One Test Every Theory of Everything Must Pass: Universal Recursive Closure and Final Synthesis — A U.F.S Addendum: A 60-Glyph Quaternionic-to-HEXAD Intergalactic Telemetry Criterion ≡ Prime Atom of Logic, under RICOLMC-DDF Γ-Gated Resource Completene

This addendum to the Prime Atom of Logic paper (10 January 2025) states Universal Recursive Closure as an admissibility criterion, not as a theory. It joins four parts of the CCT/SEXA corpus under the base paper's rule that closure must hold without invariant leakage, semantic drift or post-hoc parameterization. First, the Last Constant expansion equation is extended from one quaternionic observer to six HEXAD tracking gates. The tracking factor H6 equals 1 after enforcement and recovers the quaternion form exactly. Its planetary test is the frozen, pre-registered HEXAD v3 protocol (BepiColombo, Arase and Nançay gates, 2027–28), which is cited and not altered. Second, a seven-gate intergalactic extension from the Milky Way to Coma gives H0 = 74.6 ± 3.2 km/s/Mpc (CMB frame) and 70.5 ± 3.2 (Local-Group frame). This is not independent of SH0ES, because Coma dominates. Third, the RICOLMC-DDF completeness clauses (C1)–(C4) and the Γ gate are mapped onto the closure gates. Fourth, the dissertation's civilization theorems (Books X, XII, XIII and XIV) are restated as closure conditions. One scan-found candidate, H_late/H_early = 13/12 (73.02 on the Planck scale), has no derivation. It is registered with locked data sources, thresholds and a survive/refute/no-decision rule. Seven results from the SEXA Critical-Line Closure Theorem preprint (DOI 10.17605/OSF.IO/3ED69; Theorems III.10, III.14, III.15, III.21, III.22, III.24 and 25.4) are cited as structural correspondences only, and the Riemann Hypothesis is not claimed proved. A kill-switch table states which result refutes which component. No Theory of Everything is claimed, and gravity is not solved (internal scoreboard 6.75/19). Preprint; not peer reviewed.