Elliptic Memory Energies and Forward-Invariant Admissibility Regions

This paper formulates an abstract admissibility-invariance framework built from elliptic memory energies, geometric constraints, and rigidity principles. It defines survivability functionals and admissibility regions and proves forward invariance under admissible window-shift dynamics using viability theory. The framework is structural and non-arithmetic, providing a general invariant-set methodology without drawing global consequences. Subsequent papers instantiate this framework on arithmetic data and analyze rigidity and admissibility consequences. 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