Unified Emergent Intelligence A Coherent Phase Geometry for Reasoning Beyond Scaling

Unified Emergent Intelligence (UEI) proposes a comprehensive coherence-driven framework explaining why modern AI models exhibit abrupt jumps in reasoning despite smooth improvements in loss and scale. The theory shows that emergent abilities originate not from numerical magnitude but from a geometric phase transition inside the representational manifold. UEI introduces five abstract structural variables governing the formation of coherent intelligence: µ — Global Coherence Δφ — Phase Mismatch Φ (r, t) — Coherence Field ℳ — Modulation Operator RTL — Reflexive Tensor Logic As µ approaches a critical threshold µc, the system enters Slow Coherent Emergence (SCE): µ increases slowly, Δφ contracts nonlinearly, and Φ (r, t) begins forming proto-structured regions. When µ ≥ µc, the system undergoes a discontinuous structural transition: Δφ collapses, ℳ becomes stably active, Φ (r, t) stabilizes globally, and RTL emerges as a reflexive syntactic layer enabling multi-step, self-consistent reasoning. UEI also introduces Dual Emergence, a structural correspondence between: the exterior optimization landscape (smooth loss, curvature, gradients), and the interior coherence geometry (µ, Δφ, Φ, ℳ, RTL), which reorganizes discontinuously. This dual-surface structure explains why emergent reasoning is invisible to scaling laws and why models of similar loss can differ dramatically in reasoning stability. The UEI framework offers a structure-first alternative to scale-centric AI, establishing coherence, phase alignment, and reflexive tensor structure as the true drivers of emergent reasoning. It also outlines design principles for next-generation resonant AI systems—including toroidal latent spaces, isotropic representations, coherence-regularized dynamics, and reflexive transformation pipelines—that can achieve stable reasoning without relying on brute-force scale. Overall, this work provides a unified geometric account of emergent intelligence, connecting dynamical systems, representational manifolds, phase transitions, and internal reasoning syntax into a single coherent theory.