The Clock-Host Candidate in One Page: What Stands, What Died, What Decides

Abstract

A one-page statement of the standing relativistic candidate of the a0 = (1/2) c sqrt(G rho_Lambda) programme as of 2026-09-20: a single-metric khronometric clock hosting one screened MOND scalar (the AeST coupling without its dark sector), written out as a Lagrangian. What stands, each by a committed computation with a Lean certificate of its algebra: lensing equals dynamics derived from the action (slip 4e-7), the PPN alpha_2 reconciliation with its two passing corners (the record's old corner failed by 12x), uniform ellipticity, exactly two propagating scalar degrees of freedom with lapse, shift and Phi constrained, the cosmological scalar exactly pressureless at the deep-MOND condition, the Friedmann background G_cosmo = G/(1 + 3 c_2/2) with the BBN bound c_2 < 0.074, and the closed direction-blind EFE programme with its Gaia DR4 prediction gamma_v = 1.000. What died in the same week by the same machinery: the candidate's dark sector as the clock-scalar field's own roll, in both well shapes (the quadratic well by the BBN floor |K_2| Q_0^2 >= 1.8e23 H_0^2 and an unhealable roll mode; the exponential wall by a long-wavelength instability of the dust-loaded clock sector, 1e2-1e8 H_0 until a* = 0.5/0.2/1e-3 at k = 0.01/0.1/1 per Mpc, confirmed by the exact Minkowski dispersion), with the killer identified as the clock coupling (a metric-coupled dust is linearly healthy and is ordinary CDM). What any dark carrier must satisfy: c_s(z = 0) between 200 and 800 km/s against the forest's c_s(z = 3) <= 9.5 km/s, a heating of at least 445x in c_s^2 since z = 3, or a field-dependent pressure. kappa = 1/2 is fitted, provably free in the action, measured 0.551 +/- 0.043 and 0.465 +/- 0.076, degenerate at 2 sigma with Milgrom's and Verlinde's coefficients. The decisive tests are named: Gaia DR4 wide binaries (preregistered arms), a deep-MOND lensed rotator at z ~ 2, and kappa to 1.2 percent. Four of the week's nine lanes were corrected by the next lane; the corrections are kept. AI-assisted research programme; not peer reviewed; nothing is claimed closed.