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.
When do small views determine the whole?
For binary-cut diagrams, a sharp theorem identifies the largest natural quotient that finite observations can recover. Version 2 proves what must be relinquished and what can be preserved under that requirement.
31 October 2026. Proofs and exact finite checks; established coefficient family. AI-assisted internal review; priority and external review remain open.
From checked change to necessary loss
Connecting Hegelese to reconstruction mathematics: when does a demand determine the most informative permissible successor, and when are several losses incomparable? Proofs and finite searches give an exact answer for independent views and views over a protected common overlap.
1 November 2026. Classical lossless-join and quotient mechanisms, with explicit hypotheses and counterexamples. AI-assisted internal review; no new priority claim.
Reciprocity without losing causality
When can interacting components be simplified without inventing a causal equilibrium? A sharp finite theorem identifies cycles of partially simplified components as the exact obstruction to a universal guarantee. The question comes from Hegel's account of reciprocal causation.
7 November 2026. Complete proofs and two separately written finite checkers. AI-assisted internal review; priority and external review remain open.
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.