The Computational Horizon: Black Holes as Saturated Processors, and the Geometry of Lag

Paper 99 does not claim to have derived general relativity, a stress tensor, an Einstein equation, or the interior geometry of a black hole, nor to have shown that the physical vacuum is a graph. It shows, in one reproducible and fully deterministic calculation, that (i) a committed-budget fraction β = 2M/r, with the vacuum holding a fixed number of nodes per proper volume, gives an edge density dn/dr = 1/√(1−2M/r) that an explicitly constructed lattice reproduces to a relative error of 5.1×10⁻³; (ii) under the one-edge-per-tick rule of Paper 98 the resulting clock law is dτ/dt = √(1−2M/r), whose fitted exponent against 1−β is 0.5000 while the fractional-budget alternative 1−β measures 1.0000 and is excluded; (iii) a linearly growing mass gives a horizon that sweeps outward at 2 dM/dt, freezing clocks at t_f = rT/2M_final — linear in r through the origin, measured slope 1.500 against 1.500, with four clocks stopping at the predicted times and two never stopping; (iv) the local time banked at freeze is 2t_f/3, measured 0.6667, against t_f/2 for the alternative, a factor of 4/3 decided by a single ratio; (v) a saturated node completes √(1−β) cycles per tick against an offered load of (1−β)^(−1/2), retains 1−√(1−β) of its input, and at β ≥ 1 completes nothing while its buffer grows without bound — the one-way asymmetry of an event horizon as a queue, watchable tick by tick; and (vi) the edge count to the horizon is finite while the global tick count diverges logarithmically, so an infalling clock arrives in finite proper time and an outside observer never sees it. The construction rests on one assumption, stated in Section 4 and not derived: uniform node density per proper volume. The agreement between the capacity accounting and r = 2M is a consistency check, not an independent derivation.