Adaptive proposals for nonparametric equation-of-state inference with RIFT: iterative Gaussian-process refinement in a compressed sequence representation

Nonparametric equation-of-state (EOS) inference evaluates the likelihood on a finite ensemble drawn from a prescribed functional prior. Reweighting that ensemble suffices for the binary neutron stars detected so far, and loses effective sample size only once the likelihood concentrates --- which needs third-generation catalogues, or extra electromagnetic and nuclear-theory information folded into the same target. We develop and validate an adaptive-proposal procedure that leaves the base prior fixed: data-informed generations are combined by multiple importance sampling and, where that degenerates at large catalogue size, by a calibrated Gaussian projection. We implement it in two representations --- a compressed principal-component parametrization of the neutron-star sequence, whose draws need no stellar-structure solve, and a sound-speed parametrization with a differentiable Tolman--Oppenheimer--Volkoff solver --- both on a constrained low-density-to-pQCD bridge. Because that anchor, and not the bridge, fixes the low-density prior, we rebuild the ensemble with a crust-plus-chiral-EFT anchor in place of the wide nuclear metamodel: the maximum-mass prior is unmoved, the radius gains a hard prior ceiling at the measured NICER value. GW170817 with the specified NICER and radio factors gives the calibration-conditional R(1.4,M)=11.7 plus or minus0.4 km; in a synthetic 1000-event catalogue it reproduces the mean fixed-prior Λ(1.4,M) to 0.4 %, 1.5 times wider, as the fixed archive's effective sample size falls from about!470 to 22.