Project Phi Grid — Section 13 & Extended Analysis: φ-Ratio Shell Alignment with Local Stellar Density Structure (RECONS 80-System Catalog, 20 Light-Years) & φ×Neptune Coincidence

This record contains three notebooks comprising the stellar neighbourhood and outer solar system analysis components of Project Phi Grid.

NOTEBOOK 1 — Section 13 (original exploratory analysis): φ-ratio shells anchored at Neptune (30.069 AU) are tested for alignment with stellar density peaks in the RECONS TOP100 80-system catalog within 20 light-years. KDE with bandwidth 0.8 ly and volume correction (r^0.6) detects 4 peaks at 4.30, 11.90, 15.91, and 18.91 ly. 3/4 shells align within ±0.5 ly (φ^19=4.445 ly, φ^21=11.638 ly, φ^22=18.830 ly). p=0.0343 vs random geometric progressions, p=0.0318 vs random positions (Monte Carlo N=100,000). Anchor specificity test across 12 anchors: only Neptune (30.069 AU, p=0.0364), Kuiper Belt outer edge (50 AU, p=0.0289), and Asteroid Belt (2.7 AU, p=0.0323) return p<0.05. All planetary and arbitrary anchors return p>0.21. Both outer solar system anchors mark the outer boundary of Neptune's dynamical zone.

NOTEBOOK 2 — Section 13 Extended (80-system replication & new tests): Four pre-planned tests on the complete verified RECONS TOP100 80-system catalog with full 3D coordinates (RA/Dec/distance from SIMBAD/Hipparcos). Test A — φ×Neptune coincidence: φ × 30.069 AU = 48.653 AU, within 2.69% of the Kuiper Cliff (50 AU). p=0.0158 at ±1% threshold, p=0.0456 at ±3% threshold (Monte Carlo N=100,000 random solar system anchors). Neptune sits at the 4.2nd percentile of random anchors. Not previously noted in planetary science literature. Test B — Ripley's L(r) 3D spatial clustering: Full 3D Ripley's K-function with 999 CSR simulations. Result: all φ-shells within CSR envelope. No significant 3D clustering excess detected at shell positions on the 80-system catalog. Test C — Angular isotropy on φ-shells (corrected methodology): KS test on sin(Dec) vs Uniform(-1,1) and RA vs Uniform(0,360). Shell 11.402 ly: p_RA=0.666, p_Dec=0.831. Shell 18.448 ly: p_RA=0.537, p_Dec=0.907. Both shells isotropic — no moving group contamination or projection artifact. Test D — KDE shell alignment replication: 2/5 shells matched within ±0.5 ly. p=0.243 vs random positions, p=0.161 vs random progressions. Bandwidth sensitivity stable at 0.5–1.0 ly, collapses at 1.2+ ly.

NOTEBOOK 3 — Solar System φ-Shell Boundary Alignment (pre-registered confirmatory test): φ-shells anchored at Neptune (30.069 AU) tested against 4 pre-registered solar system boundaries within ±5% tolerance. Result: 3/4 hit — Uranus -3.31%, Kuiper Cliff -2.69%, Heliopause +4.66%. Termination shock missed at -6.28%. Monte Carlo p=0.1238 — null at pre-registered threshold. Pre-registration: OSF osf.io/3p2gb, DOI 10.17605/OSF.IO/3P2GB, registered 27 March 2026.

Pre-registration (GCNS confirmatory test): OSF osf.io/a72fp, registered 25 March 2026 before data access. Earth paper: Zenodo DOI 10.5281/zenodo.19035389. Source catalog: Henry et al. RECONS TOP100, recons.org/TOP100.