VCML Paper 130: Temporal Tomography of Internal d_H Measurement -- Gate Instability in the Self-Measurement Process

We track the internal observer fractal dimension estimate as a time series over 1999 snapshots at L=256 to characterize the statistical structure of self-measurement. The external ground truth is stable (d_H=1.568, negligible variance). The internal measurement shows: mean=0.376, std=0.151 (relative std 40%), skewness=2.34, excess kurtosis=5.72. Most significantly, the Binder cumulant of the time series is U=-1.908, far from the Gaussian value U=2/3=0.667. A negative Binder cumulant indicates an extremely heavy-tailed distribution dominated by rare large-deviation events. The autocorrelation time is short (tau~58 steps), confirming high-variance is genuine snapshot-to-snapshot fluctuation driven by domain-wall stochastic drift. Applying the Binder graduation criterion (Paper 119) to the measurement process itself: a system with U=-1.91 is gate-unstable and cannot reliably report its own geometry. Two requirements for reliable self-measurement: stable domain wall AND L > L*=317.