The Lucron Model: A Single-Scale Ontology for Space, Matter, Gravity, and Quantum Mechanics

We present the Lucron Model, a physical framework in which fundamental reality is a network of identical units called Lucrons. Each Lucron possesses intrinsic minimal properties---length, time, mass, charge, and action---that are the smallest non-zero values in every metric. The apparent absence of intrinsic properties at ordinary scales is an effect of scale, not a metaphysical absence. We show that a single-scale Lucron with scale \( \ell_L \) and coupling \( g_* \), together with the permutation symmetry \( S_3 \) of the bound-state ``candado,'' reproduces the following without fine-tuning: (i) the Planck scale, \( G = \ell_L^2 \); (ii) gauge unification with \( \alpha_{\rm GUT} = g_*^2/(4\pi) \approx 1/24 \); (iii) the Weinberg angle \( \sin^2\theta_W = 3/8 \) at the GUT scale; (iv) the electroweak hierarchy \( v/m_P = e^{-2\pi^2/g_*^2} \); (v) the electron hierarchy \( m_e/v = e^{-7/g_*^2} \); (vi) the Koide formula with \( \theta = 2/9 \) rad; (vii) the Cabibbo angle \( \sin\theta_C = \sqrt{m_d/m_s} \); (viii) the PMNS angles \( \theta_{23} \approx 45° \) and \( \theta_{13} \approx 8.5° \); (ix) the cosmological constant \( \Lambda \ell_P^2 = N^{-2/3} \approx 10^{-122} \) for \( N \sim 10^{183} \). We also identify where the model fails quantitatively: the CKM angle \( \theta_{23} \) (factor \( 1.4 \)), the CP phase \( \delta_{\rm CP} \) (factor \( 2.4 \)), and the PMNS angle \( \theta_{12} \) (factor \( 1.25 \)). These failures point to unresolved geometric details of the candado. We further show that the volume law \( V = v_0 \sum_i 1/c_i \) reproduces \( \Lambda \)CDM at the cosmological level, yielding \( \chi^2 = 12.8 \) against DESI DR2 BAO, identical to \( \Lambda \)CDM. With two fundamental parameters \( (\ell_L, g_*) \) and one symmetry (\( S_3 \)), the model accounts for approximately twenty dimensionless constants, a significant reduction over the Standard Model's nineteen free parameters.