mirror symmetry, notably in the work of mark gross and berndt siebert, identifies involutory "mirror pairs" (x,y) of (degenerating, polarized) compact calabi-yau manifolds and makes predictions relating the symplectic geometry of x with the algebraic geometry of y. those predictions range from those of the "open string sector", where homological mirror symmetry (hms) relates the lagrangian submanifolds of x to algebraic vector bundles on y, to those of the "closed string sector" where, for example, counts of holomorphic spheres in x are predicted to equal certain period integrals on y. i'll report recent work, joint with nick sheridan, which says the following: if one can prove a certain fragment of hms (a fragment which we expect to fit neatly into the gross-siebert program) then, without knowing anything more about the geometry of x and y, one can deduce (i) the full statement of hms; and (ii) certain algebraic and enumerative claims from closed-string mirror symmetry.