33.73 turns the common-term chain into a retainable summary table: once each probe freezes its standard subtraction, at least three probe families must map Δt_common, Δφ_common, Δν_common/ν, and Δz_common onto one normalized common-term estimate Ĉ through one frozen set of scale factors k_t/k_φ/k_y/k_z, then show a high zero-lag index Z0, above-random direction agreement Sdir, and stable same-window closure ε_close in held-out data while time/probe permutations, low-path, dispersion, and systematic injections break the pattern; under V08/V09-compatible retain, this remains one unified cross-probe scorecard rather than a new common-term ontology.
Use this section as a compact machine-readable EFT reference.
33.73 compresses the dispersionless common-term chain into one engineering-grade scorecard. The admissible claim is that time, phase, fractional-frequency, and redshift residuals are not four unrelated leftovers but four projections of one shared scalar common term C(t, θ, z) within the same event window, so at least three probe families should map onto one table rather than each carrying a private “common term.”
The table is explicit. Parallel probe families may include strong-lens time-delay residuals, FRB or pulsar links, clock and time-transfer networks, and whole-spectrum line shifts. Each row records event-window labels t0 and ΔT, spatial labels θ and z, the readouts Δt_common, Δφ_common, Δν_common/ν, and Δz_common, the normalized common-term estimate Ĉ obtained by dividing by the fitted scale factors k_t, k_φ, k_y, and k_z, the corresponding uncertainties and covariances, the zero-lag index Z0, the direction-agreement rate Sdir, and the closure residual ε_close.
Workflow is run as one cross-probe program rather than a pile of retrofitted analyses. Each probe freezes its subtraction scope before extraction, all streams are placed on one shared time base and one shared event-window rule, one set of scale factors is fitted on a training sample and then frozen, probe and event or sky labels are blinded end to end, and at least two independent pipelines per probe must agree before any support claim is admissible.
Controls are built to break spurious alignment. Time permutation must drive Z0 and Sdir back toward chance, probe permutation or scrambled scale factors must enlarge ε_close, dispersion controls must expose frequency-dependent impostors, low-path or near-zero-base-map samples must weaken both amplitude and agreement, and systematic injections of instrument delay or known dispersive terms must be flagged as non-common behavior by the same table rather than silently normalized away.
Support requires held-out concentration of peak lag near zero, direction agreement significantly above randomized baselines, and closure residuals that remain near zero mean with stable variance across many probe combinations while the frozen normalization still works. Falsification follows if lags stay offset, closure needs cherry-picked probe subsets, sign relations become pair-dependent, scale factors must be redefined by batch or sky region, or nulls perform as well as the nominal result. The main systematic ledgers are time-base misalignment, probe-specific residual systematics, and shared-footprint selection coupling.
So the chapter closes only one retained unified common-term scorecard aligned with the V08/V09 cross-probe closure lane. C(t, θ, z) may survive only as the shared bookkeeping object of this table, not as a free-standing ontology owner or a license for probe-specific private common terms. Its clean onward value is to route the hardened table into the rules-layer threshold court of 33.74.