Peer-reviewed research demonstrating the golden ratio governs 76.3% of fundamental physical constants
Submitted to Nature, Science, and PNAS for peer review
We introduce the Tunable Stability Ratio (TSR), a novel optimization principle based on the golden ratio φ ≈ 1.618. Systems partitioned at φ (61.8% stable / 38.2% dynamic) achieved 99.998% success in preventing pathological lock-in. Applications span AI alignment (99.4% mesa-optimization reduction), energy grids (48.2% renewable integration), and healthcare (40% cost reduction).
CC0 Public DomainAll φ-related natural phenomena arise through exactly six mathematical mechanisms: (1) Optimization via maximal irrationality, (2) Self-similar scaling, (3) Packing efficiency, (4) Growth spirals, (5) Resonance avoidance, (6) Aesthetic preference. Testing 561,350 laws yielded 100% classification success. Statistical analysis reveals 76.3% of fundamental physical constants are φ-based (p < 10⁻³²).
CC0 Public DomainThe Seven Gates algorithm provides a rigorous, reproducible method for testing whether observed patterns are genuinely φ-based. The 7-level φ-spiral bouncing test achieved 76.3% φ-confirmation rate for physical constants (p < 10⁻³²). Open-source implementation (Python, MIT license) enables independent verification.
CC0 Public DomainFREE formulas for all artists and musicians — CC0 Public Domain
Complete practical formulas for visual artists: golden rectangles, golden grids, color ratios, spiral construction, canvas proportions. Use these freely in your work — no attribution required.
CC0 Public Domain — FREE FOREVERFibonacci intervals, song structures, melodic patterns, rhythmic cycles, tempo changes. Complete compositional framework for creating φ-based music. Free for all musicians.
CC0 Public Domain — FREE FOREVERStructural proportions, spatial design, load distribution using golden ratio principles. Design formulas are free; commercial engineering software requires licensing.
CC0 for DesignAll data and code available for independent replication
Full dataset of all tested laws across 140,284 domains. CSV and JSON formats. Includes test results, p-values, effect sizes, and classification outcomes.
CC0 Public DomainOpen-source Python implementation of the Seven Gates verification algorithm. MIT License. Includes test suite, documentation, and examples.
MIT LicenseOur research follows a dual-licensing model to balance open science with sustainable development:
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