Research Programs
I work on three problems that look different on the surface but use the same math underneath: gauge fields, renormalization, and topology. Here's what each one is about.
Octophysics is a Rust library for division algebra approaches to particle physics. The central idea: the Standard Model gauge group SU(3)×SU(2)×U(1) isn't arbitrary. It falls out of octonionic structure when you build up through Clifford algebra chains.
Everything is verified computationally to machine precision (<10−10). The Weinberg angle comes out to sin²(θW) = 3/8 at the GUT scale, three fermion generations emerge from S₃ family symmetry, and Spin(10) grand unification drops out of the sterile neutrino stabilizer. 494 tests pass.
Clifford Algebra Chain
Cl(6) → Cl(8) → Cl(10) construction with exact algebraic verification of SM representations.
G₂ Lattice Gauge Theory
Quantum simulation infrastructure with glueball spectrum extraction and topological charge measurement.
494 Validated Tests
Tests cover octonion algebra, Jordan algebras, Peirce decomposition, and lattice observables.
Exceptional Lie Algebras
G₂, F₄, E₆ trajectory following Dray-Manogue-Wilson exceptional algebra tower construction.
Papers in Preparation
Writing up the review paper now. Targets: arXiv and a journal submission covering the Cl(6) through Cl(10) construction.
EmbryoSim models embryonic development across five biological scales, using the same gauge theory and fiber bundle math from Octophysics but applied to cells and tissues instead of quarks.
It starts at the quantum level (Layer 0) and coarse-grains upward through molecular, cellular, tissue, and organism scales. Each layer connects to the next via renormalization group transforms, so you don't lose the physics that matters at each scale. 46 integration tests cover everything from Turing pattern formation to full gastrulation simulations.
5-Layer Architecture
Quantum (1–10Å) → Molecular (1–100nm) → Cellular (1–100μm) → Tissue (0.1–10mm) → Organism (1–100mm).
Active Nematic Dynamics
2D/3D topological defect detection, tracking, and annihilation with Q-tensor field evolution.
Bioelectric Networks
Gap junction gating with Vmem-morphogen coupling, Nernst/GHK equations, and prepatterning.
Active Inference
Free energy principle drives tissue growth and morphogenetic decision-making at the tissue scale.
Persistent Homology
Topological invariants track pattern evolution through sublevel and Vietoris-Rips filtrations.
46 Integration Tests
Turing patterns, nematic defect annihilation, gastrulation, adaptive timestep, and checkpoint resume.
Papers in Preparation
The framework paper is in progress. Will cover the 5-layer architecture and the RG bridging between scales.
Entronomy throws out subjective utility and replaces it with information geometry. Economic value becomes a KL-divergence: V(θ) = −DKL(p(O|θ) || p(O|θeq)). Same gauge theory and Fisher information math as the other two projects, different domain.
I've tested this on FRED macroeconomic data, FX markets, and equity panels. The sloppy spectrum structure is there in all five countries I checked (R² > 0.94). Crisis detection hits 100% precision after calibration, with the 2008 GFC showing up in the eigenvalue spectrum 17 months early.
Sloppy Spectrum Confirmed
7-variable US panel: R² = 0.97 with 2.8 decades eigenvalue spread. Universal across 5 countries (all R² > 0.94).
Crisis Detection
100% recall, 100% precision (F1 = 1.0) after calibration. Pre-crisis dimension drop detected 17 months before GFC.
Gauge Structure Validated
7-currency FX Wilson loops confirm flat connections. Independent validation across FRED and ECB cross-rates.
Fisher-Optimal Portfolios
Outperforms Markowitz at short estimation windows. Information-geometric Kelly criterion for optimal bet sizing.
260 Passing Tests
8 crates covering Fisher-Rao manifolds, homeostasis inference, gauge connections, critical phenomena, and empirical pipelines.
3 Research Papers
Sloppy spectra in macro data, Fisher-optimal portfolios, and empirical gauge structure in currency markets.
Papers in Preparation
Three papers in draft: sloppy spectra in macro data, Fisher-optimal portfolios, and gauge structure in FX markets.
One Mathematical Framework, Three Domains
The same math keeps showing up. Gauge connections describe how things relate across positions. RG tells you what survives when you zoom out. Topology tells you what can't be smoothly deformed away. These aren't metaphors -- they're the actual computational tools in all three codebases.
I think that's because the underlying problem is the same: how does structure at one scale produce structure at another? Whether you're asking that about quarks, embryos, or currency markets, the math doesn't care.