Typed transfer, nonlinear packets, and obstruction theory

Abstract

Finite projector packets turn linear transfer into typed walks and arbitrary maps into exact coordinate representations. Canonical coordinate transport satisfies an exact cocycle law. A chosen connection can fail to compose, producing holonomy and packet obstruction witnesses. Nonlinear packet jets lead to higher composition, convergent rooted tree expansions, graded operations, and nonlinear refinement defects. A specified correction map produces a canonical cokernel obstruction. Relative exact sequences, mapping cones, Hilbert splitting, nonlinear correction, and filtered lifting describe how these obstructions behave. Exact elimination produces Schur formulas, and finite transport reduces gluing to fundamental cycle holonomy. For smooth orthogonal packet families, direct packet rotations converge in operator norm to canonical unitary transport. The finite formal contract and the broader ordinary proof development retain their separate scopes throughout.