Paper α–ΩΩF: Mechanical Time Without a Master Clock in Holosphere Theory Relational Duration, Local Energy-Exchange Clocks, and Native Memory-Dependent Inertia

A common mechanical duration need not be generated by one privileged oscillator. This paperconstructs that alternative within the fixed-inertia, real cosine-contact sector used in the precedingHolosphere clock papers. A fixed-energy Jacobi action selects the same native trajectories withoutprescribing the rate of an external curve parameter. Its reconstructed duration can be expressedthrough relative angular changes after a fixed-momentum reduction. More locally, the native contact-energy current becomes a work integral along the recorded configuration path. When that exchangedenergy is retained, different moving node regions reconstruct the same duration. Their readoutscan replace one another at individual turning points, and a zero-total-momentum bound shows thatno single rotor must provide the clock hand. A nonlinear thirteen-site FCC calculation tests thisconstruction with a stationary collective phase: ordered angular records, stripped of their timestampsand momenta, recover elapsed duration under uniform and nonuniform sampling. A separatecalculation addresses the coupling left open in Paper E. Eliminating the central rotor produces a realmemory kernel and a positive, rank-one low-frequency inertia correction from the native potentialinteraction itself. This correction is direction-selective rather than a universal multiplier of all clockdynamics. The resulting no-master-clock account is a conservative, model-dependent reconstructionof duration, not an additional fundamental oscillator or a derivation of universal relativistic clockloading.