Time Dilation as Computational Lag: Deriving Schwarzschild Proper Time from Graph Compression

Paper 101 does not claim to have derived general relativity, to have proposed a new law of time dilation, or to have measured a real clock. It shows, in one fully deterministic and reproducible calculation, that (i) a lattice built by integrating Paper 99's compression dn/dr = 1/√(1−β) on an explicit grid of 400,001 radii reproduces the closed form to 2.1×10⁻⁸ in density and to five significant figures in node count; (ii) a stochastic clock — Poisson unit work arriving at fixed bandwidth, committing at the local latency — driven by that lattice reproduces √(1−2M/r) over 1.05 ≤ r/r_H ≤ 50 with a worst relative residual of 2.5×10⁻³ and χ²/dof = 14.4/11; (iii) the rate estimator is unbiased to (0.014 ± 0.022)% on a thousand independent realisations; (iv) the statistical error exceeds the construction error by three to six orders of magnitude, so the agreement is not an artifact of how the lattice was built; (v) five masses from 1 to 20 collapse onto one curve in β and onto five curves in r, with a worst residual of 0.35% — a consistency check on the implementation, not an independent prediction; (vi) a work counter and a phase accumulator agree on the mean rate to 0.6σ while disagreeing entirely on their noise, so the equivalence principle constrains the mean and not the mechanism; and (vii) at every clock-based measurement of gravitational redshift, from an optical clock a centimetre above its partner (β = 2.2×10⁻¹⁸) to the white dwarf Sirius B (β = 5.1×10⁻⁴), the exact law and its weak-field form β/2 differ by at most one part in 7400, so the exponent of the law is untested. The compression assumption is Paper 99's and is used, not derived; the mass is static and no field equation is solved.