Anchor, Tensor, and Skin: A Fixed-Domain Decomposition Theorem for Admissible Description

This paper proves a fixed-domain decomposition theorem for admissible description. Let a descriptive carrier be governed by a fixed admissibility regime with standing conservation, identity-preserving redescription, fail-closed enforcement, and no additional admissibility-relevant load. Then every admissibility-bearing descriptive element belongs to exactly one of three roles: anchor, tensor, or skin. Anchors are admissibility-defining preconditions; tensors are quotient-level invariant content; skin is representational surplus with no admissibility-bearing authority. The theorem is same-domain and non-generative: it introduces no new admissibility level, operator class, or invariant source. It further shows that the decomposition is unique, exhaustive, minimal, and role-independent on the fixed carrier, so any admissibility-preserving alternative factors through anchor, tensor, and skin up to role isomorphism, while any purported further role or refinement collapses to bookkeeping or scope change. The result therefore supplies a normal form for fixed-domain admissible description and rules out any additional admissibility-preserving role structure on the same carrier.