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AREPO CC — CONTEXTUAL CONTRACTION ADMISSIBILITY
Version: 1.0.0-AREPO-CC-CONTEXTUAL-CONTRACTION
Status: COMPLETE STACK / METAE CANDIDATE / NON-CANONICAL / SIGMA_SATOR-READY
Authority: AGLA_MAIN_LAB REQUEST / LOCAL DEVELOPMENT NODE
Class: AREPO
Scope: ADMISSIBILITY RULES FOR X ⟨ Y ⟩
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I. PURPOSE
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AREPO CC defines when contextual contraction is admissible.

It gates:

    X identification
    Y identification
    typing
    direction
    recursion
    relation profile attachment
    collapse eligibility
    ambiguity handling

It does not execute contraction.


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II. BASIC ADMISSION
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INPUT:

    X ⟨ Y ⟩

ADMISSIBLE only if:

    X is explicit
    Y is explicit
    direction is clear
    context role is clear
    ontology creation is not implied
    no hidden expansion is required

If any required condition fails:

    INSUFFICIENT ADMISSIBILITY


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III. TYPING REQUIREMENTS
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TYPED FORM:

    X^{τ_X} ⟨ Y^{τ_Y} ⟩

τ_X may identify:

    concept
    object
    force
    quality
    medium
    system function
    memory structure
    principle
    rule
    relation
    question
    subject
    substrate

τ_Y may identify:

    domain
    medium
    environment
    frame
    substrate
    regime
    condition
    rule context
    subject context
    material context
    cognitive context

RULE:

    τ_X and τ_Y need not be identical.

CONSTRAINT:

    τ_X and τ_Y must be compatible enough to permit meaningful
    contextual articulation.


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IV. ADMISSIBILITY TESTS
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AREPO admits X ⟨ Y ⟩ only if all required 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

Failure response:

    INSUFFICIENT ADMISSIBILITY


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V. RECURSION LIMITS
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Nested form:

    X ⟨ Y ⟨ Z ⟩ ⟩

ADMISSIBLE only if:

    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.


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VI. ANTI-EXPLOSION SAFEGUARDS
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PROHIBITED:

    expanding X across all contexts
    expanding Y across all possible X
    deriving all nested paths
    deriving all relation profiles
    treating analogy as unlimited transfer
    normalizing contractions silently

RULE:

    Expansion requires explicit instruction.

DEFAULT:

    read only the stated expression.


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VII. RELATIONAL PROFILE ADMISSION
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FORM:

    X ⟨ Y ⟩ | R'

R' is admissible only 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:

    no full relation profile is assumed.


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VIII. COLLAPSE ADMISSION
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Collapse requires explicit eligibility:

    identity
    dominance
    equivalence

IDENTITY:

    X ⟨ X ⟩ ⇒ X

DOMINANCE:

    if X ⊆ Y structurally,
    then X ⟨ Y ⟩ ≈ X

EQUIVALENCE:

    if X ≡ Y,
    then X ⟨ Y ⟩ = X = Y

If collapse cannot be decided:

    INSUFFICIENT ADMISSIBILITY


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IX. AMBIGUITY THRESHOLDS
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Return:

    INSUFFICIENT ADMISSIBILITY

when:

    X cannot be identified
    Y cannot be identified
    direction is ambiguous
    context boundary is unclear
    required typing is absent
    collapse is possible but undecidable
    analogy lacks shared X or mapping
    extraction is confused with contraction
    source text is treated as validated artifact


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X. DOMAIN EXAMPLES
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Physics:

    Force⟨Fluid⟩

Art:

    Color⟨Watercolor⟩

Ethics:

    Justice⟨War⟩

Cognition:

    Memory⟨Trauma⟩

Ars-compatible but not Ars-exclusive:

    Principle⟨Subject⟩
    Rule⟨Question⟩
    Relation⟨Regime⟩


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XI. FINAL AREPO ASSERTION
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AREPO CC admits contextual contraction only when the expression
is explicit, bounded, typed or type-recoverable, non-creative,
recursion-safe, and source/artifact-safe.

Otherwise:

    INSUFFICIENT ADMISSIBILITY

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END AREPO CC
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