The Open Doors of a Dark-Energy-Tied Galaxy Law: Scoped No-Gos, Record Corrections, and a Cassini Split between the Unscreened Law and the Screened Theory (Working Note)

Working note, version 1.0 (2026-10-22). AI-assisted research programme; not peer reviewed.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), with kappa = 1/2 fitted; its extra gravitating mass is a collisionless 'cold energy' medium, not a particle. This note reports one rigorous pass (the 2026-10-22 'doors push', lanes D1-D9b) over every door the record had left open, followed by an audit of hidden inputs (wave E1-E5). Every lane froze its criteria before computing and ran a mutation control; both a0 footings (9.36e-11 and 1.13e-10 m/s^2) are reported and never pooled. Most results are scoped no-gos and corrections to the record. The framework's own action gives AQUAL with mu = x/(1+x), not the QUMOND three lanes used; AQUAL values supersede QUMOND ones where both exist. (1) Cassini splits the theory: the unscreened canonical law fails Cassini Q2 by 2.44-4.59x (canonical) and 2.85-5.19x (alternative) the Hees et al. 2014 2-sigma line with the action's field equation (QUMOND 1.70-3.70x / 1.91-4.03x), and the strong-field turn-off cannot help; this is the RAR-Q2 class conflict of Desmond, Hees and Famaey (2024). The screened theory (stiffness length L* = 24-90 pc) passes by 1e7-1e9: inside L* the Sun's field is a hedgehog with no quadrupole; the Cassini threshold is at most 0.069 / 0.111 pc. (2) The screened theory is the one version that passes both Cassini and the galactic law. Its open items: the satellite dwarfs sit +0.89 dex above its prediction and the needed cold mass is undecidable on Lambda-CDM-processed inputs; the L* floor is calibration-dominated (native 28.85 pc, 20-42 pc over the stellar M/L); u depends on a0 and h (0.433 at the galaxy-measured a0); no covariant parent exists in the stated classes, with or without stiffness. Gaia DR4 is decisive: screened gamma_v - 1 = 8.1e-6 for a 20 kAU binary against about 1.17 for the unscreened law-first reading. (3) kappa is not derived: no horizon-thermodynamic monomial gives 1/2 without square roots; the class's natural output is Milgrom's a0 = cH_Lambda/2pi (arXiv:1605.07458), a postulate here; the data do not select R = 4; the measured kappa is robust to the background, and the alternative footing is a pure Lambda-CDM import. (4) No member of the unscreened law family passes both Q2 and SPARC under AQUAL; on a native background with QUMOND some passed, and AQUAL raises their Q2, so their status is knife-edge. (5) The skew-sign test is retired; the wide-binary fork is decided by systematics (now sigma_sys below 0.048 / 0.058); the sealed ALMA tests are expected to be unscorable; the native 1024^3 shear run died of memory with no verdict; no tested mechanism gives the retained fraction u = 0.47. Four earlier verdicts flip under clean inputs; six errata were written fix-forward into the record. Not derived: kappa = 1/2, L*, eta/gamma, u. Companion notes: PAPER49 v1.2 (doi:10.5281/zenodo.23533323), PAPER55 (doi:10.5281/zenodo.23482936), PAPER56 (doi:10.5281/zenodo.23532875), PAPER57 (doi:10.5281/zenodo.23532885). AI assistance: Anthropic's Claude (analysis lanes, review, drafting).