{"fqn":"KLean.Bio.FickDiffusion.flux_magnitude_pos","short":"flux_magnitude_pos","module":"KLean.Bio.FickDiffusion.FluxMagnitudePos","path":"KLean/Bio/FickDiffusion/FluxMagnitudePos.lean","claim":"Flux magnitude is positive when gradient exists and D > 0","verified":true,"axiom_level":"kernel-standard","olean_sha256":"02384f728da4574899642a3887fa0711e5d40b6817bf8716444559161c3c11a1","quarantined":false,"statement":"theorem flux_magnitude_pos (D C_high C_low Δx : ℝ) (hD : 0 < D) (hΔx : 0 < Δx) (hC : C_low < C_high) : 0 < -(flux D C_high C_low Δx)","topics":["biology"],"refs":[],"depends_on":["KLean.Bio.FickDiffusion.Base","KLean.Misc.Basic"],"used_by":["KLean.Bio.FickDiffusion","KLean.Bio.FickDiffusion.FluxIncreasesWithGradient"],"compute":"/api/v1/klean/compute/fick_flux","seal":{"receipt_id":"d017cc7dffff572a7adc3c1d","digest":"ff9469cecfb2bfdf74174682d2499bf3dcc86c0d62e7197d6640fab11f61bd22","sealed_at":"2026-08-10T03:30:24.740384+00:00","time_source":"roughtime_chain"},"commit":"4b8413e1b8"}