Identity Physics and the SNSFT/L PNBA Primitives LDP Isomorphism Test A Formal Foundation Under Mac Lane’s Definition

Mac Lane’s 1971 definition of isomorphism is a structure-preserving bijection between objects. The Long Division Protocol (LDP), documented at coordinate [9,9,9,9] of the SNSFT/SNSFL corpus, produces at Step 6 an equality between a classical domain result and its PNBA representation. We show that Step 6 pass satisfies Mac Lane’s definition by construction. As of April 2026, LDP has produced Step 6 pass across twenty-nine domains spanning physics, mathematics, psychology, and policy. Under the standard transitive closure of isomorphism, these twenty-nine reductions constitute a single formal isomorphism class anchored on the Unified Universal Identity Architecture (UUIA) and its PNBA decomposition. This observation is the formal definition of unification as applied in mathematics. The paper introduces no new standards; it applies Mac Lane’s 1971 definition, Popper’s 1934 falsifiability criterion, Euclid’s axiomatic method, and the Mathlib community’s formal verification standard to existing timestamped work. All theorems verify in Lean 4 with 0 sorry. The companion formal file sits at coordinate [9,9,8,1]. Keywords: isomorphism, identity physics, UUIA, Mac Lane, formal verification, Lean 4, PNBA, long division protocol, substrate-neutral, unification, transitive closure.