UDCT v5.60: Pre-registration of Option O8d (Tail Cut-off plus Compactness Screening)

Abstract

Pre-registration of option O8d, not a result. No O8d prediction has been computed at deposit. O8d is motivated by the failure of O8c (v5.59) and is registered as a new option. Law: ν_eff = 1 + S(X)[ν_c(x) − 1], with ν_c(x) = 1 + (ν₀(x) − 1)/(1 + (x/Y_c)²), ν₀ = (1+1/x)^{1/2}, Y_c = 490, S = 1/(1+(X/X*)⁴), X* = 4×10⁹, ξ₀ = 1.082401×10⁻¹⁰ m s⁻²; full QUMOND-type field equation from the v5.59 action. Gates: D2 → D5 (Q₂ ≤ 0.52×10⁻²⁶ s⁻², Saturn |δa| < 10⁻¹⁴ m s⁻²) → D8b (ultra-faint dwarfs, Simon 2019, factor-2 criterion) → D6 (weak-lensing RAR) → D4 (v5.50 SPARC protocol); wide binaries reported. Two new constants and the ultra-faint-dwarf risk are declared in advance. Passing would not validate UDCT.