From Ricci Flow to Coherence Flow Toward a Coherence Geometrization Program

Hamilton's Ricci flow and Perelman's completion of the Poincare and Geometrization programs showed that geometric evolution can transform topological complexity into canonical structure. This report proposes a coherence-geometric extension of that insight. Instead of treating metric smoothing as merely curvature diffusion, the Coherence Geometrization Program interprets geometric flow as a special case of coherence restoration: irregularity, curvature concentration, torsion, chirality, and resonance imbalance are treated as coupled modes of incomplete closure. The central object of the report is a symmetric, positive-definite coherence tensor, replacing the Riemannian metric as the primary evolving field. Torsion and chirality are introduced through an auxiliary antisymmetric torsion-chirality field, whose symmetric quadratic correction enters the flow as a coherence-stress term. This preserves the metric character of the evolving tensor while allowing torsion, handedness, and phaseasymmetry to influence geometric evolution. The resulting coherence flow reduces to Ricci flow in the torsion-free limit. In the torsion-bounded regime, the report formulates a DeTurck-type parabolic structure, proposes augmented entropy functionals, states torsion-aware noncollapse and canonical-neighborhood principles, and introduces coherence surgery as the analogue of Ricci-flow surgery in the presence of torsion-chirality concentration. The long-time target of the flow is described as cohermization: decomposition into canonical coherence geometries, with the simply connected, coherently closed case tending toward an isotropic coherence sphere. This report should be read as a formal disclosure and research program rather than a completed proof. Its purpose is to identify the analytic objects, limiting cases, conjectural theorems, and proof pathways by which Ricci flow may be extended into a broader theory of coherence, torsion, geometry, and closure. Keywords Ricci flow; Perelman; geometric analysis; coherence flow; torsion; chirality; Riemann-Cartan geometry; entropy; noncollapse; surgery; cohermization; closure; Unified Coherence Closure Framework