The Lucron Network: A Pre-Geometric Ontological Framework and Dictionary for Spacetime, Quantum Mechanics, and Gravity

We propose the Lucron Model, a pre-geometric framework in which spacetime emerges from a network of identical fundamental units (Lucrons), each carrying one bit of information capacity. Rather than treating Lucrons as geometric atoms with intrinsic shape, we conceptualize them as pre-geometric units of informational and interactional capacity, whose collective behavior gives rise to emergent geometry, time, and mass. We establish a dictionary mapping the network's primitive parameters (interaction weight \( w_L \), causal delay \( \tau_L \), and interaction range \( \ell_L \)) to macroscopic observables (\( \hbar, G, \Lambda \)). Within this calibrated framework, we demonstrate that the Planck length, Bekenstein--Hawking entropy, and Hawking temperature emerge as exact algebraic identities or consistency requirements of the discrete ontology. We explore qualitative mechanisms for fundamental physics: particles as Gaussian conformations, the Schrödinger equation via discrete diffusion, gravity as network deformation (yielding the geometric identity \( \delta \times \lambda = \ell_P^2 \)), and a topological classification of the Standard Model. We explicitly address three ontological tensions: (1) the emergence of Lorentz invariance from a discrete substrate, (2) the conservation of information during cosmological phase transitions, and (3) the compatibility of irreversible diffusion with unitary quantum mechanics. The framework yields two independent, falsifiable predictions: a strict lower bound for black-hole masses (\( M_{\min} \approx 3 \times 10^{22} \) kg) and a bounded cosmological drift of the fine-structure constant (\( |\dot{\alpha}/\alpha| \sim 10^{-18} yr^{-1} \)). We explicitly delineate the boundary between postulates, algebraic identities, qualitative mechanisms, and genuine predictions, offering the model as a structured research programme for quantum gravity.