The Basin Rule: One Surface-Density Condition for Where Cold Dark Energy Condenses, with Sealed Lensing Predictions and Audited Failures (Working Note)

Version 1.2 (2026-10-29), UPDATE. IC 1613's prediction failed: the independent MUSE stellar-tracer inclination (36 +- 11 deg, 32 +- 11 deg; photometric ~37 deg) meets the frozen falsifier (i >= 30 deg), so IC 1613 is a failure. SLUGGS is partly confirmed: Chandra Galaxy Atlas emission measures around NGC 4374 extend to 65 kpc and give M_gas(<22 kpc) = 1.77e9 Msun vs the 1.70e9 extrapolation the pass needs (f = 1.19); NGC 5846 and NGC 4365 remain untested. Version 1.1 (2026-10-29), CORRECTION. v1.0's central claim that the threshold mass follows from the concentration level L is withdrawn: a parallel audit (CSM1) found the one-number variant used a constant concentration in the switch but the mass-dependent native slope in the cores; made consistent, isolated-lens lensing fails (delta chi2 +415.281 vs +9 allowed) and the single refit L = 2.509 fails groups (Z +2.622). The native zooms give L = 4.865 [3.831, 5.805], not converged, failing three cluster keys. T and L remain located by data. New in v1.1: IC 1613 is consistent with the law on both tracers if its inclination is ~19-27 deg (a prediction); the derived infall halo fixes X-COP cores but not both X-COP and lensing; eRASS1 cluster gas masses run 0.111 dex below X-COP's for the same clusters; the cluster halo shape remains open. Unaffected: the basin switch at a data-located T, the withdrawal of the group-sign failure, and both sealed lensing predictions. Working note, version 1.0 (2026-10-28). AI-assisted research programme; not peer reviewed. kappa = 1/2 is fitted; the theory is not closed. Follows PAPER63 (10.5281/zenodo.23708507). The programme studies a galaxy law g_N = g^2/(g + a0), a0 = kappa c sqrt(G rho_DE) (kappa = 1/2 fitted), with a gravitating w ~ 0 field component called cold dark energy (not matter, not a particle). Frozen, pre-registered, reproduced calculations reduce the halo switch to one condition: a system carries a cored cold dark energy halo iff the collapse surface density of the gravitational basin it belongs to (the region inside its zero-velocity surface) beats the galaxy floor, eta(L) Sigma_coll(M_basin) > a0/2 pi G; the same max(a0/2 pi G, eta Sigma_coll) sets the core, so the threshold mass follows from the concentration level L. On the canonical footing the rule passes every graded calibration line (SPARC, 63 groups, 15 eRASS1 x KiDS cluster keys, five Local Group dwarf classes, KiDS isolated-lens lensing) and the Milky Way; 10 of 24 random settings in the explored box pass. An X-ray-bright group 'wrong sign' is withdrawn as an artefact of binning on the observed pull (forward model; the statistic cannot see a +0.4 dex excess). SLUGGS ellipticals pass only with hot gas beyond the measured X-ray edges (a prediction). X-COP's core miss is not missing BCG stars. IC 1613 is a genuine failure on two independent tracers. Two lensing predictions are sealed by content hash; the second is unique to the basin rule: at fixed stellar mass, a central in a massive basin should lens about half as strongly at 0.3 Mpc as an isolated one (S_env = 0.484). A candidate field equation keys condensation on the expansion of the matter flow (not derived, not graded). This is not evidence for the framework over LambdaCDM. AI assistance: Anthropic's Claude (analysis lanes, review, drafting).