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.
Dmytro Panasenko (Mon,) studied this question.