V. APPENDIX Direct sampling of unpeeling dynamics within λ -DNA is prohibitively slow near B/U phase co- existence, because the junction separating unhybridized and hybridized regions of the molecule is akin to a random walker in a free energy landscape replete with barriers in excess of hun- dreds of k$_{B}$T [6]. We therefore computed thermal averages in Fig. 1(b) within a constrained ensemble (at constant force and temperature) in which the molecule possessed one free end, permitting unpeeling, and melting was disallowed. Thermal averages were computed from 〈 A 〉 ≡ $^{∑}$$_{n}$g$_{n}$ ( f, T ) A ( n ) e − βF ( n $^{)}$/ $^{∑}$$_{n}$g$_{n}$ ( f, T ) e − βF ( n $^{)}$, with F ( n ) ≡ ( L − n ) 〈 F 〉 hyb . + nF$_{U}$ + ϵ$_{BU}$δ$_{n,}$$_{0}$ . Here n ∈ [0 , L ] is the number of unpeeled basepairs; F$_{U}$ is the bulk internal energy per basepair of state U (see Equation (5) of Ref. [10]); ϵ$_{BU}$ < 0 is the U/B surface tension parameter; and 〈 F 〉 hyb . is the bulk energy per basepair of a molecule that is constrained to remain hybridized (calculated by direct Monte Carlo sampling). The degeneracy g$_{n}$ ( f, T ) accounts for the mixing entropy of B- and S-DNA within this hybridized phase. Here we have used the approximation g$_{n}$ ( f, T ) = exp $^{{}$(1 − n/L ) ln ( L m $^{)}}$, where m is half the thermal average of the number of S/B domain walls. Sequence averaging in Fig. 1 was done by dividing the basepairing-stacking parameters of the melting model of Ref. [13] into two sets, containing 1) any A or T bases, or 2) any C or G bases. As in Ref. [10], this leads to bulk free energies (at f = 0) of melting of 0 . 67 + 0 . 19 ln( M/ 0 . 150) (AT) and 2 . 78 + 0 . 19 ln( M/ 0 . 150) (CG), in units of k$_{B}$T at 310 K. Here M is the molar NaCl concentration (we use the salt-dependent correction from [6]). 6