Quadrupole spectra derived from 2.76 TeV Pb-Pb identified-hadron $\bf v_2(p_t)$ data

$p_t$-differential quantity $v_2(p_t)$ is meant to measure elliptic flow manifested by a dense QCD medium formed in high-energy nucleus-nucleus collisions. Elliptic flow may be referred to more neutrally as a cylindrical quadrupole component of the transverse motion of particle sources within a collision. As defined, $v_2(p_t)$ relies on an implicit assumption that almost all produced particles emerge from a single source. This article describes a detailed study of the algebraic structure of $v_2(p_t)$. A procedure is developed to derive a common monopole boost (radial flow) value and quadrupole $p_t$ spectra for several hadron species. The method is applied to $v_2(p_t)$ data for three hadron species from 2.76 TeV Pb-Pb collisions. According to available $v_2(p_t)$ data the assumption of a single dominant particle source within A-A collisions is unjustified. Combined with a previous study of quadrupole amplitude variation for 200 GeV $p$-$p$ collisions these results demonstrate that quadrupole structure is related to a novel QCD process separate from projectile-nucleon dissociation and jet production. Given quadrupole evolution it is unlikely that a hydrodynamic description is relevant to that process.