AI Science Experiments
Can AI help produce a useful mathematical result? I am exploring that question through small research projects where the arguments, code and checks can be inspected.
The aim is to put a claim somewhere it can be challenged. A proof, a counterexample search and a literature review answer different questions; none should be made to stand in for the others.
Faster exact network checks
Computing the curvature of a network usually involves solving transport problems. This experiment develops a shortcut for a defined family of densely connected graphs, with an exact correction when a simple shared-neighbour count fails.
A possible use is an open stress-test tool for a tightly connected communications mesh: remove links, restore them, and recompute a structural measure without repeatedly solving the full transport problem wherever the fast rule applies.
21 October 2026. AI-assisted work with Codex; candidate novelty and independent mathematical review remain open. Practical benefit on real networks has not been measured.
What belongs in this notebook
Each experiment should make the question, proposed contribution and prior work visible. Where there is code, it should be possible to reproduce the calculation. Where Lean checks part of an argument, the unchecked parts should be named too.
I direct the questions and take responsibility for what I publish here. AI assistants propose arguments and write code; that assistance is part of the research record. This section is separate from my professional product work.