HSF Time Structure: Time by Energy, Motion by Phase

HSF Time Structure: we model motion as phase-directed dynamics on a single global clock T(x). A quantum state ψ = R e^{iS/ħ} carries momentum and energy via p = ħ∇S and E = −ħ∂_T S; no new degrees of freedom are introduced. The framework keeps standard couplings (EM, gravity), the positive-energy spectral condition, and unitary, invertible evolution U(ΔT). We give clean time-reversal rules (ψ → ψ*(x,−T), B → −B, spin flip) and compact, lab-ready null tests that benchmark micro-reversibility: (i) Loschmidt/Spin echoes with fidelity M→1 in the closed limit, (ii) phase-conjugation “time mirrors” with symmetric ±Ω sidebands and Kramers–Krönig coherence, (iii) reciprocity S21(B) = S12(−B), (iv) matter-wave time lenses and Wigner delay τ(E) = 2ħ∂δ/∂E. We include worked kinematics tables (electrons at 1 eV–1 MeV) and weak-gravity shifts (negligible on Earth, sizable near compact objects). The result is a minimal, testable playbook: time from energy, motion from phase—standard physics expressed so reversibility and its failures are measurable.