A training step is usually a number that goes down on a plot. We make it a theorem. We exhibit a finite rational Kolmogorov–Arnold network whose evaluation, squared-error loss, and least-squares gradient are each a composition of a single primitive — the binary integer-arithmetic active pair, the smallest local rewrite...
The Institute for Applied Ontological Mathematics· Zenodo (CERN European Organi...· 0 citations
The boundary of the tetrahedron is a sphere, and a sphere has no boundary. We make the second fact a finite computation: over the two-element field, the boundary surface of a tetrahedron certifies its own closure by a local count — every edge lies in exactly two faces — rather than by any global topological argument. W...
The Institute for Applied Ontological Mathematics· Zenodo (CERN European Organi...· 0 citations
A proof strategy is an object with a shape, and the shape can be wrong before a single lemma is attempted. We study one such strategy for Goldbach's conjecture — the proposal to cover the even numbers by an expanding family of graphs on prime states, so that a spectral gap forces the count of prime-pair representations...
The Institute for Applied Ontological Mathematics· Zenodo (CERN European Organi...· 0 citations
A geometric research program of V. Veselov proposes to read curvature, a flow, and a spectral trace off a family of graphs built from the golden mean, and to reach — eventually — a bridge to the Riemann hypothesis. A program is not a theorem. We ask a sharper question: exactly how much of it is one? We answer by constr...
The Institute for Applied Ontological Mathematics· Zenodo (CERN European Organi...· 0 citations
AI-driven materials discovery has advanced rapidly, with projects such as Google DeepMind's GNoME identifying over 380,000 candidate stable crystals through graph-network predictions. Yet a persistent trust gap remains: surrogate models can hallucinate stability, and opaque screening pipelines make it difficult for dow...
The Institute for Applied Ontological Mathematics· Zenodo (CERN European Organi...· 0 citations
Trust in a proof is supposed to rest on a kernel small enough to read by hand. The formal-methods ecosystem has instead grown a dozen large, mutually opaque kernels—one per proof assistant—and now machine learning floods all of them with proofs and programs no human can eyeball. We report a working demonstration that t...
The Institute for Applied Ontological Mathematics· Zenodo (CERN European Organi...· 0 citations
We present Boundary (∂ ), a small interaction-style graph-rewriting language built from exactly four agent kinds and ve reduction rules. The kernel inherits the structural discipline of Lafont's interaction combinators (principal-port active pairs, one rule per unordered agent pair, local rewrites) while introducing ge...
The Institute for Applied Ontological Mathematics· Zenodo (CERN European Organi...· 0 citations
A chip is designed in software, yet the software we design chips in cannot say what a design means. Register-transfer text is written, transformed by optimizers on trust, and only afterward checked by simulating a sample of inputs; the meaning of the circuit is never an object the tools hold. The alternatives are few a...
The Institute for Applied Ontological Mathematics· Zenodo (CERN European Organi...· 0 citations
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