33.72 turns clock–ruler co-origin into a tightening court: after one frozen subtraction rule and a validated dispersionless link channel, J_clock derived from y and J_link derived from u must align within matched windows, one pair of response factors a and b must cover every generation, and ΔJ_step after definitional corrections must converge to zero across second-standard transitions without generation-specific retuning, while generation/time permutations, zero-configuration, link-swap, and held-out tests break the pattern; under V08/V09-compatible tighten, this remains only one metrology continuity court rather than a rewrite of second or meter ontology.
Use this section as a compact machine-readable EFT reference.
33.72 converts clock–ruler co-origin into one continuity court. The admissible claim is that after one frozen subtraction prescription, any generation of frequency standards and any generation of propagation links can still be explained by one shared latent trajectory J(t) rather than by generation-specific noise or era-specific refits. Continuity is therefore tested at second-standard transitions, not assumed.
The measurement ledger builds two independent reconstructions of the same trajectory. J_clock comes from y after removing y0 and scaling by a, while J_link comes from u after removing u0, scaling by b, and applying the required sign inversion. Generation label E is used only for grouping and audit. The hard metrics are ΔJ_step at each transition, the closure residual ε(t)=J_clock−J_link, same-window alignment and phase agreement, and whether one pair of response factors a and b covers every generation within uncertainties.
The workflow prevents continuity from being tuned into existence. The subtraction rules for y and u are frozen over the entire dataset, clock and link teams extract their observables independently, and a, b, y0, and u0 are fitted jointly on the full sample only once. Those fitted values are then reused generation by generation without retuning, and a held-out interval or held-out set of sites or links is reserved for arbitration. The link side must also satisfy a dispersionless requirement across at least two bands or bandwidths before entering J_link.
Controls are aimed directly at fake continuity. Generation-label permutation must destroy transition coherence, and time-label or matched-window permutation must collapse J_clock–J_link alignment toward chance. Under a near-zero configuration both trajectories should contract toward zero mean or a small calibratable constant rather than acquiring a meaningful step. Link-swap controls separate local-clock from path effects, and dispersion controls exclude any candidate Δt_common that rescales like ordinary dispersive propagation.
Support requires same-trajectory agreement within matched windows, ΔJ_step consistent with zero after correcting documented definitional differences, and one pair of response factors a and b that remains valid across generations and in held-out data. Falsification follows if generation-specific rescaling is needed, if unexplained transition jumps persist, if ε(t) drifts or flips sign by generation, if nulls stay comparably strong, or if the dispersionless condition fails. The main systematic ledgers are generation-dependent clock sensitivities, generation-dependent link delays, and independent-geometry errors in link length L that bias the scaling of u.
So the chapter closes only one tightened metrology continuity court aligned with the V08/V09 blind, holdout, and no-retuning lane. J(t) may survive only as the shared tested trajectory for this cross-era audit, not as a rewrite of second or meter ontology. Its clean onward value is to feed the unified cross-probe metrics table of 33.73.