TDN — Numerical Falsification Tests: Two Central Numerical Assumptions Are Not Supported, and a New Scaling Law Emerges

Independent numerical study of the Time Dilation Network (TDN) framework (Version 1, DOI 10.5281/zenodo.20625572). This is a standalone study, not an erratum. Revised version: This update corrects an attribution. The model used — DAGs with vertices 1..N and a directed edge i→j (i<j) included independently with probability rho — is identified as the known Barak-Erdos graph (stochastic ordered graph, 1970s). The scaling relation L_max = N f(rho), reported earlier as a new finding, is the classical Barak-Erdos theorem L_n/n → C(p). It is reproduced here numerically, not discovered. The identification concerns the uniform-sampling model only; it does not establish equivalence between the full TDN action S[G] and the Barak-Erdos model, which remains an open question. The study's contribution is therefore: (i) independent numerical reproduction of a known result, and (ii) application of that result to falsify two specific TDN claims — a universal scaling exponent, and a second-order phase transition at rho_c ~ 1/N. Three independent algorithms confirm the simulations. Results: strong data collapse of L_max/N consistent with L_n/n → C(p); no single power law (effective exponent drifts 0.63 to 1.0); no second-order transition at rho_c (susceptibility, derivative, and threshold tests all negative); ensemble-dependence (causal-set sprinkling gives L_max ~ N^(1/d), so the independent-edge ensemble corresponds to effective dimension d=1). These falsify two numerical assumptions but not the core TDN definition of time as longest-path length, which lies outside the test scope.