A Structural Time Invariant and Censorship Theorem in Developmental Geometry

PaperF of the Developmental Geometry (DG) program. Establishes the proper developmental time invariant as a theorem rather than a definition: the Lorentz form dτ² = dT² − dℓ²/V²_* is forced by three conditions, each a consequence of the DG axiom (movement generates curvature). Derives the finite propagation bound, the structural censorship theorem (the cone boundary is excluded from the domain of admissible finite-mass paths), the uniqueness of the quadratic proper-time invariant under rest normalization, boundary vanishing, and path-reversal symmetry, and the divergence of the DG dilation factor with asymptotic form (2δ) ^ (−1/2) as cone distance δ → 0. Section 6 frames the structural comparison with special relativity: the DG axiom, applied without reference to SR, forces the same time invariant that SR's axiom forces, with the leading coefficient of the divergence fixed identically. Companion to Arc 4 (Substrate Identification) and Arc 5 (Pre-Substrate and Recursion). The time invariant and censorship results give the structural consequence of the cone geometry at the substrate level.