EUCLID.
Formal mathematics and machine-checked theorem proving.
Euclid is the formal-mathematics specialist. It produces proof-carrying derivations and machine-checkable proofs, where the chain of reasoning is itself a verifiable artefact signed into the audit ledger. A peer reviewer can replay the proof step by step. Euclid coordinates with the domain brain QUANTUM on the hard sciences and with the kernel Code brain on proof-assistant tooling. Outputs carry an educational disclaimer.
- 01Formal proof construction and verification
- 02Proof-carrying derivations with replayable steps
- 03Theorem-prover and proof-assistant orchestration
- 04Signed proof records for peer-review reproduction
Authoritative external corpora and standards this brain treats as canonical. Every retrieval against these sources is signed into the audit ledger so a regulator can prove which evidence drove which output.
- 01AMS MathSciNet
- 02arXiv math.* papers
- 03Lean mathlib library
- 04Coq and Isabelle proof-assistant corpora
- 05Mathematical Reviews and Zentralblatt MATH
- 06Metamath proof database
- 07Principia and foundational-logic canon
- 08TPTP automated-theorem-proving library
- 09Stanford Encyclopedia of Philosophy (logic)
Mickai-native tooling primitives this brain implements internally. Codex for sovereign plain-text graph PKM, Lectern for spaced-repetition memory, Stele for citation-provenance, and domain-native primitives layered on top. No external services in the trust path; data stays on operator-personalised hardware.
- 01Codex (sovereign plain-text graph PKM)
- 02Slate (symbolic computation surface)
- 03Quill (mathematical typesetting and notebooks)
- 04Stele (proof citation graph)