{"fqn":"KLean.Atoms.Bio.ConcentrationPositive.concentration_pos","short":"concentration_pos","module":"KLean.Atoms.Bio.ConcentrationPositive","path":"KLean/Atoms/Bio/ConcentrationPositive.lean","claim":"The first-order concentration C0 * exp(-ke*t) is positive at every time whenever C0 > 0.","verified":true,"axiom_level":"kernel-standard","olean_sha256":"854bca2c643d6d131d2d48767ec71b3cbddd0376d93b024828521fab666c9716","quarantined":false,"statement":"theorem concentration_pos (C₀ ke t : ℝ) (hC₀ : 0 < C₀) : 0 < concentration C₀ ke t","topics":["biology"],"refs":[],"depends_on":["KLean.Atoms.Bio.DefinitionsAtom"],"used_by":[],"compute":"/api/v1/klean/compute/dilution_concentration","seal":{"receipt_id":"d017cc7dffff572a7adc3c1d","digest":"ff9469cecfb2bfdf74174682d2499bf3dcc86c0d62e7197d6640fab11f61bd22","sealed_at":"2026-08-10T03:30:24.740384+00:00","time_source":"roughtime_chain"},"commit":"4b8413e1b8"}