The 3-4-5 Pythagorean triangle predicts material properties, particle masses, and fundamental constants—all from pure geometry.
From the unique properties of the 3-4-5 triangle (the only primitive Pythagorean triple with inradius r=1), the EiG framework derives 70+ material properties, 27 Standard Model parameters, and bridges the Planck scale to everyday matter—using exact rational fractions with no adjustable parameters.
"Energy gives Information persistence. Information gives Energy purpose."
Energy and Information are the only fundamental properties. Their gradient—the tension between them—determines what becomes coherent, structured, observable. Below the threshold of discernibility, reality doesn't vanish. It simply hasn't resolved yet.
The Qrel mapping places every environment—from cosmic voids to semiconductors—on a single continuum derived from first principles. Where you sit on this curve determines how energy and information interact locally.
The 101 curve: Cosmic voids (left) through intergalactic medium, vacuum, atmosphere, liquids, glass, crystals, to semiconductors (right). Normalized effective speed of information flow (crel) decreases with increasing density.
Gravity, light, nuclear forces, the emergence of life—all expressions of the same underlying dynamic. Not separate phenomena requiring separate explanations.
Resolves the vacuum energy catastrophe. Aligns Hubble constant measurements. Derives the fine structure constant from geometry alone.
Detects structural failure before it becomes visible. Reveals subsurface features from surface signatures alone. Monitors processes in real-time.
The same ΔEi metric reveals structure across radically different physical systems.
Two interactive 3D visualizations of the 120° structure. Explore the true geometry of the elements.
Explore visualizations →The core axiom in plain language. Energy, Information, and the gradient between them.
Read more →Practical applications in NDT, welding analysis, materials science, and beyond.
See applications →The formal 9 Laws framework, preprints, simulation code, and OSF publications.
View papers →Crawford's Postulate is under active development. If you work in physics, materials science, NDT, or origin-of-life research and see something here—reach out.
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