Where Does Cold Dark Energy Switch On? A Precisely Posed Question at M >~ 10^12.4 Msun (Working Note)

Working note, version 1.0 (2026-10-27). AI-assisted research programme; not peer reviewed. kappa = 1/2 is fitted; the theory is not closed. The programme studies a galaxy law g_N = g^2/(g + a0), a0 = c^2 sqrt(Lambda/32 pi) (kappa = 1/2 fitted), with a gravitating w ~ 0 field component called cold dark energy (not matter, not a particle). The law fits isolated galaxies; groups and clusters need cold dark energy halos. The record's organising rule is environment-keyed: halos in satellites and in systems above a mass threshold. From frozen, reproduced calculations this note states what the switch must do and what the halos must look like. (1) The threshold is not the core-floor crossover: one concentration c_f cannot set both the threshold and the cores (no c_f in 3.5-6.0 passes every graded line). KiDS isolated-lens lensing needs a threshold >= 10^12.39 Msun (canonical footing) while groups need c_f >= 4.75. (2) The cluster halo budget is set by measured gas: counting X-COP-measured gas (density slope 2.777 beyond R500, 11 clusters) to the self-consistent turnaround radius and assigning the native fair share of cold dark energy, all 15 eRASS1 x KiDS cluster keys pass at c_f = 4 on both footings; correlated structure beyond turnaround contributes at most 1.3%; a self-similar infall shape fixes the cluster centres. (3) What remains of the cores is one line: groups need c_f >~ 4.25-4.75 while clusters take ~4; native zooms give c_f falling with mass, the direction required. (4) Below the threshold, the surviving exclusion mechanism (initial displacement, M6) is not decided by four native Lyman-alpha forest models; if the forest-side budget is real, galaxies needing it must retain at least 19-56% (canonical) / 28-83% (alternative) of their patch baryons. Questions posed: what switches cold dark energy on at M >~ 10^12.4 Msun independently of halo concentration, and why are groups more concentrated than clusters? This is not evidence for the framework over LambdaCDM. AI assistance: Anthropic's Claude (analysis lanes, review, drafting).