Investigation demonstrates specific alignment of E8 with geographic catalogs, suggesting methodological considerations.
Version 3.0 re-examines the hypothesis that projected E8 root-system edge networks align with sparse geographic catalogs, on cleaned data and with pre-registered testing. The primary sacred-site catalog was deduplicated from 160 to 157 sites and the orientation search expanded to 300 projection seeds. This version is reported as an investigation rather than a confirmation. Three findings are robust: (1) shape specificity — only E8 aligns both statistically and geographically, while the D8 root system, Fibonacci spheres, and 120-cell projections do not; (2) cross-catalog discrimination — the pipeline returns null on Pacific hotspots and dense catalogs, and seed 68 is significant on Indo/Atlantic hotspots yet null on sacred sites; (3) one instance of cross-catalog replication (seed 46). The 120-cell control reaches nominal statistical significance (p = 0.017) while being geographically null (1.3% of sites within 0.02 deg of an edge versus 36.3% for E8), a dissociation developed as a methodological point. Two claims do not survive. No individual orientation survives multiple-comparisons correction (nine of sixteen sacred seeds reach uncorrected p < 0.05, best p = 0.007, but none clear Bonferroni or Benjamini-Hochberg FDR at q = 0.05). An apparent sharp RMS phase transition near 0.048 deg was tested by a two-stage pre-registered protocol and returned 0/13 significant — the apparent transition was an artifact of seed selection. The low-RMS region where the uncorrected effect concentrates was exhausted by the exploratory selection and cannot be independently validated on this catalog. The deposit includes the cleaned catalogs, shape-control results, the two GPG-signed and OpenTimestamped pre-registration documents, the boundary-validationoutputs, and all figure-generation scripts. The computational pipeline is maintained in a private repository. Supersedes version 2.1.0.
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Salah-Eddin Gherbi (2026) studied this question.
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