From Dimensionless Response to Physical Range in the C0 Depletion-Field Realization

The C0 realization of the Verarmungsfeldtheorie (VFT) programme couples a Skyrme mat- ter sector to a dimensionless substrate eld χthrough a eld-state factor A(χ). We show that every static solution of C0 carries a denite dimensionless response of its rest energy to the external substrate state, κB = α(E∇χ+3EV−∆D)B/EB, a Derrick-type identity in which no new coecient appears, and we produce it for baryon numbers B = 1,3,4 under three succes- sive preregistered numerical protocols: κ∞ 1 = 2.850428370 ×10−3, κ∞ 3 = 1.108866003 ×10−3, κ∞ 4 = 9.494689164 ×10−4, converged to 10−8 across grid and domain. The response is non-zero, positive and non-universal across B. A preregistered class-(a) calibrationthe B = 1 soliton energy identied with the nucleon mass, plus the measured pion decay con- stant, xed before the resulting value was knownthen places the carrier of that response at λχ = 0.3020 ±0.0037 fm (mχ,phys = 653.5 ±8.0 MeV). The same construction therefore provides both a non-zero susceptibility and a quantitative demonstration that this suscepti- bility cannot mediate a macroscopic environmental response: beyond the atom the transfer factor is bounded by 10−1.4×105 , at the shortest macroscopic test scale by 10−1.4×1010 . This discharges Requirement 8.24 of the axiom layer for C0 as constructed, with one unconstructed metric route reserved, and it separates two notions that are easily conated: response ampli- tude and propagation range. C0's eld cannot provide macroscopic depletion gradients; any continuation that carries such gradients through a substrate mode requires an independently motivated carrier architecture with equivalence-principle control specied before construction. No such continuation is selected here.