This article develops a morphodynamic account of English possessive ’s in which the exponent isnot a morpheme in the traditional sense. Rather than functioning as a stable atomic form-meaningpair or a single categorial head, ’s is analyzed as the surface residue of predication: a mobilepredicational field that emerges when a predicational configuration collapses and its relationalremnant must be rehosted inside the adjectival domain. The Adjective Well architecture, derivedfrom first principles of categorization theory, models adjectivalization as orbital landing governedby curvature compatibility and attractor structure. Curvature is specified compositionally as afunction of possessor animacy, referential type, and possessee nominalization class – κ(H,Y) =w₁·Anim(H) + w₂·Ref(H) + w₃·Nom(Y) – making the framework directly falsifiable and its coreparameters estimable from corpus data.The apparent duality of ’s is not ambiguity but orbital bifurcation: the same exponent realizes twoformally distinct operator outputs, ’s₁ (a predicational adjective operator of type ⟨e,⟨e,t⟩⟩ filling anopen relational argument) and ’s₂ (a qualitative adjective operator of type ⟨⟨e,t⟩,⟨e,t⟩⟩ modifying aproperty). These types are not stipulated but derived from the well stratification: low-orbitallanding produces REL-type saturation (’s₁); high-orbital landing produces Q-type modification(’s₂). Landing is modeled probabilistically via a softmax function over orbital bands, makinggradience native to the model rather than appended.The analysis engages the genitive alternation corpus literature (Rosenbach 2002, 2005; Hinrichs& Szmrecsanyi 2007; Szmrecsanyi et al. 2017) and shows that κ(H,Y) unifies the animacy andtopicality predictors identified by Rosenbach under a single parameter while additionallypredicting a critical Abstraction × Environment interaction that animacy-alone regression modelsdo not capture. Corpus evidence from the English Web Treebank (EWT), stratified by possessorcomplexity, confirms the predicted interaction: the of-alternation premium for phrasal-edgepossessors is larger for abstract than for concrete hosts (Δι = +0.34 vs. +0.23 respectively). Adiscriminating competitor analysis (Barker semantics + phonological cliticization + scalarpragmatics) is provided and shown to fail the interaction prediction without additional mechanismsequivalent to the curvature gate. Cross-linguistic extension to Dutch, Swedish, German, andArabic construct-state genitives demonstrates that the curvature-gate mechanism is typologicallyportable. A fully specified confirmatory acceptability protocol (item bank + analysis scripts) isprovided as supplementary materials; the present article reports the theoretical analysis and corpusevidence.