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, with two exceptions noted on their cards · updated 2026-10-02
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. Runs as a Hugging Face Space rather than on S3.
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.
Nine ways to draw an OEIS sequence — Ulam spiral, mod-N grid, digit walks, polyarc curves, autocorrelation and more — each paired with a null-model layer: the same statistic measured on permuted, differenced, or matched-random surrogates, with confidence bands from up to a thousand of them. It answers a narrow question, whether a measurement taken off a picture belongs to the sequence or to the drawing technique, and declines to answer the broad one. Built as the apparatus for a question raised on the SeqFan list; every view has a URL that reproduces it exactly.
Rock-paper-scissors against a neural network that retrains in the browser on your last 25 rounds after every move. Three swappable architectures — dense MLP, GRU, single-head transformer — share one 15-feature input, so the comparison is between models, not pipelines. Runs entirely client-side in TensorFlow.js; telemetry is opt-in and records no IP, fingerprint, or cookie. A small, complete demo of online learning, not a result about anything. Hosted on GitHub Pages rather than S3.
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.
The sequence 3, 6, 17, 116 from the preprint above, accepted into the On-Line Encyclopedia of Integer Sequences on 29 July 2026 after a three-month editorial review (submitted 21 April). The entry carries the construction, the universality statement across singular pairwise potentials, the harmonic counterexample that closes at dimension 15, and a self-contained Python program; a(3) = 116 was verified two independent ways.
Verification paths for the projects above, and for work that has a deposit but no page of its own yet. Each is labelled by what it is; two are negative results and one is an archived exploration.
593 decomposition configurations crossed with 25 upsampling methods on one Fairfield County, Ohio LiDAR DEM: the catalog and 40-dimensional signature vectors behind RESIDUALS. The rendered residuals themselves, with UMAP coordinates, are the residuals-fingerprints dataset on Hugging Face.
Bracket-level dimension sequences for physical N-body systems and, treating SGD with momentum as a Hamiltonian system, for neural-network training dynamics across 21 configurations of depth, width, coupling, loss, and activation. The companion to the three-body result above.
1 Hz die temperature, fan state, and load from a Coral Dev Board whose Edge TPU is learning its own fan policy. The code repository is not yet public; cite tagged revisions, since the dataset grows every day.
A reinforcement-learning and DFT-surrogate pipeline for low effective-mass semiconductors, archived with its methodological finding: across three pipeline variants, zero of 24 surrogate-selected candidates validated in DFT as low-positive-effective-mass semiconductors. The 794 signed effective-mass DFT records and the 24 surrogate-versus-DFT pairs are the rl-surrogate-dft-gap dataset.
A small CNN separates round-reduced SHA-256 output from random through three rounds and collapses to chance at round four, staying there through all 64; five seeds, two dataset sizes. An apparent iterated-hash signal was a label-prior artifact, caught by the experiment's own permuted-label control. A capability exploration, not cryptography: a distinguisher failing on a hash it should fail on is the expected outcome.
The archive behind the capability probe above: derivation notebooks, parameter sweeps, the clean-room port of the Warp Factory slice with its energy-condition evaluator, and the verification batteries. An exploration of how current AI systems reason about speculative physics, not a physics result.
3D segmentation of papyrus surface and interior in micro-CT volumes of the Herculaneum scrolls, trained with nnU-Net v2 for the Kaggle surface-detection competition. An implementation of published work; the contribution is the reproducible training setup, not the architecture.