Implementation--Ready Persistence--First Holographic Systems

This paper develops an implementation–ready companion theory for Persistence–First Holographic Systems (PFHS), focusing on how to compute PFHS dynamics on real CPU/GPU hardware without committing to a particular programming framework. The starting point is the PFHS framework of Aida see also Aida Takahashi, doi:10.5281/zenodo.17518572, 10.5281/zenodo.17576361, 10.5281/zenodo.17601860). It applies equally to finite Markov chains, measure spaces, and quantum Markov semigroups, as long as suitable JKO schemes and discretisations exist. The contribution is not a new numerical method or curvature inequality, but a universal categorical interface that separates (i) analytic ET structure, (ii) PFHS multiscale organisation, and (iii) hardware–level primitives. This separation is intended to support future PFHS implementations by other researchers or autonomous AI systems, including complexity–aware designs that exploit bulk–boundary dimension gaps and multiscale structure for compute–optimal simulation.