Time-Field Divergence at the Developmental Cone Boundary and Its Structural Correspondence with Lorentz Dilation

We derive the asymptotic behavior of the geometric time-field stretch factor TDG (δ) TDG () TDG (δ) as a developmental path approaches the cone boundary in Developmental Geometry, where δ=1−∥v∥gdev/Vmax = 1 - \|v\|₆₃₄ₕ/Vₘax δ=1−∥v∥gdev/Vmax measures residual developmental capacity. From the DG axiom (movement generates curvature), we derive the complete chain: axiom → balance law → developmental metric → Euclidean density norm → quadratic cone → finite propagation bound. Each step is forced by what precedes it; no step is a design choice. The geometric time stretch factor is defined as the ratio of geometric time to proper developmental time: TDG=dT/dτTDG = dT/d TDG=dT/dτ, where proper developmental time arises from the DG metric quadratic invariant dτ2=dT2−dℓ2/Vmax2d² = dT² - d²/Vₘax² dτ2=dT2−dℓ2/Vmax2 — the unique quadratic combination of the two natural metric quantities satisfying the path-reversal symmetry condition. This gives the exact form TDG (δ) =1/δ (2−δ) TDG () = 1/ (2-) TDG (δ) =1/δ (2−δ), which diverges as (2δ) −1/2 (2) ^-1/2 (2δ) −1/2 as δ→0 0 δ→0. This asymptotic class is identical to Einstein's Lorentz factor γ= (1−v2/c2) −1/2∼ (2δSR) −1/2 = (1 - v²/c²) ^-1/2 (2SR) ^-1/2 γ= (1−v2/c2) −1/2∼ (2δSR) −1/2, with identical leading coefficient 1/21/2 1/2. The correspondence is independent: in DG the quadratic cone is forced by the axiom through the balance law; in special relativity the light cone is forced by the frame-independence of cc c through the Minkowski metric. Neither theory chose a quadratic cone. Both were driven to one by their foundational axioms for the same geometric reason. The parameter δ→0 0 δ→0 corresponds to a path approaching perfect developmental balance — the unreachable ideal limit of the theory, structurally identical to a massive particle approaching the speed of light. Version 1. 3 corrects an error in v1. 0 (the exact form 1/ (1−δ) 1/ (1-) 1/ (1−δ) did not diverge at the cone boundary; corrected to 1/δ (2−δ) 1/ (2-) 1/δ (2−δ) ), completes the forced-cone derivation, grounds proper developmental time in the DG metric quadratic invariant, closes the cross-term gap in the uniqueness proof, and makes Section 2 self-contained so the independence claim can be evaluated without opening Book 5.