Reversibility and the Autocatalytic Threshold: a Mean-Field 1/L Scaling Law and Its Limits (v2, corrected)

CORRIGENDUM (v2). This version corrects v1/v1.1. (1) Prior versions did not cite the directly relevant prior work of Mossel & Steel (2005, J. Theor. Biol. 233:327-336) and Hordijk & Steel (2011, Int. J. Mol. Sci. 12:3085), who established that the catalysis required for RAF emergence grows only ~linearly with maximum length n (so the per-reaction requirement decreases with length); the earlier "this has remained open / we resolve it" framing was overstated. (2) The headline result c_c -> 2 ln 2 / L -> 0 is a property of the MEAN-FIELD approximation only: it was checked against Monte-Carlo at L=7-9 alone, and mapping the mean-field parameter c=p*N to Hordijk-Steel's per-molecule f=p*|R| (|R|/N ~ n/2, f ~ 1.097+0.0189 n) instead implies a small POSITIVE floor c_c -> ~0.04, not 0; the mean field likely over-counts cleavage-route multiplicity (treats ~2^{j+1} routes as independent). Robust, model-independent claims: reversibility lowers the required catalysis vs the irreversible (ligation-only) case, and the requirement falls with length. The exact vanishing is mean-field-specific and awaits large-L validation. The mean-field analysis, closed-form coefficient c_c*L = -ln(1-theta)/theta, reversible-vs-irreversible floor contrast, and b/theta-robustness stand as stated within the mean field. Code (MIT); discovery tooling proprietary and not required to reproduce (see NOTICE).