Persistent atmospheric CO₂ decline onset is not determined by cumulative fossil carbon or pointwise source order

Persistent atmospheric CO₂ decline is a state-dependent first-passage observable: its turning map does not factor through cumulative fossil carbon and does not preserve pointwise fossil-source order. In FaIR, two exactly equal-cumulative fossil pathways (1532.094261 GtCO₂ each) yield persistent-three turning in 78/841 versus 804/841 configurations; a pointwise source-ordered pair yields 107 earlier turnings and none later. Independently, an emissions-driven GFDL-ESM2M pair is fossil-source ordered in every year from 2026–2150, yet persistent-five turning occurs in 2079 versus 2103, 24 years earlier in the higher-source pathway. Across continuous deformations, the persistence margin increases in all 252,300 adjacent memberwise comparisons, while susceptibility ordering transfers across held-out backgrounds (minimum ρ=0.985032) despite p3 incidence shifting from 0.258% to 36.623%. Turning is first passage of M=S−E, with inherited carbon-cycle state controlling S; MPI-ESM and Hector provide complementary cross-architecture support.