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Algorithmic prediction of RNA secondary structure has been an area of active inquiry since the 1970s. Despite many innovations since then, our best techniques are not yet perfect. The workhorses of the RNA secondary structure prediction engine are recursions first described by Zuker and Stiegler in 1981. These have well understood caveats; a notable flaw is the ad-hoc treatment of multi-loops, also called helical-junctions, that persists today. While several advanced models for multi-loops have been proposed, it seems to have been assumed that incorporating them into the recursions would lead to intractability, and so no algorithms for these models exist. Some of these models include the classical model based on Jacobson–Stockmayer polymer theory, and another by Aalberts and Nadagopal that incorporates two-length-scale polymer physics. We have realized practical, tractable algorithms for each of …