Paper α–ΩΩD: A Two-Clock Test of Mechanical Time in Holosphere Theory Exact FCC Dynamics, Stationary Strain, and a Driven Common-Rate Limit

Two distinct clock architectures are constructed from one real cosine interaction on actualoccupied FCC support: a single-site librator and an adjacent pair with an internal-bond restoringterm. The common twenty-site graph contains sixty-three contacts. Under one compatiblestationary phase strain, their complete nonlinear periods give different calibrated rate responses.The discrepancy persists at finite amplitude on a phase-protected branch with a rigoroustransverse linear-stability certificate. An isolated amplitude can match the rates at one load,but no fixed amplitude supplies a common load law. FCC triangle compatibility also obstructsa nontrivial shared positive tangent factor for the entire specified local clock family. We thenconstruct a different mechanism: a smooth four-class source protocol, with explicit prescribedclock-site torques, whose average multiplies the entire nonlinear interaction by one calculablefactor. Matched librations consequently share a rate in the controlled fast-source limit. Afinite-time error estimate, physical readout, controller work and finite-period computationsspecify this result. Removing the clock-site actuation leaves an unscaled internal bond andrestores unequal rates. The required source acceleration also exceeds the bounded native contacttorque in the fast limit, so this is a controlled driven realization rather than an autonomoussource derived from the original action. Fixed-action preparation, changing loads and motionidentify the further structure needed before a common clock response can be interpreted asuniversal proper time. Complete executable audits are embedded and printed.