The Scope of a Dark-Energy-Tied Galaxy Law: What Its Screened Khronon Theory Passes, and the Mechanisms of Its Cluster, Growth and Saddle Failures (Working Note)

Working note, version 1.0 (2026-10-23). AI-assisted research programme; not peer reviewed. kappa = 1/2 is fitted; the theory is not closed. The owner's programme studies a gravity framework whose galactic law is g_N = g^2/(g + a0), a0 = kappa c sqrt(G rho_DE), kappa = 1/2 fitted; its extra gravitating mass is a collisionless 'cold energy' sector, not a particle. PAPER59 wrote the screened theory covariantly; its Khronon form, v3, is the current best theory. Every test on the programme's status board has since been recomputed for v3 alone, each by a lane with frozen criteria and a mutation control, on both a0 footings, never pooled. This note states what v3 is a theory of, and the mechanism of each failure. What passes: the acceleration scale (MeerKAT local a0 +0.032 dex from SPARC with the same recipe), isolated galaxy groups, Cassini and the planets (screened), gravitational waves and binary pulsars, static black holes and neutron stars, and, with no knob, the tidal dwarfs and NGC 1052-DF2/DF4. Conditional: the SPARC radial-acceleration relation, inner galaxy lensing, red lenses, strong coupling. Failures and mechanisms: the Milky Way (the AQUAL disc's extra field is disc-shaped; outer slope excluded); dwarf satellites and Coma's ultra-diffuse galaxies, structurally (held dust is weightless in a static host); cluster cores, a scoped no-go for every allowed dust mass mu_K (the static dust oscillates, and the oscillation reaches galaxies before clusters); linear growth (the dust holds only below mu_K, capped at 14.8 h/Mpc, while 0.95 of the dust-limit sigma8 needs 361-2542 h/Mpc; the literal dust sector has no radiation era, and the DBI form fixes BBN only); and two-body saddles, where the screening term makes the khronon/dust pair an unbounded gradient instability. Each repair tried so far moves the failure rather than removing it. Pending: the Khronon-native nonlinear growth run (L1). kappa, L* and the dust abundance are fitted, not derived. No result here is evidence for the framework over its rivals. Companion notes: PAPER59 (doi:10.5281/zenodo.23585319), PAPER58 v1.1 (doi:10.5281/zenodo.23579379). AI assistance: Anthropic's Claude (analysis lanes, review, drafting).