This is a preprint of the manuscript submitted to the SIAM/ASA Journal on Uncertainty Quantification. It has not been peer reviewed. The upload includes the main manuscript and a supplementary executable-reference/API scaffold document.
This manuscript develops a certified finite-resolution statistical inverse-readout framework for singular density-selected phase kicks. The framework constructs a weak weighted topology directly from noisy pixelized data, certifies stability through a computable spectral gap, and returns either a strictly certified reconstruction or a certified obstruction under declared assumptions. The draft includes an initial proof-of-concept numerical trace for a two-dimensional logarithmic Coulomb benchmark and a reproducibility package. No external experimental datasets were used. Numerical material is synthetic and generated from the equations and parameters described in the manuscript and reproducibility package.
This preprint develops a certified rank-selective finite-rank tensor correction mechanism for a three-dimensional cutoff-regularized BBGKY benchmark with density-selected phase response. The construction uses an observable-dual topology matched to selected response/readout channels and a finite response menu with outcomes 3, 8, or fail. The main constructive branch is a rank-three dipole closure theorem under explicit dipole-admissibility and scale-safety gates; the rank-eight quadrupole branch is retained as a conditional diagnostic extension. The manuscript includes manufactured diagnostics and a reproducibility scaffold for the finite-dimensional response matrices and conservative exponent witness.
Finite-resolution density imaging is a central diagnostic in ultracold atomic gases and quantum simulators. In density-selected phase-imprint protocols, an unknown interaction or response kernel is encoded into a phase kick, whose subsequent short-time dynamics produces a measurable density contrast. This work develops a scaling-law theory for the resulting many-body-to-pixel inverse-readout problem, from microscopic density data to elliptic phase reconstruction and finite-band kernel recovery. The paper addresses a protocol-level question: when can finite particle number, finite frame averaging, and finite optical resolution still support certified phase or kernel recovery? Rather than reproving a propagation-of-chaos theorem, the analysis treats a controlled many-body interface as input and derives the certifiability and design theory that follows. The resulting bounds identify no-go regimes, optimal readout times, many-body-limited saturation thresholds, and a conservative pilot-calibrated rule for Richardson order selection. A finite-band kernel recovery theorem adds a bandwidth-conditioning trade-off for stable kernel recovery. This is the submitted preprint version of a manuscript submitted to The European Physical Journal D.