Notes on probability,
structure, and systems.
Paper breakdowns and essays from azide.
Small experiments in explaining math and engineering ideas clearly — sheaf-theoretic fusion, categorical probability, and whatever else I'm reading this month.
Papers
Long-form breakdowns of research I've found useful.
Categorical Probability
Probability Maps as First-Class Arrows
Treat probability maps as composable arrows with Wasserstein distance built in — clean plumbing for stochastic systems and robust belief comparison.
- category theory
- markov kernels
- wasserstein
Topos-Theoretic Probability
Descent as Epistemic Coherence
Treat uncertainty not as noise on one global picture, but as local beliefs that must agree where they overlap. Bayesian updating becomes 'make the locals compatible, then glue.'
- sheaf theory
- bayesian
- sensor fusion
Blog
Shorter notes on engineering and design.
Why Systems That Make Sense Still Fail
A quiet mathematical reason why locally correct systems produce globally wrong behavior — traced through Foucault's pendulum, the 2003 blackout, Knight Capital's forty-five minutes, and the night before Challenger.
- essays
- systems
- geometry
Teach git clone where repos belong
A tiny shell wrapper that intercepts the boring case of git clone and drops repos into a canonical path. Remove the forced context switch; leave the override path open.
- unix
- tools
- shell
A Template System for Research Writing
How I built a reusable architecture for publishing paper breakdowns and blog posts on one site — composable primitives, data-driven layouts, and responsive typography.
- engineering
- design systems
- next.js