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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

Authors: Davis, Raymond;

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

Abstract

This record contains two notebooks comprising the stellar neighbourhood analysis component 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/Hipparcos 58-system catalog within 20 light-years. KDE with bandwidth 0.8 ly and volume correction detects 4 peaks at 4.43, 11.90, 15.06, and 19.20 ly. 3/4 shells align within ±0.5 ly. p=0.0285 vs random geometric progressions, p=0.0314 vs random positions (Monte Carlo N=100,000). Anchor specificity test: of 11 solar system anchors tested, only Neptune (30.069 AU) and the Kuiper Belt outer edge (~50 AU) return p0.75. 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. Pre-registration: 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.

Keywords

Physics, Astronomy, phi ratio, golden ratio, stellar density, solar neighbourhood, RECONS, Neptune, Kuiper Belt, Ripley K-function, KDE, shell alignment, spatial statistics, pre-registered, Project Phi Grid, Solar astronomy

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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