I write software and do mathematics in Hengelo. Most of my work involves systems for small and mid-sized manufacturing companies in Twente. Some of it involves number theory, machine learning, and the places where they unexpectedly overlap.
The research started with the Hecke algebra at level 163 — the largest class-number-one Heegner prime. A singular 3-adic factor connected modular forms, error-correcting codes, and quantum information through exact computations. That work led to a broader program connecting discrete Hodge theory on byte streams, Kolmogorov complexity of machine-verified proofs, and the algebraic theory of dual numbers — all held together by one axiom: ε² = 0.
Four papers forming a loop: empirical measurement of byte streams reveals algebraic structure, which is formalized and proved in Lean 4, whose proof terms are measured for Kolmogorov complexity, and the complexity measurement validates the empirical starting point. Plus two companion papers on compression and the 𝓕-functionaal.
6 papers · 5 PDFs · Program overview · All papers →
Fourteen papers on one relation. A trace inequality, a syndrome algebra, a module classification, a singularity category, a Hamming code, a quantum stabilizer code, a finite-state automaton with confinement, a drift rate theorem, a census across all prime levels, and three negative results that bound the theory.
14 papers · 11 PDFs · All papers →
Self-contained results from the research program. The NilSquare hub (17 theorems from one axiom), Church-Rosser in three lines, Hodge decomposition of actor-critic RL, PPM Bayes-optimality, the universal beta function, spectral phylogeny, and the Conway compression framework.
9 notes · All notes →
Irreversibility depth D*, harmonic cycles, and running coupling g(D) for 49 languages. PCA on 8 topological invariants. Cross-linguistic phylogeny with Sprachbund detection. Cross-domain comparisons (music, protein, code).
49 language pages · 5 SVG charts · Browse atlas →
Eigenvalue spectra, local ring theory, resolvent curves, singularity categories, pair algebras, 3-adic scans. 51 JSON datasets with analysis notes.
54 data pages · 14 plots · Browse data →
164 prime levels classified. 95 smooth, 39 cusp, 17 split node, 13 non-split node.
MCTS on enwik8. Guarded tree search over model-choice sequences beats single-model baselines on synthetic mixed corpora. Does it beat PPM-C on real data?
BGC0 exclusion gap. The Zig runtime achieves 2.18 bpb on 2MB of enwik8 — 0.02 bpb behind the Python PPM-C. Closing this gap via the correct exclusion blend would produce a single binary matching the headline compression number.
Anti-dispersion at scale. Strong harmonic cycles die first under depth filtration, but the evidence is based on 30 n-grams. Needs thousands of n-grams across multiple corpora and languages.
The escape-nilpotency connection. The PPM-C escape mechanism has nilpotent structure analogous to ε² = 0. The analogy is stated, not proved.
Hodge at transformer scale. The three-layer architecture operates at 260K parameters. Whether harmonic efficiency survives with enough capacity to learn the decomposition implicitly is untested.
Other Hecke levels. The census finds 30+ singular factors at prime levels up to 1000. Each is an open problem: automaton, drift rate, gate signature.