Emergence of Spacetime and Inertia from 𝐸8 Admissibility Constraints

We investigate the minimal structural conditions that any physically admissible substrate must satisfy when reality is modeled as a discrete, locally updated, and composable system. Rather than postulating spacetime, quantum dynamics, or action principles, we impose only three pre-physical requirements: irreversibility of update ordering, boundedness of admissible histories, and closure under composition. We show that these admissibility conditions alone induce a nontrivial global ordering structure. In particular, the absence of admissible inverses for nontrivial update sequences forces a collapse of effective ordering to a single temporal dimension. Time therefore emerges as an intrinsic property of admissible composition, rather than as an externally introduced parameter. We further demonstrate that irreversibility and bounded history impose strong global constraints on allowable substrates. Among broad classes of discrete lattices, only a restricted subset remains admissible. In this framework, an effective four-dimensional 𝐷4 lattice arises as an admissible projection target, while alternative candidates are excluded by violations of ordering consistency, composability, or isotropy. Within this admissible setting, observation acquires a precise structural interpretation. Measurement corresponds to an irreversible informational interaction with the substrate, necessarily modifying admissible histories. This provides a natural explanation for the fundamental asymmetry of observation without invoking additional postulates. Our analysis assumes no specific interaction dynamics. Instead, admissibility precedes dynamics: the space of possible physical laws is constrained in advance by structural consis- tency. From this perspective, spacetime dimensionality, temporal structure, and constraints on interaction are not fundamental assumptions, but emergent consequences of irreversibility and composability in discrete informational substrates.