Three-Dimensional Causal Growth and the Octonionic Gauge Sector: Conditional Forcing and a Uniqueness Conjecture

Mathematical sequel to the discrete null-lattice growth to so(8) closure paper. Establishes the dimensional hinge of the HQIV framework: quadratic null-shell growth in 3+1 dimensions, conditional forcing of the octonionic layer via a shared-manifold rapidity bridge, derivation of the curvature-imprint pair (α, γ) = (3/5, 2/5) from unit-split + spanning-tree balance, and a uniqueness conjecture for the octonionic gauge sector. All cited Lean theorems are sorry-free. Full audit graph and module index provided.