Project Phi Grid — Gaia GCNS Confirmatory Test: Pre-registered Null Result (Section 14)

This deposit reports the results of a pre-registered confirmatory test of the φ-ratio stellar density hypothesis developed in Project Phi Grid, Section 13 (Zenodo DOI: 10.5281/zenodo.19227964). The hypothesis — that φ-ratio shells anchored at Neptune (30.069 AU) align with stellar density peaks in the Gaia Catalogue of Nearby Stars (GCNS, Smart et al. 2021) within 50 light-years — was pre-registered on OSF (osf.io/a72fp) on 25 March 2026 before any Gaia data were downloaded or analysed. The pre-registration locked Neptune as the single anchor, specified KDE bandwidth 0.8 ly, volume correction exponent 0.6, and significance threshold p < 0.05 on both Monte Carlo tests. Two tests were executed: (1) Full 50 ly confirmatory test: 1,148 GCNS sources within 50 ly (gcns.main, parallax error/parallax < 0.10). 6 KDE peaks detected. 2/8 shells matched within ±0.5 ly. p = 0.176 vs random geometric progressions, p = 0.218 vs random positions (N = 100,000 each). Result: null. (2) Focused 0–20 ly replication: 83 systems within 20 ly with resolved binary components collapsed via gcns.resolvedss, directly replicating the RECONS methodology of Section 13. 3 KDE peaks detected at 11.90, 16.31, 19.08 ly — consistent with Section 13 RECONS peaks at 11.90, 15.91, 18.91 ly. 0/6 shells matched. p = 1.000. Result: null. The Section 13 exploratory signal (p = 0.034, RECONS 80-system catalog) does not survive confirmatory testing in either the full 50 ly Gaia sample or the focused 0–20 ly replication. The null result is the correct scientific conclusion. This deposit includes the full reproducible notebook, input data, analysis figure, and written report. Related work: Earth notebook (Zenodo DOI: 10.5281/zenodo.19035389), under active review at the British Geological Survey.