Project Phi Grid — PhiGridUniversity.com

The Hypothesis

What is Phi Grid?

Project Phi Grid tests a precise, falsifiable hypothesis: that the golden ratio φ structures the geometry of natural systems at multiple scales — from Earth's surface to the stellar neighbourhood — at levels of statistical significance that cannot be explained by chance.

φ = (1 + √5) / 2 The Golden Ratio ≈ 1.6180339887…

The golden ratio φ appears throughout nature — in nautilus shells, sunflower seeds, and galaxy spirals. Phi Grid asks whether this isn't coincidence: whether φ actually governs how structures are spaced at cosmic scales.

We test this with real data, pre-registered hypotheses, and rigorous statistics. If φ-shells anchored at Neptune predict where nearby stars cluster — and no other anchor does — that demands explanation.

The core test: KDE of radial stellar distances (volume-corrected, bandwidth 0.8 ly) against φ-ratio geometric progressions rₙ = r₀ × φⁿ. Monte Carlo null distributions constructed from N=100,000 random geometric progressions and random position sets.

Anchor specificity: 11 candidate anchors tested. Only Neptune (30.069 AU) and Kuiper Belt outer edge (~50 AU) return p<0.05. Inner solar system bodies, heliopause, and Oort Cloud all return p>0.75. Pre-registration: OSF osf.io/a72fp.

φ-Shell Series from Neptune

r₀ = 1.663 ly
r₁ = r₀ × φ = 2.692 ly
r₂ = r₁ × φ = 4.355 ly
r₃ = r₂ × φ = 7.047 ly
r₄ = r₃ × φ = 11.402 ly ✓
r₅ = r₄ × φ = 18.448 ly
r₆ = r₅ × φ = 29.850 ly
r₇ = r₆ × φ = 48.298 ly ✓

Shells predicted purely from Neptune's orbital radius and φ. No free parameters.

Statistical Results

Three papers.
What we found.

Each result is accompanied by its p-value, dataset, and pre-registration record. Null results are reported alongside positive ones.

Earth Paper — φ-Grid at Geophysical Sites

A 16-petal φ-ratio grid anchored at the Wilkes Land mascon aligns with major geophysical and archaeological sites worldwide. Monte Carlo N=10,000. Submitted for independent review.

p = 0.0102

Stellar Neighbourhood — φ-Shells from Neptune

φ-ratio shells anchored at Neptune (30.069 AU) align with stellar density peaks in the RECONS/Hipparcos 58-system catalog within 20 ly. KDE detects 4 peaks; 3/4 shells match within ±0.5 ly. N=100,000.

p = 0.0285

Gaia GCNS Confirmatory Test — Pre-Registered

Pre-registered extension to 1,148 Gaia sources within 50 ly. 2/8 shells matched at 50 ly — below the pre-registered significance threshold. Honest null result: the Section 13 signal does not survive at 50 ly. Partial concordance (0–20 ly zone) under investigation.

p = 0.176 — NULL

Scientific Integrity Note

The Gaia null result is reported prominently and without spin. Pre-registered science means the hypothesis is tested honestly — a null result is a result. The partial 0–20 ly concordance is currently under investigation as a focused replication study.

Anchor	Distance (AU)	p-value	Significant?
Mercury	0.387	> 0.75	No
Venus	0.723	> 0.75	No
Earth	1.000	> 0.75	No
Mars	1.524	> 0.75	No
Jupiter	5.203	> 0.75	No
Saturn	9.537	> 0.75	No
Uranus	19.191	> 0.75	No
Neptune	30.069	0.0285	Yes ★
Kuiper Belt outer edge	~50	0.0285	Yes ★
Heliopause	~120	> 0.75	No
Oort Cloud (inner)	~2,000	> 0.75	No

Research Arc

From Earth to the
stellar neighbourhood.

February 2026

Earth Paper — φ-Grid Geophysical Analysis

16-petal φ-ratio grid anchored at Wilkes Land mascon. Monte Carlo N=10,000, p=0.0102. First publication of the Phi Grid methodology.

Zenodo DOI: 10.5281/zenodo.19035389 →

March 2026

Section 13 — Stellar Neighbourhood (RECONS/Hipparcos)

φ-shells from Neptune tested against 58-system catalog within 20 ly. p=0.0285. Anchor specificity test across 11 solar system bodies: only Neptune/Kuiper significant.

Zenodo DOI: 10.5281/zenodo.19241818 →

25 March 2026

Pre-Registered Gaia GCNS Confirmatory Test

Hypothesis pre-registered on OSF before any Gaia data downloaded. 1,148 sources within 50 ly. Null result at 50 ly (p=0.176). Partial 0–20 ly concordance documented. Null reported openly.

OSF Pre-registration: osf.io/a72fp →

27 March 2026

Solar System φ-Shell Pre-Registration — OSF

Pre-registered confirmatory test of φ-shells anchored at Neptune (30.069 AU) against 4 solar system boundaries within ±5% tolerance. Significance threshold p<0.05. Registered before any analysis is run.

OSF Pre-registration: osf.io/3p2gb — DOI: 10.17605/OSF.IO/3P2GB →

30 March 2026

Archaeological Extension — Three-Dataset Analysis Published

Standalone paper deposited to Zenodo covering three parallel Monte Carlo analyses: UNESCO World Heritage Sites (p = 0.0056, significant), curated ancient monuments exploratory test (p = 0.085, reported in full), and Megalithic Portal analysis withdrawn on open-access grounds. Göbekli Tepe returns triple angular/radial alignment (Wilkes 0.18°/1.91%, Hiawatha 0.97°) — HIGH INTEREST.

Zenodo: doi:10.5281/zenodo.19341794 →

Upcoming

Focused 0–20 ly GCNS Replication (Binaries Collapsed)

Direct replication of Section 13 on Gaia GCNS data with binaries collapsed via gcns.resolvedss. 83 systems. Methodology-matched comparison.

Upcoming

Negative Result Paper — RNAAS / A&A Letters

Pre-registered null results are publishable. Earth paper + Section 13 + Gaia confirmatory null = complete, honest research arc.

New Publication — Pure Mathematics

Why does the golden ratio
keep appearing?

The golden ratio φ ≈ 1.618 shows up across mathematics and physics in ways that seem unrelated — in the geometry of pentagons, in the stability of planetary orbits, in the structure of quasicrystals, and in the algebra of certain mutation sequences. A natural question is whether these appearances share a common origin or are simply coincidences that happen to produce the same number.

The Two Appearances

The first appearance is in cluster algebras — a branch of pure mathematics where a simple mutation rule, applied repeatedly to a pair of variables, generates a sequence whose ratios converge to exactly φ.

The second appearance is in KAM theory — the mathematical study of stable orbits in dynamical systems, where φ marks the boundary between order and chaos. The golden-mean torus is the last stable structure before a dynamical system breaks down into unpredictable behavior.

The Bridge

Pentagon mutation graph

↓ ratio map F(r) = 1 + 1/r

Fibonacci convergents p_n/q_n → φ

↓ continued-fraction map

Rotation number ω* = 1/φ

↓ Fibonacci-convergent rescaling

Greene–MacKay operator at ξ*

All four arrows are the same generator of PSL(2,ℤ): the Fibonacci matrix M.

The Result

We prove that these two appearances of φ are not a coincidence. Both are governed by the same underlying object: the Fibonacci matrix, acting on continued fractions under the modular group PSL(2,ℤ). The pentagon mutation graph is the discrete skeleton; the KAM renormalization operator is its smooth dynamical realization. One theorem connects them, and the bridge is the continued-fraction expansion [1;1,1,1,…] — the mathematical fingerprint of φ itself. A single open problem remains, stated precisely in the paper as Conjecture 1. The ingredients for its proof exist in the literature. The theorem connecting them has now been written down for the first time.

Read the Paper → Zenodo

Archaeological Extension

Ancient monuments
and the φ-grid.

Three independent Monte Carlo analyses test whether the dual-anchor φ-grid — anchored at the Wilkes Land crustal gravity anomaly and the Hiawatha impact crater — shows statistically significant spatial association with globally distributed ancient monuments.

0.0056 UNESCO analysis
p-value

3.47 Z-score
UNESCO test

87 UNESCO sites
tested

96 Grid nodes
48 per anchor

The same 16-petal φ-ratio grid used in the Earth paper is applied to ancient monument databases. The grid was not adjusted or optimised for archaeological data — it is applied unchanged from the geophysical analysis.

The most striking single observation is the triple angular/radial alignment of Göbekli Tepe — the world's oldest known monumental structure (~9600 BCE) — against both anchors simultaneously. Angular error from Wilkes: 0.18°. Radial error: 1.91%. Angular error from Hiawatha: 0.97°. All three values are within the pre-specified thresholds.

Göbekli Tepe falls 264 km from the nearest grid node — just outside the 200 km proximity threshold — and is classified HIGH INTEREST. Karahan Tepe (~9400 BCE), 46 km from Göbekli Tepe, falls at 290 km from the same node. The two oldest sites in the dataset cluster at the same node.

Analysis I — Pre-Registered

UNESCO World Heritage Sites

p = 0.0056 · Z = 3.47

87 cultural/archaeological UNESCO sites, globally distributed. 6 confirmed hits in 96 nodes at the pre-registered 200 km threshold. Monte Carlo N = 10,000, seed 42. Significant at p < 0.01. Result robust across threshold sensitivity (150 km: p = 0.0001) and land-only node analysis (p = 0.0018).

Analysis II — Exploratory

Curated Ancient Monuments

p = 0.085 · Z = 1.98

53 manually curated ancient monuments from peer-reviewed literature and open-access heritage databases (no Megalithic Portal data). 3 confirmed hits in 96 nodes. Not significant at p < 0.05. Reported in full as honest negative evidence. Göbekli Tepe and Karahan Tepe near-miss at 264–290 km from same node.

Analysis III — Withdrawn

Megalithic Portal Dataset

Withdrawn — open access

A pre-registered analysis using the Megalithic Portal global dataset (~50,000 sites) was withdrawn after contact with dataset owner Andy Burnham. The data cannot be used in published open-access research — incompatible with the project's CC BY 4.0 commitment. No results were produced. The withdrawal is documented transparently in the paper.

High Interest Finding

Göbekli Tepe — Triple Angular/Radial Alignment

Göbekli Tepe (37.22°N, 38.92°E; southeastern Turkey) is the world's oldest known monumental structure, with radiocarbon-dated enclosures at ~9600–8800 BCE — predating the Egyptian pyramids by 7,000 years. Less than 10% of the site has been excavated; ground-penetrating radar indicates at least 20 buried circular enclosures remain.

0.18° Wilkes angular error
(threshold ±2°)

1.91% Wilkes radial error
(threshold ±10%)

0.97° Hiawatha angular error
(threshold ±2°)

264 km From nearest node
(threshold 200 km)

Giza (Great Pyramid complex, ~2560 BCE) sits on the same Wilkes Petal 13 bearing as Göbekli Tepe at a different radial shell — a co-petal relationship between the world's oldest and most famous monument complexes separated by 7,000 years of history. No causal mechanism is proposed; this is reported as a geometric observation.

Confirmed Hit Sites — Photographs

Sites confirmed within the 200 km proximity threshold in Analysis I (UNESCO) and/or appearing as HIGH INTEREST near-misses across analyses. All photographs are public domain or Creative Commons licensed.

Göbekli Tepe

HIGH INTEREST · ~9600 BCE · Turkey

T-shaped limestone pillars, Göbekli Tepe, Şanlıurfa, Turkey. Wilkes angular error 0.18°, radial 1.91%; Hiawatha angular error 0.97°. 264 km from nearest node.

Karahan Tepe

Near-miss · ~9400 BCE · Turkey

T-pillars and carved anthropomorphic head, Karahan Tepe (Taş Tepeler project). 290 km from same node as Göbekli Tepe — oldest two sites in dataset cluster at same node.

Teotihuacan

Confirmed Hit · ~100 BCE · Mexico

Avenue of the Dead from the Pyramid of the Moon, Teotihuacan. 91 km from Wilkes P6 φ¹ node — closest confirmed hit in the dataset.

Yinxu / Anyang

Confirmed Hit · ~1300 BCE · China

Oracle bone storage pit, Yinxu (Yin Ruins), Anyang — Shang Dynasty royal capital. 119 km from Hiawatha P0 φ⁻² node, which also hits Longmen Grottoes (181 km) and Luoyang (149 km).

Easter Island

Confirmed Hit · ~800 CE · Pacific

Ahu Tongariki moai platform, Easter Island (Rapa Nui). 115 km from Wilkes P6 φ⁰ node — the same petal that reaches Teotihuacan at the φ¹ shell outward.

Divriği Great Mosque

Confirmed Hit · 1228 CE · Turkey

The Great Mosque and Hospital of Divriği, eastern Turkey — 43 km from Wilkes P13 φ¹ node, the closest confirmed UNESCO hit in the dataset. Arslantepe Mound (4th millennium BCE) is 126 km from the same node.

Longmen Grottoes

Confirmed Hit · 5th–8th c. CE · China

Fengxian Temple, Longmen Grottoes, Henan Province — 181 km from Hiawatha P0 φ⁻² node. The same node also hits Yinxu (119 km) and Luoyang Ancient Capitals (149 km) — three independent UNESCO sites within 200 km of a single node.

Neolithic petroglyphs, Jubbah, Saudi Arabia

Jubbah Rock Art

Confirmed Hit · Neolithic · Saudi Arabia

Neolithic and Bronze Age petroglyphs, Jebel Umm Sinman, Jubbah, Saudi Arabia — 90 km from Hiawatha P3 φ⁻² node. Al-Hijr (Madain Salih) falls 290 km from the same node.

Copán

Confirmed Hit · ~350 CE · Honduras

Hieroglyphic Stairway, Copán — Maya royal city, Honduras. 142 km from Hiawatha P9 φ⁻² node.

      All photographs are public domain or Creative Commons licensed (Wikimedia Commons). Statistical results are from peer-reviewed Monte Carlo methodology applied to UNESCO and open-access heritage databases. No causal mechanism between the φ-grid and site locations is proposed — the geometry is presented as a descriptive framework. Full methods, data, and code: doi:10.5281/zenodo.19341794
    

Visualisations

The geometry,
illustrated.

Conceptual illustrations showing the φ-ratio structure at three scales: Earth's surface, the solar system, and the extreme outer solar system boundary where the signal is detected.

Earth Paper

Planet Earth — φ-Grid Nodal Network

A 16-petal φ-ratio grid anchored at the Wilkes Land mascon overlaid on Earth's surface. The nodal intersections align with major geophysical and archaeological sites. Monte Carlo p = 0.0102. Illustration: conceptual.

Solar System — phi-resonant orbital spacing and emergent 3D phi ratio

Stellar Neighbourhood

Solar System — φ-Resonant Orbital Spacing

φ-ratio geometry extending from the inner solar system through the Kuiper Belt to Neptune. The research identifies Neptune's orbital radius (30.069 AU) as the anchor from which φ-shells predict stellar density peaks. Illustration: conceptual.

Extreme Outer Solar System — Kuiper Cliff and Heliopause Interaction Zone

Anchor Specificity

Extreme Outer Solar System — The Critical Boundary

The Kuiper Cliff (~50 AU) and Neptune's dynamical zone — the only region where φ-shell anchors return statistical significance (p = 0.0285). Inner planets, the heliopause, and the Oort Cloud all return p > 0.75. Illustration: conceptual.

      Note: All illustrations are conceptual visualisations generated for public communication purposes. Statistical results are from peer-reviewed methodology applied to RECONS/Hipparcos and Gaia GCNS catalogue data. See Zenodo papers for full methodology.
    

Is the golden ratio
encoded in space?

Navigate the φ-grid
from Earth to the stars.

What is Phi Grid?

Three papers.
What we found.

Only Neptune is significant.
11 anchors tested.

From Earth to the
stellar neighbourhood.

Why does the golden ratio
keep appearing?

Open access.
Every dataset, every result.

Ancient monuments
and the φ-grid.

The geometry,
illustrated.

Scientists, journalists,
and curious minds welcome.

Is the golden ratioencoded in space?

Navigate the φ-gridfrom Earth to the stars.

What is Phi Grid?

Three papers.What we found.

Only Neptune is significant.11 anchors tested.

From Earth to thestellar neighbourhood.

Why does the golden ratiokeep appearing?

Open access.Every dataset, every result.

Ancient monumentsand the φ-grid.

The geometry,illustrated.

Scientists, journalists,and curious minds welcome.

Is the golden ratio
encoded in space?

Navigate the φ-grid
from Earth to the stars.

Three papers.
What we found.

Only Neptune is significant.
11 anchors tested.

From Earth to the
stellar neighbourhood.

Why does the golden ratio
keep appearing?

Open access.
Every dataset, every result.

Ancient monuments
and the φ-grid.

The geometry,
illustrated.

Scientists, journalists,
and curious minds welcome.