Structural Compatibility IV: Maintenance Breakdown, Adaptive Thresholds, and Spectral Filtering

Structural Compatibility IV develops the fourth step of the Structural Compatibility series, explicitly on the basis of the broader Finite-Horizon Structures I–VI framework. Starting from the Hermitian-projective operatorial regime established in the preceding Structural Compatibility articles, it addresses the first major question left open at the end of Structural Compatibility III: what becomes of that operatorial regime when the supplementary maintenance conditions cease to remain admissible. The article introduces an explicit notion of stable maintenance regime and defines maintenance breakdown as a loss of admissible continuation within that regime. It shows that such breakdown should be understood not as annihilation of the state and not as a primitive collapse postulate, but as a regime transition: a previously admissible structural setting reaches a boundary beyond which the same maintenance-compatible description can no longer be sustained. To make this transition analyzable, the paper develops a threshold structure through a stability margin and shows that threshold crossing cannot, in general, be produced by the internal unitary evolution alone when the maintenance scalar is preserved. This leads to the introduction of a contextual coupling parameter and an adaptive admissibility threshold, providing a minimal structural mechanism for regime exit without modifying the inherited Hermitian generator. On this basis, the article derives a regime-dependent spectral filtering principle. When the full state becomes globally inadmissible, admissible continuation is restricted to those spectral sectors that remain individually below the updated threshold. The result is therefore a structural theory of post-breakdown sectorial restriction: threshold crossing does not yet determine a unique outcome, but it does reduce the admissible continuation space to a stable spectral subspace. An optional refinement then introduces robustness-based sector weights, understood not as empirical probabilities but as comparative indices measuring how deeply surviving sectors remain inside the admissible domain. Under additional projective-Hermitian assumptions, the same surviving sectors also carry canonical quadratic projective comparison quantities associated with the inherited spectral projector structure, distinct in general from the robustness weights themselves. The scope of the article remains deliberately limited. No Born rule, no complete collapse dynamics, no unique microscopic selection mechanism, and no distinguished observational coupling are assumed or derived. The paper does not claim to provide a full theory of measurement, but rather isolates the missing transition layer between the stable Hermitian-projective operatorial core of Structural Compatibility III and a first structural account of admissibility loss, contextual threshold crossing, and post-breakdown spectral restriction. This article is part of the Ranesis framework, developed by Alexandre Ramakers.