# The Structure of Admissibility: Bivalent Qualification, Exhaustion, and the Unique Admissible Interior

Publication reference; manuscript cover date 2026-09-21; publisher release date 2026-09-21; 46 PDF pages.

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Amos Jay Maley. The Structure of Admissibility: Bivalent Qualification, Exhaustion, and the Unique Admissible Interior. Publication reference, 2026-09-21. SHA256 065979305b2fc1593abb343e72a86d0ed9c967c089d1a9cbf91be650de25eff2. DOI: 10.5281/zenodo.22874934.

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## Imports

Reconstructs kernel version 49 and AMetric boundary arguments locally; §1.4 distinguishes this support from using later conclusions as premises.

## Establishes

Bivalent qualification is an exact quotient only when all required original observations are constant on the bit fibres. It constructs the greatest safe interior relative to independently fixed qualification and continuation edges, and gives finite failed-path and exhaustion witnesses.

## Supplies downstream

Supplies complete-profile and continuation-interior machinery used in fixed-domain exhaustion and referenced by ATS. The downstream cited edition is the 20 September examples reference.

## Scope and limits

The interior may be empty. Uniqueness concerns the complete/maximal interior for fixed data, not every safe subset or a unique physical occupant. Failure retention and negative endpoint absorption have different conditions.

## Evidence

- [Section 1.4, PDF pp. 6–7](https://constraintsystemsinstitute.org/manuscripts/structure/sha256-065979305b2fc1593abb343e72a86d0ed9c967c089d1a9cbf91be650de25eff2/manuscript.pdf#page=6)
- [Theorems 5.5-5.6, PDF pp. 16–17](https://constraintsystemsinstitute.org/manuscripts/structure/sha256-065979305b2fc1593abb343e72a86d0ed9c967c089d1a9cbf91be650de25eff2/manuscript.pdf#page=16)
- [Theorems 6.3-6.6, PDF pp. 20–21](https://constraintsystemsinstitute.org/manuscripts/structure/sha256-065979305b2fc1593abb343e72a86d0ed9c967c089d1a9cbf91be650de25eff2/manuscript.pdf#page=20)
- [Theorem 7.2, PDF pp. 23–23](https://constraintsystemsinstitute.org/manuscripts/structure/sha256-065979305b2fc1593abb343e72a86d0ed9c967c089d1a9cbf91be650de25eff2/manuscript.pdf#page=23)
- [Theorem 8.6, PDF pp. 29–29](https://constraintsystemsinstitute.org/manuscripts/structure/sha256-065979305b2fc1593abb343e72a86d0ed9c967c089d1a9cbf91be650de25eff2/manuscript.pdf#page=29)