The Recurrence of the Coexistence Problem: Why four independent sciences pose one structural question about the many, and how we know it is one

Abstract

Four scientific domains (physics, biology, chemistry, cognition), each with its own objects, methods, and vocabulary, developed their coexistence problems independently of a common relational architecture. Each asks, in its own terms, when several persisters form one configuration, when that configuration is the same, and how it breaks — answering these questions locally, case by case, but with no single architecture connecting relational existence, relational identity, transformation, fragmentation, and fusion. This paper shows that the four pose the coexistence question in one and the same shape: the same relational existence, the same two depths of relational sameness, the same internal change regimes, and the same lower failure wall, fragmentation. A further element recurs alongside these: in each of the four, a configuration integrated tightly enough is treated as a persister in its own right — the point at which the horizontal axis crosses into the vertical — governed by one criterion the architecture makes explicit and each science leaves implicit. The foundational architecture further shows that this regime space is bounded above by a second wall, fusion; that upper wall is realized as a process in some of the four domains and remains a limiting possibility in others, and the paper marks the difference rather than forcing every column to the same edge. A single pattern, differing across the four only in what it is made of. The structure itself is derived and established in The Structural Law of Everything That Persists (Maibom 2026, doi.org/10.5281/zenodo.21459294); what this paper adds is the evidence of its recurrence. Four fields that never coordinated their relational concepts each draw the same figure, each driven to it by its own subject matter. §6 proves that, once the domain facts are granted, the shared structure is forced rather than read in. The recurrence is the finding. Two further domains, immunology and ecology, were audited after the four-domain comparison was fixed and are reported only as confirmation: they meet the same architecture and add no new role, depth, regime, or crossing.