# A Fixed-Domain Exhaustion Theorem: Standing, Consequence, and Compositional Closure

Publication reference; manuscript cover date 2026-09-21; publisher release date 2026-09-21; 39 PDF pages.

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

Amos Jay Maley. A Fixed-Domain Exhaustion Theorem: Standing, Consequence, and Compositional Closure. Publication reference, 2026-09-21. SHA256 d06d39b381edddaafe899f20769b0ba551802b23d7b83121530ecab346feece0. DOI: 10.5281/zenodo.22875070.

[Read the exact PDF](https://constraintsystemsinstitute.org/manuscripts/exhaustion/sha256-d06d39b381edddaafe899f20769b0ba551802b23d7b83121530ecab346feece0/manuscript.pdf)

## Imports

Reuses the 20 September Structure profile/interior results with short local proofs. Ref.6 names kernel v49; ref.7 names AMetric editorial reference. ATS is a comparison and is explicitly not assumed.

## Establishes

Adds compositional coverage and joint-constructor descent to complete semantic profiles; exhausts specified failure-witness families under typed boundary discipline. Separates original obligation coverage, closure and candidate identification.

## Supplies downstream

Supplies the finite-use compositional foundation and candidate readout criterion imported by ATS. ATS cites the 20 September composition reference rather than this preferred 21 September publication reference.

## Scope and limits

Arbitrary semantic coordinates are not automatically a finite implementation. Candidate-set constant readout, single occupant, and unique decomposition are separate results with separate assumptions. Retaining a failure history does not itself force every later endpoint negative; the edge 0-to-0 condition is additional.

## Evidence

- [Section 1.4, PDF pp. 5–6](https://constraintsystemsinstitute.org/manuscripts/exhaustion/sha256-d06d39b381edddaafe899f20769b0ba551802b23d7b83121530ecab346feece0/manuscript.pdf#page=5)
- [Section 3 / Theorem 3.3, PDF pp. 9–10](https://constraintsystemsinstitute.org/manuscripts/exhaustion/sha256-d06d39b381edddaafe899f20769b0ba551802b23d7b83121530ecab346feece0/manuscript.pdf#page=9)
- [Theorem 4.3 / Theorem 4.8, PDF pp. 13–16](https://constraintsystemsinstitute.org/manuscripts/exhaustion/sha256-d06d39b381edddaafe899f20769b0ba551802b23d7b83121530ecab346feece0/manuscript.pdf#page=13)
- [Theorem 5.9, PDF pp. 21–22](https://constraintsystemsinstitute.org/manuscripts/exhaustion/sha256-d06d39b381edddaafe899f20769b0ba551802b23d7b83121530ecab346feece0/manuscript.pdf#page=21)
- [Theorem 6.2 / Theorem 6.4, PDF pp. 23–24](https://constraintsystemsinstitute.org/manuscripts/exhaustion/sha256-d06d39b381edddaafe899f20769b0ba551802b23d7b83121530ecab346feece0/manuscript.pdf#page=23)
- [Theorem 8.1 / Corollary 8.2 / Proposition 8.4, PDF pp. 26–27](https://constraintsystemsinstitute.org/manuscripts/exhaustion/sha256-d06d39b381edddaafe899f20769b0ba551802b23d7b83121530ecab346feece0/manuscript.pdf#page=26)
- [Appendix C / References 6-8 and 12, PDF pp. 38–39](https://constraintsystemsinstitute.org/manuscripts/exhaustion/sha256-d06d39b381edddaafe899f20769b0ba551802b23d7b83121530ecab346feece0/manuscript.pdf#page=38)