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

Four scientific domains (physics, biology, chemistry, cognition), each with its own objects, methods, and vocabulary, developed their identity problems independently of a common identity architecture. Each states its problem in its own terms and cannot settle it from inside. This paper shows that the four pose the identity question in one and the same shape: the same two depths of sameness, the same three roles, the same three outcomes. 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; what this paper adds is the evidence of its recurrence. Four fields that never coordinated their identity concepts each draw the same figure, each driven to it by its own subject matter, and each stuck at the same point for want of it. §6 proves that, once the domain facts are granted, the shared structure is forced rather than read in. The recurrence is the finding. Where a structure that could have differed across four unrelated sciences instead appears identically in all four, that convergence is what identity being one structure looks like from the outside. 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 depth, role, or outcome.