P79 Hadronic Scheme Selection in CCEGA: Why ΛhadQCD and Not ΛMS Sets the Critical Density ρc

The CCEGA framework contains a phenomenological critical density ρc = 7. 4 ρnuc, which was conjectured in P74 (doi: 10. 5281/zenodo. 20440384) to coincide with Λ³QCD / ℏ³c³ at ΛQCD = 208. 7 MeV. The recent high-precision lattice QCD determination by Dalla Brida et al. (Nature 652, 328–334, 2026; doi: 10. 1038/s41586-026-10339-4) yields Λ (3) MS = 344. 4 (8. 7) MeV in the MS scheme, which gives ρ/ρnuc = 33. 2 — a factor of 4. 5 above ρc. We show that this discrepancy is not a failure of the P74 conjecture but rather a scheme selection result: the internal physics of CCEGA requires the hadronic low-energy scheme, not the perturbative MS scheme, for an independent physical reason — the radion saturation mechanism is triggered by the suppression of hadronic condensates at the deconfinement transition. The Dalla Brida 2026 result therefore discriminates between QCD renormalization schemes and identifies the hadronic scheme as the physically relevant one for the CCEGA critical density. The derivation of ρc from first principles remains an open problem.