Closure Conservation, Transfer Laws, and Cross-Domain Invariance

Addresses what happens when a closure conclusion is carried from one mathematical domain/representation/proof system to another. Defines cross-domain transfer as a partial mapping governed by a “closure transfer contract” (domain map, object map, invariant map, state map, bridge, loss, debt, version), sorted into three classes: conservative (invariants and theorem authority preserved), lossy (partially preserved, authority must be downgraded), and non-transferable (no bridge/scope/semantic map, upgrade forbidden). Core non-collapse principle: transferable structure ≠ transferable closure authority — a lemma/operator/pattern can be formally carried into another domain, but its original theorem status, scope, and NO-GO authority do not automatically travel with it. Demonstrates this concretely across NS’s three domains: a formal-NS result can serve as a “special-case anchor” for generalized-family or physical-modeling work, but cannot be automatically upgraded to family-level or physical-law-level status.