The Holographic Bottleneck: Information Re-Routing and the Area Law

Paper 100 does not claim to have resolved the information paradox, derived the holographic principle, or shown that the physical vacuum is a graph. It shows, in one fully deterministic calculation, that (i) on a cubic ball of frozen interior the records scale as R^3.011 and the still-active ports as R^1.949, so that the load per port grows as 0.9991 R − 1.6577 — slope one, intercept a lattice constant of ball-and-shell counting; (ii) with a per-port capacity C = 6 the individually stored content follows A^1.0000 above the crossover, an area law with measured exponent 1 against 3/2 for a volume law; (iii) the crossover is predicted as ⌈C − b⌉ from the load fit alone and is measured at 3, 4, 6, 8, 10 for C = 1, 2, 4, 6, 8 — five agreements from one constant; (iv) the records counted before and after the re-routing are identical, 2,618,004 against 2,618,004 with a difference of zero at every one of twenty-eight radii; (v) the compression ratio follows R_eff/C with slope 0.1672 against 1/6 = 0.1667 and the resolved fraction follows C/R_eff with slope −0.9993 against −1, crossing at exactly (C, 1), so that at R = 30 only 20.6% of records keeps an address of its own; and (vi) an equal-area paving of the shell shows the load uniform to 2×10⁻¹⁵ records per pixel over full coverage. Two results are explicitly not predictions: the *coefficient* of the area law is a calibration requiring one port per Planck area at a quarter bit each, a factor of 24 from the value used here; and the uniformity of the screen follows from the re-routing being a hash. The exponent of the area law, and the crossover, are the results.