Cluster cores cool faster than they live, classical theory predicted deposition of hundreds of solar masses per year, and the spectra refuse: intermediate-temperature lines are missing and cold products run at a few percent of prediction. AGN cavities balance the energy budget, but the thermostat must hold within tens of percent for gigayears in every cool core while stirring nothing, and Hitomi-XRISM quiescence (kinetic pressure under 10 percent) now forbids the turbulence the heating models use to spread their heat.
The model's cores are radiative runaways by construction: gas assembled cold-capable, with nothing structural to set a floor, so stability must be manufactured dynamically by a feedback loop tuned to gentleness the simulations only reach by subgrid fiat. The thermostat carries the whole building because the building has no foundation.
SCT pours the foundation: the ICM carries relic entropy deposited at thermalization, the collision-cascade floor K₀ of 100 to 300 keV cm² conserved adiabatically since birth (P22, P25, P29, P30), and an entropy floor is precisely the structural stabilizer a cooling core needs. Gas radiating toward the floor meets rising effective resistance, the deposition's thermodynamic memory, so cores hover above catastrophe without requiring the feedback loop to balance the books alone: the missing cooling lines mark where the relic floor, not a perfectly tuned duty cycle, refuses the runaway. AGN remain real and their cavities genuinely heat, but as the secondary modulation trimming around a deposited equilibrium rather than the sole pillar holding it.
The quiescence paradox resolves in the same stroke: a floor stabilizes without stirring, which is exactly what the calm cores demand and what distributed-heating models cannot deliver. The registered tests already exist: the floor must be universal across cluster masses, present equally in AGN-quiet and AGN-active systems, and unchanged from z of 2 to now, the K₀ evolution and AGN-dichotomy checks of the entropy-floor prediction set.
This is the same relic-entropy physics behind the entropy floors, the L_X-T slope, and the quiet ICM entries: one deposited boundary condition, four observables. There is no need for a gigayear thermostat tuned to gentleness in every core in the sky.
The registered kills: Athena-class measurement finding K₀(z = 2)/K₀(z = 0) far below unity, the floor assembled late rather than deposited, falsifies the relic reading directly, as does AGN-quiet groups showing a shallower L_X-T slope than AGN-active ones, which would certify preheating by feedback. A first-principles AGN thermostat reproducing the gentle, quiet, universal balance without tuned subgrid recipes would also retire the need for the floor.