Plain English: before touching data, the paper says to lock in a registered analysis and then hammer it with nulls. The physics gives you two fingerprints that are hard to fake: (i) the sign of the drift follows the sign of the flux (outgoing → negative drift; ingoing → positive), and (ii) the amplitude falls off exactly like 1/r. The pipeline must recover those two features and a zero-lag template correlation; lab runs are for software-injection validation, not detections.
What to pre-register (flux-template channel): choose the analysis band, vetoes, stacking rule, and a pass/fail defined by sign + strict 1/r scaling (or, in the visibility channel, a pre-set visibility threshold). Then whiten \(\dot y(t)\) using the measured \(S_y(f)\), build \(s(t)=\int^t L(t')dt'\) so that \(s(f)=L(f)/(i2\pi f)\), and estimate the coefficient \(\lambda\) with GLS: \(\dot y(t)=-\lambda L(t)+\dots\) where GR predicts \(\lambda=G/(c^4 r)\).
Core discriminants (how you tell gravity from junk):
Registered nulls (you should pass all of these): shutter the source with the same drive, use a cold dump, run time-slides between sites, and do off-band analyses. Outcome: either \(\lambda\simeq G/(c^4 r)\) within errors, or a clear upper limit; for visibilities, quote a bound on \(S_\Phi\) (both Markovian and filter-weighted).
What lab runs are (and aren’t): near-field EM/thermal couplings swamp the gravitational signal, so lab flux runs are pipeline validations using software injections with strict 1/r scaling; astrophysical campaigns (e.g., a Galactic SN) are where you apply the real template test (sign, zero-lag, and \(\lambda=G/(c^4 r)\)).
Practical geometry notes: define \(r\) as the straight-line source-to-clock-pair distance; keep the two clocks \(\ll r\) so they see the same \(L(t)\); in lab, use \(r\gtrsim 5\text{–}10\,\mathrm{m}\) to tame near-field effects. Demonstrate 1/r by repeating at \(r=\{5,10,20\}\,\mathrm{m}\).
| Symbol | Name | Meaning (units) | Typical value/example | Metaphor |
|---|---|---|---|---|
| \(\lambda\) | Flux–drift coefficient | \(G/(c^4 r)\) so \(\dot y=-\lambda L\) (s²·kg\(^{-1}\)·m\(^{-2}\)) | \(r=10\,\mathrm{m}\Rightarrow \lambda\approx8.3\times10^{-46}\) | “Gain knob” from flux to drift |
| \(L(t)\) | Luminosity | Power crossing sphere at \(r\) (W) | Lab pulse or SN neutrino \(L_\nu(t)\) | “Brightness of the source” |
| \(r\) | Areal/straight-line distance | Sets 1/r falloff (m) | Move source to test 1/r | “Distance lever” |
| \(\dot y(t)\) | Redshift drift | Slope of \(\ln(\nu_\infty/\nu_r)\) (s\(^{-1}\)) | Cross-correlate with \(L(t)\) at zero lag | “Pitch change rate” |
| \(S_y(f)\) | Clock noise PSD | One-sided fractional-freq spectrum (Hz\(^{-1}\)) | Used to whiten \(\dot y\) | “Noise map of the dial” |
Ready for Step 8 — Lever A in detail: the controlled-flux (lab) protocol, estimators, and uncertainty propagation (the nuts and bolts you’d run in code).