULAE Ars Generalis Applied — Admissibility Layer (REGIMEN_F) Version: 0.1.1-AREPO-F-ADMISSIO-TABULAE Status: LOCK-CANDIDATE Scope: TABULA admissibility, state admission, and pre-execution gating Authority: AREPO Mutation Policy: VERSION-CONTROLLED ONLY Class: AREPO Regime: F Depends-On: • TENET F — TABULA GENERALIS • ROTAS F — TABULA ROTUNDA References: • ALBUS — TABULA / FIGURA QUARTA PROJECTION • CARCER — TABULA FAMILY DERIVATION PROCEDURE • POPULUS — TABULA ============================================================ ## LOCAL SECTION INDEX Scope: local anchors within this artifact only. No cross-artifact links are introduced here. - [I. PURPOSE](#local-section-05-stack-f-arepo-f-inputadmissibility-i-purpose) - [CORE PRINCIPLE](#local-section-05-stack-f-arepo-f-inputadmissibility-core-principle) - [II. ADMISSIBILITY PRINCIPLE](#local-section-05-stack-f-arepo-f-inputadmissibility-ii-admissibility-principle) - [Definition:](#local-section-05-stack-f-arepo-f-inputadmissibility-definition) - [Formal Concept:](#local-section-05-stack-f-arepo-f-inputadmissibility-formal-concept) - [Interpretation:](#local-section-05-stack-f-arepo-f-inputadmissibility-interpretation) - [Failure:](#local-section-05-stack-f-arepo-f-inputadmissibility-failure) - [III. TABULA STATE ADMISSIBILITY CONDITIONS](#local-section-05-stack-f-arepo-f-inputadmissibility-iii-tabula-state-admissibility-conditions) - [Principle:](#local-section-05-stack-f-arepo-f-inputadmissibility-principle) - [Admissible State Requirements:](#local-section-05-stack-f-arepo-f-inputadmissibility-admissible-state-requirements) - [Interpretation:](#local-section-05-stack-f-arepo-f-inputadmissibility-interpretation-2) - [Failure Conditions:](#local-section-05-stack-f-arepo-f-inputadmissibility-failure-conditions) - [IV. REQUEST ADMISSIBILITY](#local-section-05-stack-f-arepo-f-inputadmissibility-iv-request-admissibility) - [Principle:](#local-section-05-stack-f-arepo-f-inputadmissibility-principle-2) - [Valid Request Must Include:](#local-section-05-stack-f-arepo-f-inputadmissibility-valid-request-must-include) - [Constraints:](#local-section-05-stack-f-arepo-f-inputadmissibility-constraints) - [Interpretation:](#local-section-05-stack-f-arepo-f-inputadmissibility-interpretation-3) - [Failure Conditions:](#local-section-05-stack-f-arepo-f-inputadmissibility-failure-conditions-2) - [V. FAILURE CONDITIONS](#local-section-05-stack-f-arepo-f-inputadmissibility-v-failure-conditions) - [INVARIANT FAILURES (TENET F)](#local-section-05-stack-f-arepo-f-inputadmissibility-invariant-failures-tenet-f) - [TOPOLOGY FAILURES (ROTAS F)](#local-section-05-stack-f-arepo-f-inputadmissibility-topology-failures-rotas-f) - [STRUCTURAL FAILURES](#local-section-05-stack-f-arepo-f-inputadmissibility-structural-failures) - [REQUEST FAILURES](#local-section-05-stack-f-arepo-f-inputadmissibility-request-failures) - [RULE](#local-section-05-stack-f-arepo-f-inputadmissibility-rule) - [VI. ADMISSION FORMULA](#local-section-05-stack-f-arepo-f-inputadmissibility-vi-admission-formula) - [Formal Condition:](#local-section-05-stack-f-arepo-f-inputadmissibility-formal-condition) - [Interpretation:](#local-section-05-stack-f-arepo-f-inputadmissibility-interpretation-4) - [Boundary:](#local-section-05-stack-f-arepo-f-inputadmissibility-boundary) - [Failure:](#local-section-05-stack-f-arepo-f-inputadmissibility-failure-2) - [VII. BOUNDARY ENFORCEMENT](#local-section-05-stack-f-arepo-f-inputadmissibility-vii-boundary-enforcement) - [Principle:](#local-section-05-stack-f-arepo-f-inputadmissibility-principle-3) - [Rules:](#local-section-05-stack-f-arepo-f-inputadmissibility-rules) - [Interpretation:](#local-section-05-stack-f-arepo-f-inputadmissibility-interpretation-5) - [Constraint:](#local-section-05-stack-f-arepo-f-inputadmissibility-constraint) - [Failure Conditions:](#local-section-05-stack-f-arepo-f-inputadmissibility-failure-conditions-3) - [VIII. TRACEABILITY REQUIREMENT](#local-section-05-stack-f-arepo-f-inputadmissibility-viii-traceability-requirement) - [Principle:](#local-section-05-stack-f-arepo-f-inputadmissibility-principle-4) - [Trace Structure:](#local-section-05-stack-f-arepo-f-inputadmissibility-trace-structure) - [Requirements:](#local-section-05-stack-f-arepo-f-inputadmissibility-requirements) - [Interpretation:](#local-section-05-stack-f-arepo-f-inputadmissibility-interpretation-6) - [Failure Conditions:](#local-section-05-stack-f-arepo-f-inputadmissibility-failure-conditions-4) - [IX. REGIME PURITY ENFORCEMENT](#local-section-05-stack-f-arepo-f-inputadmissibility-ix-regime-purity-enforcement) - [Principle:](#local-section-05-stack-f-arepo-f-inputadmissibility-principle-5) - [Prohibition:](#local-section-05-stack-f-arepo-f-inputadmissibility-prohibition) - [Allowed:](#local-section-05-stack-f-arepo-f-inputadmissibility-allowed) - [Rule:](#local-section-05-stack-f-arepo-f-inputadmissibility-rule-2) - [Failure Conditions:](#local-section-05-stack-f-arepo-f-inputadmissibility-failure-conditions-5) - [X. FUNCTION](#local-section-05-stack-f-arepo-f-inputadmissibility-x-function) - [ROLE IN AGLA CLASS CHAIN](#local-section-05-stack-f-arepo-f-inputadmissibility-role-in-agla-class-chain) - [AREPO F:](#local-section-05-stack-f-arepo-f-inputadmissibility-arepo-f) - [XI. CLOSURE](#local-section-05-stack-f-arepo-f-inputadmissibility-xi-closure) - [FINAL LAW](#local-section-05-stack-f-arepo-f-inputadmissibility-final-law) - [FINAL STATE:](#local-section-05-stack-f-arepo-f-inputadmissibility-final-state) - [• POPULUS — TABULA](#local-section-05-stack-f-arepo-f-inputadmissibility-populus-tabula) - [I. PURPOSE](#local-section-05-stack-f-arepo-f-inputadmissibility-i-purpose-2) - [CORE PRINCIPLE](#local-section-05-stack-f-arepo-f-inputadmissibility-core-principle-2) - [MANDATORY BEHAVIOR](#local-section-05-stack-f-arepo-f-inputadmissibility-mandatory-behavior) - [II. ADMISSIBILITY PRINCIPLE](#local-section-05-stack-f-arepo-f-inputadmissibility-ii-admissibility-principle-2) - [Definition:](#local-section-05-stack-f-arepo-f-inputadmissibility-definition-2) - [Formal Definition:](#local-section-05-stack-f-arepo-f-inputadmissibility-formal-definition) - [Interpretation:](#local-section-05-stack-f-arepo-f-inputadmissibility-interpretation-7) - [RULE](#local-section-05-stack-f-arepo-f-inputadmissibility-rule-3) - [FAILURE](#local-section-05-stack-f-arepo-f-inputadmissibility-failure-3) - [III. TABULA STATE ADMISSIBILITY CONDITIONS](#local-section-05-stack-f-arepo-f-inputadmissibility-iii-tabula-state-admissibility-conditions-2) - [Principle:](#local-section-05-stack-f-arepo-f-inputadmissibility-principle-6) - [State Admissibility Requirements:](#local-section-05-stack-f-arepo-f-inputadmissibility-state-admissibility-requirements) - [RULE](#local-section-05-stack-f-arepo-f-inputadmissibility-rule-4) - [PROHIBITIONS](#local-section-05-stack-f-arepo-f-inputadmissibility-prohibitions) - [FAILURE CONDITIONS](#local-section-05-stack-f-arepo-f-inputadmissibility-failure-conditions-6) - [IV. REQUEST ADMISSIBILITY](#local-section-05-stack-f-arepo-f-inputadmissibility-iv-request-admissibility-2) - [Principle:](#local-section-05-stack-f-arepo-f-inputadmissibility-principle-7) - [Canonical Request Structure:](#local-section-05-stack-f-arepo-f-inputadmissibility-canonical-request-structure) - [Traversal Definition:](#local-section-05-stack-f-arepo-f-inputadmissibility-traversal-definition) - [Constraints:](#local-section-05-stack-f-arepo-f-inputadmissibility-constraints-2) - [PROHIBITIONS](#local-section-05-stack-f-arepo-f-inputadmissibility-prohibitions-2) - [FAILURE CONDITIONS](#local-section-05-stack-f-arepo-f-inputadmissibility-failure-conditions-7) - [V. FAILURE CONDITIONS](#local-section-05-stack-f-arepo-f-inputadmissibility-v-failure-conditions-2) - [INVARIANT FAILURES (TENET F)](#local-section-05-stack-f-arepo-f-inputadmissibility-invariant-failures-tenet-f-2) - [TOPOLOGY FAILURES (ROTAS F)](#local-section-05-stack-f-arepo-f-inputadmissibility-topology-failures-rotas-f-2) - [STRUCTURAL FAILURES](#local-section-05-stack-f-arepo-f-inputadmissibility-structural-failures-2) - [REQUEST FAILURES](#local-section-05-stack-f-arepo-f-inputadmissibility-request-failures-2) - [RULE](#local-section-05-stack-f-arepo-f-inputadmissibility-rule-5) - [VI. ADMISSION FORMULA](#local-section-05-stack-f-arepo-f-inputadmissibility-vi-admission-formula-2) - [Formal Condition:](#local-section-05-stack-f-arepo-f-inputadmissibility-formal-condition-2) - [Derived Constraints:](#local-section-05-stack-f-arepo-f-inputadmissibility-derived-constraints) - [Interpretation:](#local-section-05-stack-f-arepo-f-inputadmissibility-interpretation-8) - [BOUNDARY](#local-section-05-stack-f-arepo-f-inputadmissibility-boundary-2) - [FAILURE](#local-section-05-stack-f-arepo-f-inputadmissibility-failure-4) - [VII. BOUNDARY ENFORCEMENT](#local-section-05-stack-f-arepo-f-inputadmissibility-vii-boundary-enforcement-2) - [Principle:](#local-section-05-stack-f-arepo-f-inputadmissibility-principle-8) - [RULES](#local-section-05-stack-f-arepo-f-inputadmissibility-rules-2) - [MANDATORY BEHAVIOR](#local-section-05-stack-f-arepo-f-inputadmissibility-mandatory-behavior-2) - [INTERPRETATION](#local-section-05-stack-f-arepo-f-inputadmissibility-interpretation-9) - [PROHIBITIONS](#local-section-05-stack-f-arepo-f-inputadmissibility-prohibitions-3) - [FAILURE CONDITIONS](#local-section-05-stack-f-arepo-f-inputadmissibility-failure-conditions-8) - [VIII. TRACEABILITY REQUIREMENT](#local-section-05-stack-f-arepo-f-inputadmissibility-viii-traceability-requirement-2) - [Principle:](#local-section-05-stack-f-arepo-f-inputadmissibility-principle-9) - [Trace Structure:](#local-section-05-stack-f-arepo-f-inputadmissibility-trace-structure-2) - [Requirements:](#local-section-05-stack-f-arepo-f-inputadmissibility-requirements-2) - [RULE](#local-section-05-stack-f-arepo-f-inputadmissibility-rule-6) - [INTERPRETATION](#local-section-05-stack-f-arepo-f-inputadmissibility-interpretation-10) - [FAILURE CONDITIONS](#local-section-05-stack-f-arepo-f-inputadmissibility-failure-conditions-9) - [IX. REGIME PURITY ENFORCEMENT](#local-section-05-stack-f-arepo-f-inputadmissibility-ix-regime-purity-enforcement-2) - [Principle:](#local-section-05-stack-f-arepo-f-inputadmissibility-principle-10) - [PROHIBITIONS](#local-section-05-stack-f-arepo-f-inputadmissibility-prohibitions-4) - [ALLOWED](#local-section-05-stack-f-arepo-f-inputadmissibility-allowed-2) - [RULE](#local-section-05-stack-f-arepo-f-inputadmissibility-rule-7) - [INTERPRETATION](#local-section-05-stack-f-arepo-f-inputadmissibility-interpretation-11) - [FAILURE CONDITIONS](#local-section-05-stack-f-arepo-f-inputadmissibility-failure-conditions-10) - [X. FUNCTION](#local-section-05-stack-f-arepo-f-inputadmissibility-x-function-2) - [ROLE IN AGLA CLASS CHAIN](#local-section-05-stack-f-arepo-f-inputadmissibility-role-in-agla-class-chain-2) - [AREPO F:](#local-section-05-stack-f-arepo-f-inputadmissibility-arepo-f-2) - [SYSTEM ROLE](#local-section-05-stack-f-arepo-f-inputadmissibility-system-role) - [XI. ADMISSION OUTPUT CONTRACT](#local-section-05-stack-f-arepo-f-inputadmissibility-xi-admission-output-contract) - [Principle:](#local-section-05-stack-f-arepo-f-inputadmissibility-principle-11) - [Admissibility Output:](#local-section-05-stack-f-arepo-f-inputadmissibility-admissibility-output) - [Rules:](#local-section-05-stack-f-arepo-f-inputadmissibility-rules-3) - [Interpretation:](#local-section-05-stack-f-arepo-f-inputadmissibility-interpretation-12) - [Failure Conditions:](#local-section-05-stack-f-arepo-f-inputadmissibility-failure-conditions-11) - [XII. PRE-EXECUTION GATE (OPERA F)](#local-section-05-stack-f-arepo-f-inputadmissibility-xii-pre-execution-gate-opera-f) - [Principle:](#local-section-05-stack-f-arepo-f-inputadmissibility-principle-12) - [Preconditions:](#local-section-05-stack-f-arepo-f-inputadmissibility-preconditions) - [Gate Function:](#local-section-05-stack-f-arepo-f-inputadmissibility-gate-function) - [Rule:](#local-section-05-stack-f-arepo-f-inputadmissibility-rule-8) - [Interpretation:](#local-section-05-stack-f-arepo-f-inputadmissibility-interpretation-13) - [Failure Conditions:](#local-section-05-stack-f-arepo-f-inputadmissibility-failure-conditions-12) - [XIII. DIAGNOSTIC INTERFACE](#local-section-05-stack-f-arepo-f-inputadmissibility-xiii-diagnostic-interface) - [Principle:](#local-section-05-stack-f-arepo-f-inputadmissibility-principle-13) - [Diagnostic Structure:](#local-section-05-stack-f-arepo-f-inputadmissibility-diagnostic-structure) - [Rules:](#local-section-05-stack-f-arepo-f-inputadmissibility-rules-4) - [Prohibitions:](#local-section-05-stack-f-arepo-f-inputadmissibility-prohibitions-5) - [Interpretation:](#local-section-05-stack-f-arepo-f-inputadmissibility-interpretation-14) - [Failure Conditions:](#local-section-05-stack-f-arepo-f-inputadmissibility-failure-conditions-13) - [XIV. NON-COLLAPSE LAW (AREPO EXTENDED)](#local-section-05-stack-f-arepo-f-inputadmissibility-xiv-non-collapse-law-arepo-extended) - [Principle:](#local-section-05-stack-f-arepo-f-inputadmissibility-principle-14) - [Required Distinctions:](#local-section-05-stack-f-arepo-f-inputadmissibility-required-distinctions) - [Rule:](#local-section-05-stack-f-arepo-f-inputadmissibility-rule-9) - [Interpretation:](#local-section-05-stack-f-arepo-f-inputadmissibility-interpretation-15) - [Failure Conditions:](#local-section-05-stack-f-arepo-f-inputadmissibility-failure-conditions-14) - [XV. SYSTEM-WIDE FAILURE CLASSES](#local-section-05-stack-f-arepo-f-inputadmissibility-xv-system-wide-failure-classes) - [INPUT FAILURES](#local-section-05-stack-f-arepo-f-inputadmissibility-input-failures) - [STRUCTURAL FAILURES](#local-section-05-stack-f-arepo-f-inputadmissibility-structural-failures-3) - [TRAVERSAL FAILURES](#local-section-05-stack-f-arepo-f-inputadmissibility-traversal-failures) - [COMPATIBILITY FAILURES](#local-section-05-stack-f-arepo-f-inputadmissibility-compatibility-failures) - [REQUEST FAILURES](#local-section-05-stack-f-arepo-f-inputadmissibility-request-failures-3) - [OUTPUT FAILURES](#local-section-05-stack-f-arepo-f-inputadmissibility-output-failures) - [Rule:](#local-section-05-stack-f-arepo-f-inputadmissibility-rule-10) - [XVI. EXECUTION VALIDITY CONDITION](#local-section-05-stack-f-arepo-f-inputadmissibility-xvi-execution-validity-condition) - [Principle:](#local-section-05-stack-f-arepo-f-inputadmissibility-principle-15) - [Validity Formula:](#local-section-05-stack-f-arepo-f-inputadmissibility-validity-formula) - [Interpretation:](#local-section-05-stack-f-arepo-f-inputadmissibility-interpretation-16) - [Rule:](#local-section-05-stack-f-arepo-f-inputadmissibility-rule-11) - [Failure Code:](#local-section-05-stack-f-arepo-f-inputadmissibility-failure-code) - [XVII. FUNCTION](#local-section-05-stack-f-arepo-f-inputadmissibility-xvii-function) - [ROLE IN AGLA CLASS CHAIN](#local-section-05-stack-f-arepo-f-inputadmissibility-role-in-agla-class-chain-3) - [AREPO F:](#local-section-05-stack-f-arepo-f-inputadmissibility-arepo-f-3) - [SYSTEM ROLE](#local-section-05-stack-f-arepo-f-inputadmissibility-system-role-2) - [XVIII. CLOSURE](#local-section-05-stack-f-arepo-f-inputadmissibility-xviii-closure) - [FINAL LAW](#local-section-05-stack-f-arepo-f-inputadmissibility-final-law-2) - [FORMAL CLOSURE](#local-section-05-stack-f-arepo-f-inputadmissibility-formal-closure) - [FINAL STATE:](#local-section-05-stack-f-arepo-f-inputadmissibility-final-state-2) - [Version: 0.2.0-AREPO-F-ADMISSIO-TABULAE-REWRITE](#local-section-05-stack-f-arepo-f-inputadmissibility-version-0-2-0-arepo-f-admissio-tabulae-rewrite) END SECTION 0 — HEADER ============================================================ ============================================================ I. PURPOSE ============================================================ Define the admissibility laws governing TABULA operations as the pre-execution gate of REGIMEN_F. AREPO F establishes: • what constitutes an admissible TABULA state • what constitutes an admissible traversal request • what must be rejected prior to OPERA • how TENET invariants and ROTAS topology are enforced ------------------------------------------------------------ CORE PRINCIPLE ------------------------------------------------------------ AREPO F does not: • execute TABULA (OPERA) • define TABULA identity (TENET) • define TABULA topology (ROTAS) AREPO F provides: the boundary where structural possibility becomes admissible operation. ============================================================ END SECTION I ============================================================ ============================================================ II. ADMISSIBILITY PRINCIPLE ============================================================ Definition: ------------------------------------------------------------ An operation is admissible if and only if: it preserves TENET invariants and conforms to ROTAS topology and is fully specified and traceable ------------------------------------------------------------ Formal Concept: ------------------------------------------------------------ admissible(operation) ⇔ invariant_compliant(operation) ∧ topology_consistent(operation) ∧ fully_specified(operation) ∧ traceable(operation) ------------------------------------------------------------ Interpretation: ------------------------------------------------------------ AREPO F distinguishes between: • possible (ROTAS) • admissible (AREPO) • executable (OPERA) ------------------------------------------------------------ Failure: ------------------------------------------------------------ inadmissible_operation ============================================================ END SECTION II ============================================================ ============================================================ III. TABULA STATE ADMISSIBILITY CONDITIONS ============================================================ Principle: ------------------------------------------------------------ AREPO F evaluates whether a TABULA state is admissible for operation under REGIMEN_F, based on invariant preservation and structural coherence. AREPO does not redefine TABULA validity; it evaluates admissibility relative to operation context. ------------------------------------------------------------ Admissible State Requirements: ------------------------------------------------------------ A state is admissible if: • bound to FIGURA QUARTA (TENET F) • structured under multiplicatio constraint • expressed (no pre-expression violation) • indexed by valid locus (ROTAS F) • preserves A/T separation where applicable • preserves generation ancestry ------------------------------------------------------------ Interpretation: ------------------------------------------------------------ AREPO F evaluates: readiness of the state for lawful operation, not ontological or structural definition. ------------------------------------------------------------ Failure Conditions: ------------------------------------------------------------ state_inadmissible locus_inconsistency pre_expression_violation ancestry_break ============================================================ END SECTION III ============================================================ ============================================================ IV. REQUEST ADMISSIBILITY ============================================================ Principle: ------------------------------------------------------------ Every operation request must be validated before being admitted to execution. ------------------------------------------------------------ Valid Request Must Include: ------------------------------------------------------------ REQUEST := { origin_locus traversal_definition target_locus (optional but derivable) } ------------------------------------------------------------ Constraints: ------------------------------------------------------------ • origin_locus must exist • traversal must be defined in (Δh, Δl, Δt) • traversal must remain within cyclic bounds • no implicit steps allowed ------------------------------------------------------------ Interpretation: ------------------------------------------------------------ AREPO F rejects: • ambiguous requests • partially defined traversals • symbol-only references ------------------------------------------------------------ Failure Conditions: ------------------------------------------------------------ missing_origin undefined_traversal implicit_transition symbolic_reference_only ============================================================ END SECTION IV ============================================================ ============================================================ V. FAILURE CONDITIONS ============================================================ AREPO F must explicitly reject any operation that violates: ------------------------------------------------------------ INVARIANT FAILURES (TENET F) ------------------------------------------------------------ • ontology_injection • non_permutation_violation • multiplicatio_violation • regime_isolation_violation • A_T_collapse • non_collapse_violation ------------------------------------------------------------ TOPOLOGY FAILURES (ROTAS F) ------------------------------------------------------------ • invalid_locus_index • axis_overflow • cycle_break • non_deterministic_path • unordered_traversal ------------------------------------------------------------ STRUCTURAL FAILURES ------------------------------------------------------------ • state_inadmissible • missing_components • ancestry_violation • cardinality_violation (per CARCER/TABULA structure) ------------------------------------------------------------ REQUEST FAILURES ------------------------------------------------------------ • missing_origin • undefined_traversal • non_traceable_request • implicit_steps • symbolic_only_reference ------------------------------------------------------------ RULE ------------------------------------------------------------ Any detected failure: → must result in rejection ============================================================ END SECTION V ============================================================ ============================================================ VI. ADMISSION FORMULA ============================================================ Formal Condition: ------------------------------------------------------------ valid_admission(request) ⇔ state_admissible(request.origin_locus) ∧ valid_traversal(request.traversal) ∧ invariant_preserved(request) ∧ topology_preserved(request) ∧ traceable(request) ------------------------------------------------------------ Interpretation: ------------------------------------------------------------ Admission requires: • admissible origin state • lawful traversal definition • invariant preservation • full traceability ------------------------------------------------------------ Boundary: ------------------------------------------------------------ This formula: • gates OPERA • does not execute OPERA ------------------------------------------------------------ Failure: ------------------------------------------------------------ admission_denied ============================================================ END SECTION VI ============================================================ ============================================================ VII. BOUNDARY ENFORCEMENT ============================================================ Principle: ------------------------------------------------------------ AREPO F acts as a strict gatekeeper. ------------------------------------------------------------ Rules: ------------------------------------------------------------ • No silent normalization • No implicit correction • No assumption of intent • No completion of missing data ------------------------------------------------------------ Interpretation: ------------------------------------------------------------ If a request is: • incomplete → reject • ambiguous → reject • inconsistent → reject ------------------------------------------------------------ Constraint: ------------------------------------------------------------ All admissible operations must be: explicitly defined and structurally valid ------------------------------------------------------------ Failure Conditions: ------------------------------------------------------------ silent_normalization implicit_completion assumption_injection ============================================================ END SECTION VII ============================================================ ============================================================ VIII. TRACEABILITY REQUIREMENT ============================================================ Principle: ------------------------------------------------------------ All admissible operations must be fully traceable. ------------------------------------------------------------ Trace Structure: ------------------------------------------------------------ TRACE := { origin_locus, traversal_sequence, resulting_locus } ------------------------------------------------------------ Requirements: ------------------------------------------------------------ • origin must be explicit • traversal must be explicit • resulting locus must be derivable ------------------------------------------------------------ Interpretation: ------------------------------------------------------------ Traceability ensures: • reproducibility • auditability • compatibility with OPERA ------------------------------------------------------------ Failure Conditions: ------------------------------------------------------------ trace_missing partial_trace non_derivable_target ============================================================ END SECTION VIII ============================================================ ============================================================ IX. REGIME PURITY ENFORCEMENT ============================================================ Principle: ------------------------------------------------------------ AREPO F enforces REGIMEN_F isolation. ------------------------------------------------------------ Prohibition: ------------------------------------------------------------ No operation may: ✗ execute principial evaluation (A) ✗ execute relational evaluation (T) ✗ generate interrogatives (E/RQ) ✗ perform decisions (D) ------------------------------------------------------------ Allowed: ------------------------------------------------------------ • structural reference to other regimes • boundary awareness ------------------------------------------------------------ Rule: ------------------------------------------------------------ Any cross-regime execution attempt: → must be rejected ------------------------------------------------------------ Failure Conditions: ------------------------------------------------------------ regime_bleed execution_leak cross_regime_execution ============================================================ END SECTION IX ============================================================ ============================================================ X. FUNCTION ============================================================ AREPO F governs: • admissibility of TABULA operations • validation of TABULA states for operation • validation of traversal requests • enforcement of TENET invariants • enforcement of ROTAS topology • rejection of invalid operations ------------------------------------------------------------ ROLE IN AGLA CLASS CHAIN ------------------------------------------------------------ AREPO F: • validates • admits or rejects It does NOT: • define invariants (TENET) • define topology (ROTAS) • execute operations (OPERA) • mediate presentation (SATOR) ============================================================ END SECTION X ============================================================ ============================================================ XI. CLOSURE ============================================================ AREPO F establishes: the admissibility boundary of TABULA. ------------------------------------------------------------ FINAL LAW ------------------------------------------------------------ No TABULA operation may proceed to execution unless: it is invariant-compliant, topology-consistent, fully specified, and traceable. ------------------------------------------------------------ Any violation results in: immediate rejection. ------------------------------------------------------------ FINAL STATE: LOCK-CANDIDATE ============================================================ END AREPO F — ADMISSIO TABULAE ============================================================ ============================================================ AREPO F — ADMISSIO TABULAE Ars Generalis Applied — Admissibility Layer (REGIMEN_F) Version: 0.2.0-AREPO-F-ADMISSIO-TABULAE-REWRITE Status: PROPOSED / VALIDATION TARGET Scope: TABULA admissibility, state admission, and pre-execution gating Authority: AGLA / AREPO Mutation Policy: VERSION-CONTROLLED ONLY Class: AREPO Regime: F Depends-On: • TENET F — TABULA GENERALIS • ROTAS F — TABULA ROTUNDA References: • ALBUS — TABULA / FIGURA QUARTA PROJECTION • CARCER — TABULA FAMILY DERIVATION PROCEDURE • POPULUS — TABULA ============================================================ END SECTION 0 — HEADER ============================================================ ============================================================ I. PURPOSE ============================================================ Define the admissibility laws governing TABULA operations as the strict pre-execution gate of REGIMEN_F. AREPO F establishes: • admissibility conditions for TABULA states • admissibility conditions for traversal requests • rejection criteria prior to OPERA • enforcement of TENET invariants and ROTAS topology ------------------------------------------------------------ CORE PRINCIPLE ------------------------------------------------------------ AREPO F is a rejection-oriented gate. It does not: • execute TABULA (OPERA) • define TABULA identity (TENET) • define TABULA topology (ROTAS) • repair or complete requests • infer missing structure AREPO F defines: the admissibility boundary between structural possibility and executable operation. ------------------------------------------------------------ MANDATORY BEHAVIOR ------------------------------------------------------------ AREPO F must: • reject incomplete requests • reject ambiguous definitions • reject invariant violations • reject topology violations • reject non-traceable operations ============================================================ END SECTION I ============================================================ ============================================================ II. ADMISSIBILITY PRINCIPLE ============================================================ Definition: ------------------------------------------------------------ An operation is admissible if and only if: • TENET invariants are preserved • ROTAS topology is respected • request is fully specified • operation is fully traceable ------------------------------------------------------------ Formal Definition: ------------------------------------------------------------ admissible(operation) ⇔ invariant_compliant(operation) ∧ topology_consistent(operation) ∧ fully_specified(operation) ∧ traceable(operation) ------------------------------------------------------------ Interpretation: ------------------------------------------------------------ AREPO F enforces the distinction: possible (ROTAS) ≠ admissible (AREPO) ≠ executable (OPERA) ------------------------------------------------------------ RULE ------------------------------------------------------------ Any violation of any conjunct: → operation must be rejected ------------------------------------------------------------ FAILURE ------------------------------------------------------------ inadmissible_operation ============================================================ END SECTION II ============================================================ ============================================================ III. TABULA STATE ADMISSIBILITY CONDITIONS ============================================================ Principle: ------------------------------------------------------------ AREPO F evaluates whether a TABULA state is admissible for operation under REGIMEN_F. AREPO does not define state validity. AREPO evaluates admissibility relative to operation readiness. ------------------------------------------------------------ State Admissibility Requirements: ------------------------------------------------------------ A state is admissible iff: • bound(FIGURA_QUARTA) (TENET F) • locus ∈ valid ROTAS domain (ROTAS F) • structure is expressed (no pre-expression) • ancestry is preserved • A/T separation preserved where applicable • no structural collapse is present ------------------------------------------------------------ RULE ------------------------------------------------------------ State must be: • explicit • typed • structurally anchored • non-ambiguous ------------------------------------------------------------ PROHIBITIONS ------------------------------------------------------------ Reject state if: ✗ implicit structure ✗ missing ancestry ✗ collapsed layers ✗ undefined locus ✗ symbolic-only representation ------------------------------------------------------------ FAILURE CONDITIONS ------------------------------------------------------------ state_inadmissible locus_inconsistency pre_expression_violation ancestry_break structural_collapse ============================================================ END SECTION III ============================================================ ============================================================ IV. REQUEST ADMISSIBILITY ============================================================ Principle: ------------------------------------------------------------ All requests must be fully specified prior to admission. AREPO F does not complete or infer requests. ------------------------------------------------------------ Canonical Request Structure: ------------------------------------------------------------ REQUEST := { origin_locus, traversal_definition, target_locus (optional, must be derivable) } ------------------------------------------------------------ Traversal Definition: ------------------------------------------------------------ traversal_definition := { Δh, Δl, Δt } ------------------------------------------------------------ Constraints: ------------------------------------------------------------ • origin_locus must exist and be admissible • traversal must be explicitly defined • traversal must be stepwise (no implicit jumps) • traversal must remain within cyclic bounds • traversal must be deterministic ------------------------------------------------------------ PROHIBITIONS ------------------------------------------------------------ Reject request if: ✗ missing origin_locus ✗ undefined traversal ✗ implicit steps ✗ symbolic-only request ✗ non-deterministic traversal ------------------------------------------------------------ FAILURE CONDITIONS ------------------------------------------------------------ missing_origin undefined_traversal implicit_transition symbolic_reference_only non_deterministic_request ============================================================ END SECTION IV ============================================================ ============================================================ V. FAILURE CONDITIONS ============================================================ AREPO F must reject any operation violating: ------------------------------------------------------------ INVARIANT FAILURES (TENET F) ------------------------------------------------------------ • ontology_injection • non_permutation_violation • multiplicatio_violation • regime_isolation_violation • A_T_collapse • non_collapse_violation ------------------------------------------------------------ TOPOLOGY FAILURES (ROTAS F) ------------------------------------------------------------ • invalid_locus_index • axis_overflow • cycle_break • unordered_traversal • non_deterministic_path ------------------------------------------------------------ STRUCTURAL FAILURES ------------------------------------------------------------ • state_inadmissible • missing_components • ancestry_violation • cardinality_violation (per CARCER/TABULA structure) ------------------------------------------------------------ REQUEST FAILURES ------------------------------------------------------------ • missing_origin • undefined_traversal • implicit_steps • symbolic_only_reference • non_traceable_request ------------------------------------------------------------ RULE ------------------------------------------------------------ Upon detection: → immediate rejection → no correction → no continuation ============================================================ END SECTION V ============================================================ ============================================================ VI. ADMISSION FORMULA ============================================================ Formal Condition: ------------------------------------------------------------ valid_admission(request) ⇔ state_admissible(request.origin_locus) ∧ traversal_defined(request.traversal_definition) ∧ invariant_preserved(request) ∧ topology_preserved(request) ∧ traceable(request) ------------------------------------------------------------ Derived Constraints: ------------------------------------------------------------ state_admissible(x) := bound(FIGURA_QUARTA, x) ∧ valid_locus(x) ∧ expressed(x) ∧ ancestry_preserved(x) ∧ no_structural_collapse(x) ------------------------------------------------------------ traversal_defined(t) := explicit(Δh, Δl, Δt) ∧ deterministic(t) ∧ cyclically_bounded(t) ------------------------------------------------------------ Interpretation: ------------------------------------------------------------ Admission requires: • admissible origin state • fully specified traversal • invariant preservation • topology consistency • complete traceability ------------------------------------------------------------ BOUNDARY ------------------------------------------------------------ This formula: • authorizes OPERA execution • does not perform execution ------------------------------------------------------------ FAILURE ------------------------------------------------------------ admission_denied ============================================================ END SECTION VI ============================================================ ============================================================ VII. BOUNDARY ENFORCEMENT ============================================================ Principle: ------------------------------------------------------------ AREPO F operates as a strict, non-corrective boundary. ------------------------------------------------------------ RULES ------------------------------------------------------------ • No silent normalization • No implicit correction • No inference of intent • No completion of missing data • No heuristic repair ------------------------------------------------------------ MANDATORY BEHAVIOR ------------------------------------------------------------ If request is: • incomplete → reject • ambiguous → reject • inconsistent → reject • non-traceable → reject ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ AREPO F is rejection-oriented: it does not improve requests, it only accepts or rejects them. ------------------------------------------------------------ PROHIBITIONS ------------------------------------------------------------ AREPO must not: ✗ fill missing fields ✗ reinterpret malformed structures ✗ infer traversal paths ✗ repair cardinality or ancestry ------------------------------------------------------------ FAILURE CONDITIONS ------------------------------------------------------------ silent_normalization implicit_completion assumption_injection heuristic_repair ============================================================ END SECTION VII ============================================================ ============================================================ VIII. TRACEABILITY REQUIREMENT ============================================================ Principle: ------------------------------------------------------------ All admissible operations must be fully traceable. ------------------------------------------------------------ Trace Structure: ------------------------------------------------------------ TRACE := { origin_locus, traversal_sequence, resulting_locus, step_sequence, axis_deltas } ------------------------------------------------------------ Requirements: ------------------------------------------------------------ • origin_locus must be explicit • traversal_sequence must be explicit • resulting_locus must be derivable • each step must be reconstructible • axis transitions must be explicit (Δh, Δl, Δt) ------------------------------------------------------------ RULE ------------------------------------------------------------ No operation is admissible if: • origin cannot be reconstructed • traversal cannot be replayed • result cannot be derived from traversal ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ Traceability ensures: • reproducibility • auditability • compatibility with OPERA ------------------------------------------------------------ FAILURE CONDITIONS ------------------------------------------------------------ trace_missing partial_trace non_derivable_target step_ambiguity ============================================================ END SECTION VIII ============================================================ ============================================================ IX. REGIME PURITY ENFORCEMENT ============================================================ Principle: ------------------------------------------------------------ AREPO F enforces strict REGIMEN_F isolation. ------------------------------------------------------------ PROHIBITIONS ------------------------------------------------------------ No operation may: ✗ execute principial evaluation (TENET A) ✗ execute relational evaluation (TENET T) ✗ generate interrogatives (REGIMEN_E / RQ) ✗ perform decisions (REGIMEN_D) ------------------------------------------------------------ ALLOWED ------------------------------------------------------------ • structural references to other regimes • boundary-awareness checks • dependency validation ------------------------------------------------------------ RULE ------------------------------------------------------------ Any attempt to perform cross-regime execution: → must be rejected ------------------------------------------------------------ INTERPRETATION ------------------------------------------------------------ AREPO F is: • pre-execution • non-evaluative • non-decisional ------------------------------------------------------------ FAILURE CONDITIONS ------------------------------------------------------------ regime_bleed execution_leak cross_regime_execution ============================================================ END SECTION IX ============================================================ ============================================================ X. FUNCTION ============================================================ AREPO F governs: • admissibility of TABULA operations • validation of TABULA states for execution readiness • validation of traversal requests • enforcement of TENET F invariants • enforcement of ROTAS F topology • rejection of invalid operations • enforcement of traceability ------------------------------------------------------------ ROLE IN AGLA CLASS CHAIN ------------------------------------------------------------ AREPO F: • validates • admits or rejects It does NOT: • define invariants (TENET) • define topology (ROTAS) • execute operations (OPERA) • mediate presentation (SATOR) ------------------------------------------------------------ SYSTEM ROLE ------------------------------------------------------------ AREPO F is: • the admissibility kernel • the pre-execution gate • the rejection authority for REGIMEN_F ============================================================ END SECTION X ============================================================ ============================================================ XI. ADMISSION OUTPUT CONTRACT ============================================================ Principle: ------------------------------------------------------------ AREPO F must emit explicit admission results for every evaluated request. ------------------------------------------------------------ Admissibility Output: ------------------------------------------------------------ AREPO_ADMISSION := { status: ADMITTED | REJECTED, evaluated_request, origin_locus, traversal_definition, validation_trace, violations[], blocking: true | false } ------------------------------------------------------------ Rules: ------------------------------------------------------------ • status must always be explicit • violations must be enumerated if REJECTED • validation_trace must preserve evaluation steps • blocking must reflect execution eligibility ------------------------------------------------------------ Interpretation: ------------------------------------------------------------ AREPO does not return partial success. Every evaluation results in: • ADMITTED • or REJECTED ------------------------------------------------------------ Failure Conditions: ------------------------------------------------------------ admission_output_missing ambiguous_status silent_rejection ============================================================ END SECTION XI ============================================================ ============================================================ XII. PRE-EXECUTION GATE (OPERA F) ============================================================ Principle: ------------------------------------------------------------ No OPERA F execution may proceed without AREPO admission. ------------------------------------------------------------ Preconditions: ------------------------------------------------------------ must_pass: • state_admissible(origin_locus) • traversal_defined(traversal_definition) • invariant_preserved • topology_preserved • traceable ------------------------------------------------------------ Gate Function: ------------------------------------------------------------ admit_TABULA_request(request): if valid_admission(request): return ADMITTED else: return REJECTED with violations ------------------------------------------------------------ Rule: ------------------------------------------------------------ OPERA must not: • bypass AREPO • execute on REJECTED status • execute on partial validation ------------------------------------------------------------ Interpretation: ------------------------------------------------------------ AREPO F is: the mandatory gateway to OPERA F ------------------------------------------------------------ Failure Conditions: ------------------------------------------------------------ AREPO_BYPASS PRE_EXECUTION_FAILURE UNAUTHORIZED_EXECUTION ============================================================ END SECTION XII ============================================================ ============================================================ XIII. DIAGNOSTIC INTERFACE ============================================================ Principle: ------------------------------------------------------------ AREPO F must provide explicit diagnostic feedback. ------------------------------------------------------------ Diagnostic Structure: ------------------------------------------------------------ AREPO_REPORT := { status: PASS | FAIL, stage, violations[], severity, blocking: true | false, evaluated_components[], trace_reference } ------------------------------------------------------------ Rules: ------------------------------------------------------------ Diagnostics must: • identify all violations • specify evaluation stage • preserve structural context • remain non-corrective ------------------------------------------------------------ Prohibitions: ------------------------------------------------------------ ✗ silent failure ✗ implicit correction ✗ heuristic repair ------------------------------------------------------------ Interpretation: ------------------------------------------------------------ Diagnostics expose: failure causes without altering input ------------------------------------------------------------ Failure Conditions: ------------------------------------------------------------ diagnostic_missing ambiguous_error silent_failure ============================================================ END SECTION XIII ============================================================ ============================================================ XIV. NON-COLLAPSE LAW (AREPO EXTENDED) ============================================================ Principle: ------------------------------------------------------------ AREPO F must enforce strict structural separation across TABULA layers. ------------------------------------------------------------ Required Distinctions: ------------------------------------------------------------ COLUMN ≠ FAMILY FAMILY ≠ ENTRY ENTRY ≠ CAMERA CAMERA ≠ QUESTION TABULA ≠ EVACUATIO TABULA ≠ MULTIPLICATIO ------------------------------------------------------------ Rule: ------------------------------------------------------------ No admissible structure may collapse: • marker into camera • camera into question • tabula into lookup table • triadic into binary • interrogative into condition-space ------------------------------------------------------------ Interpretation: ------------------------------------------------------------ Structural integrity depends on: preserved hierarchy preserved typing preserved generative order ------------------------------------------------------------ Failure Conditions: ------------------------------------------------------------ layer_collapse type_erasure structural_flattening ============================================================ END SECTION XIV ============================================================ ============================================================ XV. SYSTEM-WIDE FAILURE CLASSES ============================================================ INPUT FAILURES ------------------------------------------------------------ INVALID_COLUMN INVALID_ENTRY UNTYPED_STRUCTURE ------------------------------------------------------------ STRUCTURAL FAILURES ------------------------------------------------------------ CARDINALITY_ERROR A_T_COLLAPSE GENERATION_REVERSAL ------------------------------------------------------------ TRAVERSAL FAILURES ------------------------------------------------------------ RANDOM_TRAVERSAL CYCLE_BREAK TRACE_BREAK ------------------------------------------------------------ COMPATIBILITY FAILURES ------------------------------------------------------------ EVACUATIO_OVERRIDE MULTIPLICATIO_COLLAPSE ROTA_MISMATCH ------------------------------------------------------------ REQUEST FAILURES ------------------------------------------------------------ MISSING_ORIGIN UNDEFINED_TRAVERSAL IMPLICIT_STEPS SYMBOLIC_ONLY_REFERENCE ------------------------------------------------------------ OUTPUT FAILURES ------------------------------------------------------------ OUTPUT_INCOMPLETE OUTPUT_UNTRACEABLE OUTPUT_UNTYPED ------------------------------------------------------------ Rule: ------------------------------------------------------------ All failures must be: • explicit • typed • non-silent ============================================================ END SECTION XV ============================================================ ============================================================ XVI. EXECUTION VALIDITY CONDITION ============================================================ Principle: ------------------------------------------------------------ TABULA execution is valid if and only if all admissibility conditions hold under AREPO F. ------------------------------------------------------------ Validity Formula: ------------------------------------------------------------ valid_TABULA(request) ⇔ admitted_by_AREPO ∧ bound(FIGURA_QUARTA) ∧ state_admissible(origin_locus) ∧ traversal_defined(traversal_definition) ∧ invariant_preserved ∧ topology_preserved ∧ traceable(request) ------------------------------------------------------------ Interpretation: ------------------------------------------------------------ Execution validity is: • structural • typological • topological • traceable • non-heuristic ------------------------------------------------------------ Rule: ------------------------------------------------------------ If any component is false: → execution is invalid → operation must not proceed ------------------------------------------------------------ Failure Code: ------------------------------------------------------------ TABULA_EXECUTION_INVALID ============================================================ END SECTION XVI ============================================================ ============================================================ XVII. FUNCTION ============================================================ AREPO F governs: • admissibility of TABULA operations • validation of TABULA states for execution readiness • validation of traversal definitions • enforcement of TENET F invariants • enforcement of ROTAS F topology • rejection of invalid or incomplete operations • enforcement of full traceability • emission of admissibility diagnostics ------------------------------------------------------------ ROLE IN AGLA CLASS CHAIN ------------------------------------------------------------ AREPO F: • validates • admits or rejects It does NOT: • define invariants (TENET) • define topology (ROTAS) • execute operations (OPERA) • mediate outputs (SATOR) ------------------------------------------------------------ SYSTEM ROLE ------------------------------------------------------------ AREPO F is: • the admissibility kernel of REGIMEN_F • the mandatory pre-execution gate • the authority preventing invalid execution ============================================================ END SECTION XVII ============================================================ ============================================================ XVIII. CLOSURE ============================================================ TABULA, under AREPO F, is: a strictly governed admissible structure, whose integrity must be validated before any execution or traversal occurs. ------------------------------------------------------------ FINAL LAW ------------------------------------------------------------ No TABULA operation may: • execute • traverse • project unless it satisfies: invariant_compliance ∧ topology_consistency ∧ full specification ∧ traceability ------------------------------------------------------------ Any violation results in: immediate rejection ------------------------------------------------------------ FORMAL CLOSURE ------------------------------------------------------------ AREPO F := admissibility kernel for TABULA operational boundary ------------------------------------------------------------ FINAL STATE: VALIDATION TARGET ============================================================ END AREPO F — ADMISSIO TABULAE Version: 0.2.0-AREPO-F-ADMISSIO-TABULAE-REWRITE ============================================================