Splitting as Evaluation-Collapse Wrong Attractor: The Idealization-Devaluation Oscillation, All-or-Nothing Basin, and the Return to Integrated Appraisal

Splitting — the cognitive pattern of evaluating persons, situations, and self in all-or-nothing terms without the capacity to hold ambivalence — is here formally reconceptualized as a wrong attractor W_SP in the landscape of integrated appraisal. The healthy ground state S^0 is defined as integrated appraisal: the capacity to perceive persons and situations as containing simultaneously positive and negative qualities, holding ambivalence without collapsing into categorical evaluation.

W_SP is rigorously distinguished from healthy categorical evaluation, moral clarity, and appropriate discrimination. Three interlocking mechanisms maintain the basin: the idealization trap (placing objects on perfection pedestals ensures inevitable devaluation — idealization is not a stable position, as any perceived flaw triggers collapse to all-bad), the devaluation cascade (once triggered, positive memories are retroactively rewritten and the object becomes wholly negative — the switch is near-instantaneous and total), and the certainty function (ambivalence generates anxiety; all-or-nothing evaluation provides false clarity, making splitting a primitive but effective anxiety-management strategy).

The oscillation dynamic is central: idealization → disappointment → devaluation → sometimes re-idealization — a cycle that confirms rather than resolves the pattern. Nine formal propositions characterize the all-or-nothing basin, idealization trap, devaluation cascade, certainty function, the oscillation dynamic, clinical contexts, interpersonal costs, return paths, and the distinction from appropriate categorical evaluation.