Unified Rigidity Geometry: Constraint-Driven Identity Dynamics

Constraint-geometric identity theory defines identity as invariance regions within a possibility field shaped by structural, dynamical, and interpretive constraints [Thomas, 2025]. This paper operationalizes that geometric foundation for recursive social conversion systems through two dimensionless control parameters: Trigger Tension measuring constraint misalignment along the conversion axis, and rigidity quantifying basin stability versus conversion efficiency. The canonical 15-phase lifecycle of identity capture maps precisely as trajectories through the (TT, ξ) constraint plane. Phase 11 identity fusion manifests as a constraint-induced region merger where recovery time to pre-fusion states diverges exponentially. Tier 1 (social): Validated 15-phase field guide. Tier 2 (engineering): ξ ≈ 1.2 sweet-spot hypothesis across domains. Tier 3 (speculative): USTT's 15 cosmological vacua with 1.2% photon ring deviation. The theory predicts recursive systems cluster near the universal ξ ≈ 1.2 sweet-spot optimizing both stability and conversion competence. Social and engineering tiers stand independent of cosmological falsification. ngEHT (2028–2030) will test Tier 3.