URM3 Quantitative Closure Roadmap Mathematical Derivations, Experimental Protocols, and Falsification Criteria

URM3 Quantitative Closure Roadmap: Mathematical Derivations, Experimental Protocols, and Falsification Criteria This document presents a structured quantitative roadmap for completing the open proof obligations of the Unified Resonance Model (URM3). Building on the canonical grammatical framework established in URM3 V2.1 and its generative extension in V2.2, the roadmap translates qualitative unification claims into explicit mathematical derivations, experimental designs, and falsification criteria. The work addresses four core closure programmes: (1) derivation of the Born rule from an admissibility functional, (2) reclassification of dark-matter-attributed phenomena as stability geometry under conditional tests, (3) identification of the quantum–classical boundary as a record-bearing closure threshold, and (4) verification of cross-scale stability invariance. Each programme is presented with clear mathematical targets, concrete experimental or observational protocols, and strict failure conditions. No claim is asserted without an explicit path to confirmation or falsification. The document also introduces URMLab, an executable grammar framework used to demonstrate internal consistency, generate testable predictions, and expose assumption ledgers—without substituting for empirical validation. The roadmap is deliberately conservative in posture: it neither asserts completion nor presumes success. Instead, it defines how URM3 must be tested, where it could fail, and what would count as genuine closure. As such, it is intended as a working research programme for independent scrutiny rather than a finished theory.