Finite Capacity, Unresolved Load, and Threshold Collapse

This article develops a theorem-driven structural account of individual load-bearing failure under conditions of persistent unresolved structural pressure. Its central claim is that finite human carriers cannot sustain stable long-run functioning indefinitely when they are required to bear prolonged load that they cannot resolve individually and that is insufficiently buffered by relational, institutional, material, or temporal support. The argument begins from five minimal structural commitments: finite biological, cognitive, and affective regulatory capacity; persistent structural load that is not individually resolvable; accumulation of unresolved load over time; dependence on external buffering; threshold failure when accumulated load exceeds available regulatory and buffering capacity. From these commitments, the article develops a wider theorem architecture organized into four linked families: collapse; manifestation and misrecognition; propagation and institutional persistence; conditional correction. The collapse family is developed in full. It derives three principal claims: degradation or collapse becomes inevitable within a finite time horizon when persistent unresolved load is combined with insufficient buffering; strategies relying exclusively on individual coping, adaptation, resilience, or effort cannot constitute a sufficient solution to a structurally unresolved load condition; deterioration becomes increasingly nonlinear and brittle as regulatory and buffering limits are approached. The article translates these claims into observable implications, negative implications, temporal-ordering expectations, falsification conditions, and boundary conditions. It distinguishes prolonged compensation from genuine sustainability and argues that visible continuity should not be treated as reliable evidence of underlying viability. The article also separates collapse from institutional correction. Individual breakdown does not automatically produce structural learning or reform. Correction requires additional conditions: collapse must become legible as structural failure, accountability-bearing, institutionally actionable, and more costly to ignore than to address. Two contrastive empirical instantiations are used to illustrate this distinction: the death of Matsuri Takahashi following prolonged overwork at Dentsu in Japan, and the death of Errol Graham following welfare benefit withdrawal and administrative failure in the United Kingdom. The cases are not presented as inductive proof, but as tests of whether the theorem architecture can discriminate between collapse followed by institutional correction and collapse without substantial correction. The contribution is theoretical and diagnostic rather than clinical, epidemiological, or policy-prescriptive. The article does not explain all forms of distress, trauma, burnout, or institutional failure. Its scope is limited to situations in which finite human carriers bear persistent unresolved structural load under insufficient buffering over time. Within the wider research programme on structural viability, drift, and human load-bearing, this article functions as a foundational theorem paper on finite capacity, unresolved load, buffering, brittleness, and threshold collapse. The article is not a criminological theory and does not form part of the core crime-process model. Its concepts may nevertheless be used as supporting theoretical infrastructure in adjacent research areas, including criminology, youth antisocial organization, institutional analysis, relational breakdown, organizational viability, and prevention. In those applications, the article provides a bounded account of load-bearing limits; it does not itself explain crime, offending, or criminal organization.