Investigating the thermodynamic and computational constraints of discrete manifolds and sub-quadratic architectures.
Abstract: This volume collects the first five papers of The Discrete Ontology, a framework that replaces the continuous spacetime manifold of standard physics with an irreducibly discrete, information-theoretic simplicial complex governed by strict holographic bounds. Beginning from five foundational axioms—Spatiotemporal Discreteness, Topological Mass, Holographic Interfaces, Landauer Reversibility, and the Geometric Projection Tax—the framework derives the fundamental constants and particle phenomenology of the Standard Model as deterministic geometric consequences of projecting high-dimensional informational defects across a discrete macroscopic lattice.
The series analytically retrodicts the fine-structure constant (α ≈ 1/137.036), the proton-to-electron mass ratio (µ ≈ 1836.152), the neutrino mass scale, and the inflationary e-fold count (N = 63.26) entirely from fundamental geometric constraints. Furthermore, it establishes the Generalized Uncertainty Principle, resolves the Muon g-2 anomaly, and provides falsifiable predictions for cosmological void dynamics and the topological stability limits of massive particles.
Status: Prepublication Review. (Includes Papers I–V).
Abstract: This volume collects the final three papers (VI–VIII) of The Discrete Ontology, culminating the framework's replacement of continuous quantum fields with discrete infodynamic routing bounds. Building directly upon the holographic foundation established in Volume I, this volume formally discretizes the continuous affine connection of differential geometry to mathematically derive the remainder of the Standard Model particle spectrum.
This volume analytically derives the bare, tree-level Weinberg mixing angle, Sargent's rule for particle decay, the bare quark mass spectrum, and the resolution of the CODATA fine-structure constant anomaly. Finally, by formalizing the Discrete Christoffel Error Tensor, this volume demonstrates that elementary particles are the localized processing latency of irreducible geometric remainders, and uniquely derives the macroscopic mass limits of the W (80.4 GeV) and Z (91.2 GeV) gauge bosons strictly from the structural fracture thresholds of the local manifold.
Status: Prepublication Review. (Includes Papers VI–VIII).
Abstract: The continuous metrics of General Relativity predict an inherently smooth, scalar Hubble flow, whereas the Discrete Ontology framework explicitly bounds spatial expansion with local thermodynamic limits. Because the Bekenstein Bound prohibits node generation in thermal saturation, the DO framework dictates that spatial expansion natively shuts off inside dense galaxy clusters, generating new spatial volume exclusively inside deep cosmic voids.
This addendum integrates Discrete Topological Expansion with linear perturbation gravity and evaluates the resulting kinematic predictions against the empirical Cosmicflows-3 (CF3) dataset. By shielding non-linear virialized superclusters from artificial linear approximations via a strict local phase-drag threshold, the Discrete Ontology model successfully pierces the intrinsic lognormal distance noise floor of the CF3 catalog. Operating with zero Bayesian statistical priors, the discrete structural framework systematically corrects macroscopic bulk flows and achieves a 9% relative error reduction over the standard continuous GR baseline.
Status: Experimental Validation / Framework Addendum.
[ DOWNLOAD VALIDATION PAPER ]Abstract: The current Artificial Intelligence paradigm relies almost exclusively on dense matrix mechanisms, a system mathematically constrained by the quadratic O(N²) computational and memory complexity of standard attention. As sequence lengths scale toward millions of tokens, the industry is colliding with a fundamental thermodynamic and Von Neumann memory wall.
This project implements a novel structural architecture directly inspired by the topological limits of the physical universe as derived in the Discrete Ontology framework. By mapping sequence logic onto continuous-space topological boundaries and bounding memory retrieval with strict thermodynamic limits, the architecture shifts global informational capacity from an O(N²) dense matrix to a highly optimized, deterministic state-space manifold. This development establishes strict sub-quadratic algorithmic bounds for recursive semantic deductions. Furthermore, the underlying structural logic provides a natively interpretable, mathematically rigid foundation that scales seamlessly from silicon emulation to future non-von Neumann hardware environments, bypassing the classical attention bottleneck.
Status: Proprietary Architecture / Grant Allocation Phase.