What question did this study set out to answer?

The central aim is to derive a unified theory of all physics from a single axiom using crystal dynamics and tessellation.

May 24, 2026Open Access

Crystal Dynamics and the Ultraviolet-Complete Unified Theory

Key Points

The central aim is to derive a unified theory of all physics from a single axiom using crystal dynamics and tessellation.
A unique binary oscillation field in four spacetime dimensions was used as the core axiom.
The 24-cell tessellation was established as the structure of spacetime, leading to derivations of fundamental physics principles.
Nine falsifiable predictions related to particle physics and gravity were proposed based on the established theory.
All physical quantities were derived with no free parameters, including explicit values for Newton's constant and graviton characteristics.
Nine predictions were articulated, such as the exact neutrino mass ratio and potential observations at various high-energy facilities.
The classification of Standard Model particles and the complete neutrino sector were achieved through geometric and group-theoretic frameworks.

Abstract

We present a UV-complete unified theory of all known physics derived from a single axiom: a binary oscillation field in four spacetime dimensions. The unique self-dual regular tessellation of R⁴ — the 24-cell honeycomb 3, 4, 3, 3 — emerges from this axiom and constitutes spacetime itself (not merely a model of it). Its Wilson-loop correlation matrix Q, with spectrum +8³, +4¹2, 0²7, -2²4, -4⁶, generates the complete Standard Model Lagrangian plus general relativity through a single spectral action SQ. Building on Papers 1–3, Paper 4 closes all deferred derivations and establishes three new layers of structure. Dynamics: the Skyrme coupling β = π²/8 is proved from the 24-cell packing fraction; Newton's constant is fully derived with zero free parameters as G = ℏc/ (mSG² φ¹91) where 191 = nᵥ·z − 1; the graviton is identified as the harmonic zero mode of the crystal graph Laplacian; and background independence is established by showing the D4 root lattice satisfies R_μν = 0. Spectrum: the group (Z/24Z) * ≅ (Z/2) ³ classifies all Standard Model particles by three binary quantum numbers; the boson/fermion split is proved three independent ways (Weyl group, algebraic number theory, Legendre symbol) ; and the complete neutrino sector is derived geometrically from the three non-gauge distance graphs G2, G3, G4 of the 24-cell, with masses m_ν2 = (α/π) ·mₑ²/ (mW·cosθW) = 8. 62 meV (−0. 65%) and Δm²₃1/Δm²₂1 = Nc (z + Nc) = 33 both proved from first principles. Moonshine and quantum gravity: the six-step constructive chain 24-cell → D4 → Golay → Leech → Conway → Monster establishes the Monster group M as the symmetry group of the crystal quantum gravity, with Tr (Q³) = j (i) = 1728 (exact), 744 = nᵥ · MF5, and the graviton-stimulated-emission gain G = z²/ (z² − M3²) = 64/15 identified as a Monster-invariant. In total, 28 physical quantities are derived from the crystal numbers Nc, nᵥ, z, L4, F5, M3 and the single physical bridge mSG = 134. 59 MeV with no free parameters. Nine falsifiable predictions are stated, including Δρ = 0 exactly (testable at FCC-ee), λH = (1/6) cos²θW (HL-LHC), Majorana neutrinos (0νββ experiments), and the neutrino mass ratio = 33 (a group-theoretic integer, unambiguous).

Crystal Dynamics and the Ultraviolet-Complete Unified Theory

Key Points

Abstract

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