Universal Mathematics & Collapse Platform (UMCP): Protocol Mapping for Regime Assignment in Gold Nanocrystal Coalescence

Description: This data paper provides a fully explicit and empirically grounded protocol for assigning structural regimes during the coalescence of gold nanocrystals, using the Universal Mathematics & Collapse Platform (UMCP) formalism. The document systematically translates recent atomic-level experimental studies into operational mathematical logic, mapping physical observables—such as nanocrystal size, planar defect density, and coalescence pathway geometry—into symbolic invariants and collapse regimes. For each nanocrystal coalescence event, the protocol details the measurement, logging, and regime assignment procedure, specifying the thresholds that delineate “de-twinning” versus “multi-twinning/defect migration” behavior. Each regime is defined by critical empirical thresholds, directly calibrated from experimental data and made auditable for reproduction or extension to new materials. The UMCP logging protocol is presented as a closed, stepwise sequence that captures all relevant state variables and their transformation under collapse.