Finite-Resolution Tomography of the Quadratic Transverse Action Jet in an Interacting Dark Sector

This paper studies the first quadratic transverse action freedom left after fixing one interacting-dark-sector background and its complete linear response. In the pressureless Type-2 reconstruction, the first hidden coefficient is a history-dependent function C2(phi), whose polarized long-short contribution is Delta M_LS^(2) = C2 deltaF_L deltaF_S. The paper propagates finite-dimensional profiles of this function through the source-correct finite-k Einstein-scalar-CDM-baryon system and then through progressively more realistic observational maps. Across the declared finite-resolution profile spaces the source operator remains non-rank-one, while individual source singular functions are not invariant under functional-resolution changes. In the shell-capped common-kL/H0=10 statistic, the canonical p=6 spectrum is (1, 0.269, 0.0577, ...), with a second observable direction retained under p=4,6,8 resolution stress. Redshift tomography supplies that second direction, whereas absolute normalization remains degenerate with primordial CIP normalization and tracer response. The release does not claim a detection, coupling constraint, or survey-level measurement of C2.