{"fqn":"KLean.Bio.Logistic.population_pos","short":"population_pos","module":"KLean.Bio.Logistic.PopulationPos","path":"KLean/Bio/Logistic/PopulationPos.lean","claim":null,"verified":null,"axiom_level":"kernel-standard","olean_sha256":null,"quarantined":false,"statement":"theorem population_pos (K N₀ r t : ℝ) (hK : 0 < K) (hN₀ : 0 < N₀) (hN₀K : N₀ ≤ K) : 0 < population K N₀ r t","topics":["biology"],"refs":[],"depends_on":["KLean.Atoms.Quantum.ConjugateCubeChirality","KLean.Atoms.Quantum.GaussianTripleDefs","KLean.Bio.Logistic.Base","KLean.Misc.Basic"],"used_by":["KLean.Bio.Logistic","KLean.Bio.Logistic.PopulationLeK"],"compute":"/api/v1/klean/compute/logistic_growth","seal":{"receipt_id":"d017cc7dffff572a7adc3c1d","digest":"ff9469cecfb2bfdf74174682d2499bf3dcc86c0d62e7197d6640fab11f61bd22","sealed_at":"2026-08-10T03:30:24.740384+00:00","time_source":"roughtime_chain"},"commit":"4b8413e1b8"}