Operational Spacetime from Fundamental Time Uncertainty

We present a robust protocol for reconstructing an operational causal geometry from noisy, spatially inhomogeneous correlation data on dynamical lattices. The method combines a high-frequency spatial filter (Laplacian/gradient response) witha quantile-based estimator of the correlation-front radius, using the 98th percentile rather than the maximum to suppress rare outliers and lattice-scale spikes. Applying this reconstruction to branching correlation dynamics, we recover a well-defined expanding front consistent with an effective lightcone and extract a minimal operational metric from the measured front speed and locally calibrated coherence resources. We further identify a systematic information–geometry lag: an entropy-based information proxy spreads earlier, while the geometric response proxy follows with a delayed relaxation, approaching the information front only as the wavefront matures. This lag supports an interpretation in which operational geometry behaves as a delayed response to correlation transport rather than an instantaneous co-moving field.