Arithmetic Consequences of Admissibility Invariance

This paper records arithmetic consequences of forward invariance of admissibility regions associated with elliptic memory energies. It identifies which arithmetic configurations correspond to admissible states and shows that configurations exhibiting persistent instability are excluded under admissible dynamics. The argument introduces no new definitions or estimates and proceeds entirely from previously established admissibility and rigidity results. Global arithmetic admissibility emerges as a structural consequence within the framework. Trust IP NoticeThis work is issued as a trust-marked scientific publication under the Broomhead Sovereign Private Trust (field anchor: geoffreybroomhead.eth).Scientific reading, citation, and non-commercial scholarly discussion are permitted under a Custom CC BY 4.0 (Scientific Theory Only) license.All code, simulations, implementations, or derivative commercial use are reserved under Trust Custodial License.For licensing or implementation inquiries, contact: recursive.broomhead@proton.me