Conclusion: what this paper actually delivers

Thesis (one sentence): Rewriting GR in lapse-first variables \(N=e^{\Phi}\) makes gravity “clock-native,” yielding two practical observables—(i) a sign-locked \(1/r\) flux→redshift-drift template and (ii) a visibility kernel that maps interferometer contrast into bounds on lapse fluctuations—without adding new degrees of freedom.

What is actually testable now (and how):

Classical lever (flux→drift): outgoing luminosity \(L(t)\) at distance \(r\) enforces \(\partial_t\Phi\simeq-(G/c^4)\,L/r\). Measure the clock redshift slope \(\dot y(t)\) and fit \(\dot y=-\lambda L\) with \(\lambda=G/(c^4 r)\); demand correct sign, zero-lag, and strict \(1/r\) across baselines.
Quantum lever (visibility): any two-path sequence with indicator \(f(t)\) obeys \(-\ln V=\dfrac{\omega^2}{2}\!\int_0^\infty \dfrac{d\Omega}{2\pi}\,S_{\Phi}(\Omega)\,|F(\Omega)|^2\) (with \(F\) set by your timing); publish both the filter-weighted bound and, if used, the Markovian \(S_{\Phi}(0)\) bound.

Protocol & posture (discipline over wishful thinking):

Pre-register band, vetoes, stacking, and pass/fail; release data, filters, code, and all nulls (shuttered source, cold dump, time-slides, off-band). Outcomes: either \(\lambda\simeq G/(c^4 r)\) within errors, or a published upper limit; for visibilities, quote both bounds.
Bounds-first sensitivity: numbers are ideal analysis limits using measured \(S_y(f)\); lab flux runs are pipeline validations with software injections (sign + strict \(1/r\) scaling). Target-of-opportunity: Galactic SN with SNEWS 2.0 triggers; Sgr A* flares are sub-threshold today.

Scope (what this is not): No extra propagating scalar or new polarization: \(\Phi\) and \(\omega\) enforce constraints; only the two TT modes propagate. The visibility correlator \(C_{\Phi}\) is the constraint-projected imprint of linearized metric/stress fluctuations on clocks—i.e., standard GR, just reorganized.

Outlook (templates you may explore, carefully labeled): Speculative horizon-phase ideas are provided only as templates for future analog platforms or exotic scenarios—not near-term claims.

One-line takeaway: This paper turns “gravity as time geometry” into two analysis-ready tests you can run today: a sign-fixed, \(1/r\) flux template and a general visibility-to-\(S_{\Phi}\) bound—both strictly within GR and packaged with reproducible workflows.

Glossary (conclusion snapshot)

Symbol	Name	Meaning (units)	Typical value/example	Metaphor
\(N=e^{\Phi}\)	Lapse	Proper-time scale, \(d\tau=N\,dt\) (–)	\(N\approx1\) in weak fields	“Time gear ratio”
\(\Phi\)	Time potential	\(\ln N\); controls clock rate (–)	\(\partial_t\Phi\simeq-(G/c^4)L/r\)	“Altitude of time”
\(\omega\)	Shift	Gravitomagnetic potential (flows/rotation)	Lives in frame-dragging, not \(\Phi\)	“River current of space”
\(y=\ln(\nu_\infty/\nu_r)\)	Log-redshift	What clocks report (–)	\(\dot y=\partial_t\Phi\)	“Pitch log”
\(V\)	Visibility	Fringe contrast \([0,1]\) (–)	Decays with \(\Phi\) noise	“Stripe sharpness”
\(F(\Omega)\)	Filter of \(f(t)\)	Weights \(S_{\Phi}\) in \(-\ln V\) (s)	Rectangular → sinc²	“Sieve for noise tones”
\(S_{\Phi}(\Omega)\)	Lapse PSD	One-sided spectrum (s)	Bound via \(-\ln V\) integral	“Noise color of time”
\(\lambda\)	Flux→drift gain	\(G/(c^4 r)\) in \(\dot y=-\lambda L\)	Test sign, zero-lag, \(1/r\)	“Gear from light to time”
\(L(t)\)	Luminosity	Power crossing sphere (W)	Drives sign-locked drift	“Brightness push”
\(r\)	Areal distance	Source→clock separation (m)	Exact \(1/r\) falloff	“Lever arm”

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