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

Publication reference; manuscript cover date 2026-09-21; publisher release date 2026-09-21; 36 PDF pages.

**Attributed reading aid, not a complete manuscript conversion or independent proof verification.**

Amos Jay Maley. Anchor, Tensor, and Skin: A Fixed-Domain Decomposition Theorem for Admissible Description. Publication reference, 2026-09-21. SHA256 1624eacd530dcdaaedec184414c8a7eab8d5096805aee9ffa5452b6f51638c7b. DOI: 10.5281/zenodo.22875011.

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## Imports

States a one-way order: Kernel, AMetric, Structure, fixed-domain exhaustion, then ATS. References name kernel v49, AMetric editorial reference, Structure examples reference 20 September and Exhaustion composition reference 20 September.

## Establishes

Decomposes a fixed-domain admissible description into context (Anchor), complete semantic content (Tensor) and identity-preserving realization (Skin), with reconstruction maps; characterizes minimal realization uniqueness up to commuting bijection and finite-use envelopes/substitution.

## Supplies downstream

Supplies a typed organization for assembling/checking admissible descriptions and certificates. It does not serve as a premise for the earlier general exhaustion theorem.

## Scope and limits

A complete semantic profile is not merely an admissibility bit and need not identify a unique occupant. Minimal-realization uniqueness does not imply uniqueness among every adequate realization. Sequential substitution requires joint original-domain factorization; a licence alone is not execution.

## Evidence

- [Section 1.4, PDF pp. 3–3](https://constraintsystemsinstitute.org/manuscripts/ats/sha256-1624eacd530dcdaaedec184414c8a7eab8d5096805aee9ffa5452b6f51638c7b/manuscript.pdf#page=3)
- [Section 2.4 / Theorem 3.1 / Theorem 3.3 / Section 3.4, PDF pp. 6–8](https://constraintsystemsinstitute.org/manuscripts/ats/sha256-1624eacd530dcdaaedec184414c8a7eab8d5096805aee9ffa5452b6f51638c7b/manuscript.pdf#page=6)
- [Theorem 7.3, PDF pp. 22–23](https://constraintsystemsinstitute.org/manuscripts/ats/sha256-1624eacd530dcdaaedec184414c8a7eab8d5096805aee9ffa5452b6f51638c7b/manuscript.pdf#page=22)
- [Theorem 7.5, PDF pp. 24–24](https://constraintsystemsinstitute.org/manuscripts/ats/sha256-1624eacd530dcdaaedec184414c8a7eab8d5096805aee9ffa5452b6f51638c7b/manuscript.pdf#page=24)
- [Theorem 9.1, PDF pp. 29–29](https://constraintsystemsinstitute.org/manuscripts/ats/sha256-1624eacd530dcdaaedec184414c8a7eab8d5096805aee9ffa5452b6f51638c7b/manuscript.pdf#page=29)
- [References 1-4, PDF pp. 36–36](https://constraintsystemsinstitute.org/manuscripts/ats/sha256-1624eacd530dcdaaedec184414c8a7eab8d5096805aee9ffa5452b6f51638c7b/manuscript.pdf#page=36)