Dynamical Tensor Networks from Information Congestion: Page Curves and Entropy Cancellation

The black hole information problem involves four interrelated challenges: preserving unitarity, deriving the Bekenstein–Hawking entropy, producing the Page curve, and addressing the AMPS firewall argument. We present a model in which spacetime is a causal graph whose edges carry finite channel capacity and traversal cost but no internal Hilbert space. Mass-energy generates information traffic; the resulting congestion produces gravitational time dilation, with the horizon defined as the surface of maximum channel utilisation. Four results follow from this structure. First, the Stinespring dilation theorem with trivial edge environment guarantees unitary transfer across every edge, including horizon-crossing edges. Second, counting the channel capacity of boundary edges and deriving Newton's constant self-consistently from the congestion dynamics yields S = A/(4ℓ²P), with all microscopic network parameters cancelling. Third, treating the black hole interior as a capacity-limited reservoir whose occupancy is bounded by the Bekenstein–Hawking entropy produces the Page curve Sent(t) = min(nrad(t), SBH(t)) with no additional free parameters. Fourth, a temporal queue buffer addresses the AMPS monogamy tension at every instant. The model predicts that the post-Page-time information release rate is twice the Hawking emission rate. The causal graph enriches causal set structure with edge-level channel capacity, complementing the purely order-theoretic framework with a dynamical mechanism—information congestion—that produces gravitational phenomena from network traffic. We discuss connections to discrete curvature convergence, the local d'Alembertian on causal sets, spatial distance measurement via causal overlaps, and open problems concerning navigability and the continuum limit.