Spatial Level Repulsion in the Stratigraphic Record: A Random Matrix Theory Test of Cyclostratigraphic Bed Spacing

A four-racetrack program established that the temporal spacing of geological events follows random matrix theory (RMT) level repulsion when a single long-memory source is isolated, and Poisson randomness when many sources superpose. This work begins a fifth racetrack that translates the law from the time domain to the spatial domain. Part I establishes the methodology on the cleanest spatial system — cyclostratigraphy — and reports the first real-data test. A validated spatial RMT pipeline (local unfolding to remove density trends; spatial declustering to remove fractal aggregation) is confirmed on synthetic ground truth to distinguish Poisson from repulsive spatial point patterns, and the spacing ratio is shown to be naturally robust to smooth density gradients. Applied to two independent, openly downloadable cyclostratigraphic proxy series — the Gubbio Contessa magnetic-susceptibility section (Tethyan, Danian; PANGAEA 864450) and the Blue Lias section (UK, Hettangian; PANGAEA 896875) — the down-core spacings of Milankovitch cycles show strong GUE-class spatial repulsion in both (spacing ratio 0.73 in each; bootstrap confidence intervals excluding Poisson; surrogate test p < 0.0001). As a negative control, turbidite successions, triggered by many independent power-law earthquake events, are shown via a forward model anchored to published Woodlark Basin statistics (Awadallah et al. 2001) to give Poisson/clustered spacing. The Poisson baseline (0.386) cleanly separates the two regimes. Honest scope: the repulsion in cyclic strata reflects astronomical quasi-periodic forcing — an external clock — rather than the spatial-shadow depletion mechanism that motivates the racetrack. The spatial-shadow hypothesis awaits the structural and metallogenic analogs (Parts II and III). The negative control is a literature-anchored forward model, not raw per-bed measurements; the original data have been requested from the authors. GOE-versus-GUE is not sharply resolved at present sample sizes. Fifth in an RMT program spanning Earth from core to crust. Real proxy data are redistributed under their respective PANGAEA CC-BY licenses.