GH
Gift Horse Mouth Inspections
Automated theorem proving, inspected
Laboratory full
neurosymbolic systems • certified automation

Do not look a Gift Horse in the mouth unless you are inspecting it for mathematics

We build novel and verifiable automata (programs) for mathematics that leverage, multiple strategies. Large language models propose; proof assistants dispose. Search is guided by models, but every claim is replayed and checked in a small core so it is auditable, reproducible, and boringly correct.

Not taking new clients: the laboratory is at capacity. Introduce yourself anyway with a short academic note or a phone number; we will call when a bench opens.

Methods

Sketch of the pipeline
LLM guidance

Model-guided search

Language models propose tactics, rewrite hints, and high-level plans; the search space is pruned by cost functions derived from proof states and domain constraints.

Synthesis

Tactic synthesis + repair

We synthesise small certified tactics and patch failure modes with counterexample-guided repair. No hallucinations: failing branches become training data.

Verification

Certified replay

Every successful path is replayed inside a proof assistant (Lean/Coq/Isabelle) with a tiny trusted core. Outputs are artefacts, not vibes.

Research areas

Programmes, not products

Finite groups & algebraic number theory

  • Profinite gymnastics for rewriting and decision procedures
  • Dessins d'enfants and Belyi map certification
  • Typed proofs as programs: search that compiles

Neurosymbolic systems

  • Representation learning on proof traces
  • Curricula from counterexamples
  • Self-play for tactics with correctness contracts

Algorithm archaeology

  • Recovering lost heuristics from old code and papers
  • Reproducible pipelines and open datasets
  • Audits that are fun to read

Stack

Pieces that matter

FAQ

Question.
Are you open to engaging outside parties currently?

A. At the moment, our laboratory is in its early stages, and we are working with only a few select partners. The laboratory benches are full, however, please feel free to introduce yourself via the waitlist and we will reach out when capacity increases.

Question.
Do you rely on model authority?

A. No. Linguistic models are used as weak guidance for propose steps; proof assistants and solvers check them and inform backtracking. If it does not replay, it does not ship.

Question.
Will you share datasets and code?

A. Where licenses allow and require, yes, and similarly as contracts permit when working with private organisations. We prefer results that can be inspected, replicated, and extended.

Question.
Why the odd aesthetic?

A. Because why ever not? Isn't what we're doing rather strange to begin with?

Waitlist

We are not onboarding clients right now. If you want to be notified when a bench frees up, leave a short academic note or a phone number. Minimal forms, maximal signal.

No spam. One email when capacity changes.
Or just email [email protected].