{"fqn":"KLean.Bio.NussinovOptimal.nussinov_optimal","short":"nussinov_optimal","module":"KLean.Bio.NussinovOptimal","path":"KLean/Bio/NussinovOptimal.lean","claim":"Optimality of the Nussinov DP value. nussinov s i j equals the maximum base-pair count over all valid nested secondary structures on [i, j]: * (achievability) it is attained by some valid structure, and * (soundness) no valid structure exceeds it. Stated as: there is an optimal structure, and it dominates every valid one.","verified":true,"axiom_level":"kernel-standard","olean_sha256":"2398d5ec92c6feac2f12349858027d43589770903c6a7563b6f0115506dbb3e8","quarantined":false,"statement":"theorem nussinov_optimal (s : List Base) (i j : ℕ) : ∃ P, ValidStructure s i j P ∧ score P = nussinov s i j ∧ ∀ Q, ValidStructure s i j Q → score Q ≤ score P","topics":["biology","ramanujan"],"refs":["https://doi.org/10.1073/pnas.77.11.6309"],"depends_on":["KLean.Misc.Basic"],"used_by":["KLean.Bio.PlddtBounds"],"compute":"/api/v1/klean/compute/nussinov","seal":{"receipt_id":"d017cc7dffff572a7adc3c1d","digest":"ff9469cecfb2bfdf74174682d2499bf3dcc86c0d62e7197d6640fab11f61bd22","sealed_at":"2026-08-10T03:30:24.740384+00:00","time_source":"roughtime_chain"},"commit":"4b8413e1b8"}