Testing the deductive content of a topological free-energy gating framework against the closed-biopolymer record: four audits, one decisive non-host, three pre-registered predictions

A topological free-energy framework proposes that, in systems where the geometric sector is thermal and the topological sector is superselected, long-lived organisation is selected by a free-energy gate acting on topological sectors rather than by local geometry. The claim is a claim about deduction as much as about physics: given the freedom hierarchy and the conservation law, the framework must output which topological classes can persist, which are forbidden, and how their abundances order. We test that deductive content against the closed-biopolymer record, using only published measurements and no fitted parameters. Four audits are reported. The equilibrium topoisomer ladder of closed circular DNA is read in the primary literature as a direct demonstration of the Boltzmann distribution over a quantised variable; the gate output coincides with it exactly, so the case is compatible but not discriminating. Equilibrium knotting probabilities of cyclised phage DNA (0.031 for 10 kb, 0.017 for 7 kb) are reproduced by Monte Carlo simulation of wormlike chains with one fitted parameter, the effective diameter; again coincident. Type II topoisomerases drive knotting below equilibrium by factors of fifty to ninety (0.00062 and 0.00019), a genuinely non-Boltzmann topological selection, but one that enzyme mechanism accounts for without any gate. Torsional buckling under magnetic tweezers, the most precisely characterised molecular topological transition, is a decisive non-host: it conserves the linking number, and its barrier is 10 kBT at coexistence and grows at 0.268 kBT per turn, vanishing only at Lk = -11.9, outside the accessible range. The single geometry-matched twin in the record, knot threading in a 5_2-knotted protein, is the one place a discriminator could arise, but the published quantities are unfolding forces and end-to-end deficits, not the barrier law the framework predicts. We conclude that the framework is compatible with the entire audited record and exclusive against none of it, give the structural reason (every candidate dataset is either sector-preserving or sector-randomising), restate the correspondence that would make a closed chain a genuine host, derive the correction that an integer reaction coordinate forces on the kernel, and fix three pre-registered predictions together with the precision floor a decisive experiment would have to meet.