On the Origin of Energy

This paper is grounded in a single foundational principle: energy is always conserved. We propose that energy is the primordial basis of all nature and the universe — the one quantity that is universally preserved across every scale and every phenomenon. This work is motivated by the desire to understand that foundation, and to ask whether all known forces and structures might emerge from it. We propose a geometric theory — the Origin Of Energy (OOE) — in which all forms of energy (mass, electromagnetism, strong nuclear force, weak nuclear force, and gravity) are derived from a single energy conservation equation: E_total(θ, φ, ρ) = E_family·cos²θ − k·cosφ / ρ − k·sinφ_A·sinφ_B / ρ_AB − (3/4)·k·cos²θ / ρ³ + p²/2m = constant Here θ is the mass angle, φ is the charge angle, and ρ is the spatial scale. These three variables are fully determined by the vertex geometry of two dual regular tetrahedra embedded in three-dimensional space. The framework reproduces the lepton mass spectrum via the Koide relation (error 0.014%), the gravitational constant G (error 0.011%), the deflection of light by the Sun (error 0.05%), and the W boson mass (error 0.52%). Several results — particularly in gravity and the strong nuclear sector — are exploratory in nature; this is stated explicitly throughout. [v2 update] The fine-structure constant α = 1/137.03598 is derived from OOE tetrahedral geometry via 24πα(1 + 3α/2n + α²/n) = arccos(23/27), n = ln(2/α). Error 0.000012% — within experimental uncertainty (±0.000021%). α is no longer an empirical input; it emerges from the dual tetrahedron structure (Section 2A). [v2.1 update] Added exact geometric derivation of arccos(23/27) via the cosine triple-angle identity: arccos(23/27) = 3·arccos(1/3) − π. This confirms that the electron solid angle Ω — and through it α — arises from three quark phase rotations. Numerical verification: difference 3.3×10⁻¹⁶ (machine precision). This is an exact trigonometric identity, not a numerical fit (Eq. 2A.1b, Section 2A.1).