Fundamental research.
State a law, test it on an exact or simulated world, then prove it or refute it.
Here, mathematics and physics share one loop: state a conjecture or a law, test it on a world whose rules are exact or simulated, then prove it or refute it with a counterexample. Two strands run today, on small worlds chosen on purpose.
Runs today in Slean worlds and on synthetic oscillator data. Real-world data: future work.
See an example
Prove it, refute it, or say the data cannot tell.
A law is accepted with a proof that covers every case, rejected with a checked counterexample, and two models are separated only by observations chosen where they disagree.
Is this law true, or did it only hold on the cases we tried?
The problem
An AI can propose a law that fits every example it has seen and still be wrong, or two different laws that fit the same data equally well.
Why it is hard
More examples never prove a statement about all cases, and a closer fit to old data does not decide between two explanations. Sometimes the data cannot decide at all.
How Mutome approaches it
Ask for a proof where one is possible, a checked counterexample where the law is false, and an observation chosen to separate competing models where it is not. “Neither” and “abstain” are valid answers.
Mathematics: a law proved for every lattice size
Slean’s worlds are cellular automata: rows of cells on a ring, updated by a fixed local rule. The figure runs the textbook traffic rule known as rule 184, where a dark cell is a car that moves right when the cell ahead is free. It shows the kind of law Slean checks; it is not a Slean result.
Physics: which observation separates two models?
A synthetic oscillator protocol. Two models fit a short trace generated from a rule hidden from the search. The curves are an illustration, not data.
What runs today
Lean-checked laws and counterexamples in Slean’s cellular-automaton worlds, and versioned synthetic oscillator protocols for rediscovering a model and telling two models apart, with four possible outcomes: H0, H1, neither, or abstain.
Not yet
Formal proof search beyond Slean worlds, physics worlds built on Physlib, and predictions made in advance and checked against real data. Nothing here is yet a claim about open mathematical problems or about the physical world.