PhronesisWe present a formal analysis of chronic role-reversal, the relational dynamic in which a child assumes functional caregiving responsibilities for a parent or primary attachment figure, foreclosing age-appropriate developmental positions and installing a self-sustaining wrong attractor. Drawing on the displacement framework developed in prior Phronesis Issues, we model the ground state S^0 as calibrated developmental alignment—the configuration in which a child occupies an age-appropriate relational position with respect to their caregiver.
Chronic role-reversal constitutes a displacement from S^0, with associated cost function D() that accumulates into a parentification potential = D()\,dt. We demonstrate that beyond a critical displacement _c, the parentified configuration becomes a wrong attractor W: a locally stable minimum that resists return even after the triggering relational context dissolves. We introduce the Age-Appropriate-Position Foreclosure Basin (AAPFB) as the basin of attraction surrounding W, and characterize its depth, width, and the phase transitions that govern entry and exit.
Nine formal propositions (P1–P9) establish the theoretical architecture. We conclude with intervention theory, recovery dynamics, and the ethical geometry of reinstating S^0 in adult life. Keywords: parentification, wrong attractor, displacement framework, developmental alignment, role-reversal, ground state, foreclosure basin, phase transition