Meson-isospectral pair interactions and the residual three-quark force
Meson-isospectral pair rotations can closely reproduce low-lying baryon energies while producing a substantial connected action under their consistent three-body embedding. Starting from an independently calibrated S-wave meson model, we compare ground-mass fits, joint ground-level and gap fits, and direct minimization of the connected remainder. With eighteen shared coefficients, a four-packet joint fit reproduces the nine calibration ground masses and first gaps with RMS errors of $\JointGroundTrain$ and $\JointGapTrain$ MeV, respectively. The excluded ground masses and gaps have RMS errors of $10.7$ and $8.1$ MeV in the same enlarged radial space. Its connected action on the eighteen calibrated inputs is $\JointActionCal$ times the unrotated source action. Eigenvalue agreement and removal of the connected interaction thus impose different tests. Separately optimizing the action with five packets gives a normalized residual of $\ShortActionAll$ for an intermediate-distance fifth packet; a long-distance extension also leaves a substantial remainder. An eliminated-state construction realizes the central color--color structure of an intermediate-configuration mechanism together with correlated pair dressing. These results favor a connected operator basis with three fitted strengths as an economical description within the tested pair family, and quantify its relation to the representation freedom of equivalent few-body Hamiltonians.