Cortical Informational Field Theory — III: From the Node of Ranvier to the Cortical Field

This paper is the third in the CIFT series. It derives the biophysical value of the effective diffusion coefficient D_eff from axonal cable theory and cortical coarse-graining, providing the microscopic foundation for the scalar diffusion term of the canonical equation established in the CIFT-Canonical paper. The present derivation reduces D_eff from a free phenomenological parameter to a measurable biophysical quantity: D_eff = α·v_axon·l_conn = 12,000 mm²/s, with λ_CIFT ∈ [19, 480] s⁻¹ as the remaining single free parameter. An unexpected result emerges: the admittance field χ(x,t) introduced phenomenologically in the CIFT-Admittance paper is identified formally as the collective ephaptic coupling of the axonal population — χ(x,t) = 1 + γ_D·Φ(x,t) — closing the deductive chain across all three papers of the CIFT program. Numerical verification confirms D_eff = 12,000 mm²/s produces predicted coherence lengths with errors below 6% after a documented correction factor f_NL = 1.35 for the interacting Ginzburg-Landau field.