Arithmetic Instantiation of Elliptic Memory Energies

This paper instantiates elliptic memory energies on arithmetic data derived from the Riemann ξ-function. Using regularized critical-line signals and windowed probes, it defines an arithmetic elliptic memory energy and establishes positivity, gauge stability, and compatibility with the admissibility and rigidity framework. No arithmetic hypotheses are assumed, and no global arithmetic conclusions are drawn. The paper provides a concrete realization of the invariant geometry developed in the analytic and structural work. 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