Finding and characterizing structure in complex systems, with the methodology chosen to fit the data. Each subdomain below is one self-contained piece of work, sorted by what it actually is rather than what field it touches.
*.briansheppard.com · static / S3 + CloudFront · updated 2026-04-25
I'm a data analyst who works on the structure of complex systems. The recurring habit across these projects is the same: identify the structure of the data first, test what is invariant under transformation, and choose the method that fits the object rather than picking the object to fit a method. The domains differ; the methodology doesn't.
This work is developed in collaboration with frontier AI systems. Conversation logs are archived alongside code where relevant; wins and losses are shared between me and the model. I treat the collaboration as a methodological detail — like “the code is in Python” — not as a headline.
The projects below are sorted into the categories that honestly describe them: research findings (verifiable contributions, with preprints linked under Papers), capability probes (studies of what current tools — including frontier AI systems — can produce when pointed at a hard problem), and infrastructure tools (artifacts other people can run). Anything that didn't reach one of those bars stays in its GitHub repo and isn't promoted here.
The posture across all of it is exploratory rather than argumentative. Each project attempts to point an honest method at something I find interesting and reports what it actually returns. The goal is to look carefully, not to defend a predetermined thesis. I do this work on my own time because I want to, and I would like to apply the same instinct at a larger scale.
The Lie algebra generated by the three pairwise interaction Hamiltonians of the planar Newtonian three-body problem has dimension sequence 3, 6, 17, 116 at the first four bracket levels — invariant across mass ratios and identical for the 1/r and 1/r² potentials, while the integrable harmonic case stabilizes at 15. The dashboard hosts the symbolic sweeps, composite-potential scans, and helium-atlas comparisons that produced and verified the result. Preprint linked below.
Multi-method differential feature detection on LiDAR digital elevation models: an exhaustive sweep across decomposition and upsampling combinations surfaces terrain features invisible in the raw DEM. Built for archaeological prospection on the Hopewell Road and Newark Earthworks; generalizes to any DEM. Companion site exposes the algorithm zoo, parameter-sweep videos, UMAP atlas, and a Blender flythrough of the residual space.
A study of how current AI systems reason about speculative general relativity, using the Alcubierre warp metric as the test problem. The dashboard collects the artifacts the probe produced — a κβ/C scaling argument, six adjacent metric slices, a Fell–Heisenberg multi-mode shift, and an independent Warp Factory MATLAB reproduction — and labels them as exploratory output, not physics findings. The object of interest is the reasoning trace, not the warp drive.
A five-step agentic pipeline (parse → reason → drug-interaction check → RAG over guidelines → synthesize) wrapped around an open-weight medical model. A study of how a frontier open model behaves in a clinical-decision-support shape — explicitly a probe of the architecture, not a clinical tool, not for patient care.
Single pane of glass for my personal AWS estate: region cards, canary status, and rolled-up infrastructure ground-truth across deployed services. Auto-refreshing terminal-style dashboard — useful when something looks off and I want one place to confirm it.
Interactive D3.js visualization of how map projections distort area, shape, and angles. Pick a projection, drag a shape across the globe, and watch the transform in real time. Educational rather than novel — a concrete intuition pump for an idea most people only encounter as a meme.
Exact symbolic computation of the Lie algebra generated by the three pairwise interaction Hamiltonians of the planar Newtonian three-body problem under the Poisson bracket. Proves the dimension sequence 3, 6, 17, 116 for the first four bracket levels and a numerical lower bound d(4) ≥ 4,501, establishing super-exponential (infinite Gelfand–Kirillov) growth. The sequence is invariant under mass-ratio changes and identical for the Newtonian (1/r) and Calogero–Moser (1/r²) potentials, while the integrable harmonic potential stabilises at dimension 15 — exposing a sharp structural dichotomy driven by the singularity class of the potential rather than integrability.
A topological-complexity approach to coordinating two robots on a figure-eight track without collisions. Configuration-space invariants relate motion-planning instabilities to the topology of the workspace; we show the topological complexity of the problem is 3 and construct an explicit algorithm with three continuous instructions. Published in the PUMP Journal of Undergraduate Research, vol. 6, 224–249.