Every Door a Verdict: the Closure Record of the a0 Galaxy Law and its Screened Khronon Action (Working Note)

Working note, version 1.0 (2026-11-06). AI-assisted research programme; not peer reviewed; not reproduced by any outside group. kappa = 1/2 is fitted; the theory is not closed; nothing here says the data favour this framework over any other. Closure here means every gate the programme set itself carries a frozen verdict, not that every gate passes. For the galaxy law g_N = g^2/(g + a0), a0 = kappa c sqrt(G rho_DE), its adopted scoped action (v3s, PAPER68) and its candidate successor (AC2q), each lane froze criteria before computing and ran a mutation twin that must fail. Full covariant field equations of both actions are derived and checked against direct variation. PASS: SPARC on the action's exact field on both footings, Solar System, PPN, tensor speed, galaxy lensing, PN sign. FAIL as proven no-gos over the action's whole term class: clusters, CMB lensing and linear growth, early black holes. Primary CMB (Planck PR4 + ACT DR6) passes only with a cold component that the record excludes in galaxies; baryons only fails. Galaxies: X-ray ellipticals, Malin 1 and AGC 114905 fail. The law's misses form a step between hot pressure-supported systems and cold discs (+0.32 to +0.37 dex at matched variable); environment, cold gas, kinematic support and morphology keys are each killed or give no verdict, and IMF variation removes about half of the step in ellipticals only. Light-cone causality fails at an unobservable level; the moving Sun is NO VERDICT with every planet far under its line. Gates waiting on data: Gaia DR4 wide binaries, a0(z), the unscored ALMA rows. Companion to PAPER67 (10.5281/zenodo.23968171) and PAPER68 (10.5281/zenodo.23990944).