TERRA–ZERRA: A Physical Distinguishability and Finite-Realization Framework
ALEXANDAR BALEVSKY, KRASIMIRA IVANOVA · Zenodo (CERN European Organization for Nuclear Research) · 2026
TERRA–ZERRA is presented as a physical-operational framework for distinguishability, finite realizability, and capacity, together with a finite-realization protocol for controlled mathematical and experimental use. For a declared physical sector Ω, procedure/readout context Π, admissibility conditions A, and positive distinguishability threshold ζ, ZERRA specifies the context-declared physical distinguishability criterion, while TERRA is the maximal physically admissible capacity of mutually distinguishable states at that criterion. In the metric case, TERRA is represented exactly by ε-packing cardinality; outside the metric case, the physical definition is expressed through a declared distinguishability relation. The paper formalizes TERRA-admissible realizations, a TERRA capacity profile, inverse-capacity thresholds, finite distinguishability graphs for pairwise-reducible cases, simultaneous-uncertainty lower and upper graphs, and a Certified TERRA Plateau. It develops constructive finite-to-continuum error certificates, two finite-realization allocation laws, finite-operator realizations, causal and Hilbert-space examples, relativistic realization boundaries, and explicit falsification criteria. A separately preregistered ACL–OUXSPACE confirmatory evaluation returned a reported numerical PASS for the frozen TERRA–ZERRA state-distinguishability branch on sealed Adriano Ciardo Labs (ACL) data. The result supports reproducibility of a non-trivial, uncertainty-certified TERRA structure across the predetermined tested ZERRA interval within that dataset and protocol. It is limited to that operational test and is not interpreted as proof of a universal fundamental ZERRA, ontological discreteness, or the complete OUXSPACE framework.