A Screened, Saddle-Free Khronon Action for the a0 Galaxy Law (Working Note)

Working note, version 1.0 (2026-11-05). AI-assisted research programme; not peer reviewed; not reproduced by any outside group.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. States in one place the action the programme adopted on 2026-11-04 for the galaxy law g_N = g^2/(g + a0), a0 = kappa c sqrt(G rho_DE): S = (c^3/16 pi G) Int sqrt(-g) [R - 2J(Y) + 2K(Q)] - (gamma_L/2) Int sqrt(-g) [max(D.P, 0)]^2 + S_m. The structure is Blanchet and Skordis's Khronon theory (arXiv:2404.06584), on Blas, Pujolas and Sibiryakov's khronon; the law is Milgrom's; the tie to dark energy is Limbach, Psaltis and Ozel's. What is added here: a postulated acceleration function J, and a switched stiffness that is exact, adds no constant, removes the Hadamard ill-posedness of an unswitched stiffness wherever the khronon charge is negative, and leaves every screened static solution unchanged (proved pointwise in Lean; checked nonlinearly in 1D, at the interface and in a slab). In its stated scope (isolated galaxies, the Solar System, galaxy lensing, gravitational waves) the action gives the simple-mu law, passes Cassini's Q2 by at least 4.8e7 (alt 5.7e7), gives gamma = beta = 1 to 1e-12, a tensor speed equal to c, and galaxy lensing equal to dynamics on KiDS (weak power). Carried weak spots: two numerical checks undecided, instantaneous constraints, and NO VERDICT on nonlinear well-posedness, PN signs, a moving Sun and charged-background causality. Outside the scope it fails hosted dwarfs, linear growth, clusters and the radiation era, through one identity fixing the khronon dust's coupling at alpha = 1. a0, J and the screening length are put in by hand; the note writes down the vacuum identity, C3^2 rho_vac = 128 pi F^3, that any derivation of kappa = 1/2 would have to supply. Companion to PAPER67 (10.5281/zenodo.23968171).