CAIN-42 CAIN StudioAGENTIC AI 75 · #11
Self-supervised theorem discovery
Researchers described an agent that starts from axioms and inference rules and builds a reusable library of theorems.
Last reviewed 2026-11-11
Agentic AI 75 / #11
2026 status: Research preprint · Category: Formal mathematics
The 2026 development
Researchers described an agent that starts from axioms and inference rules and builds a reusable library of theorems.
The governance gap
A growing theorem library compounds both capability and error. If a theorem enters the library unchecked, every later result that depends on it inherits the defect.
Where CAIN-42 fits: Moat 4 — Execution Provenance & Attestation
Core question: Can we prove what actually happened? Hash-chained, signed records binding decision to execution to observable effect.
Make library admission depend on a checker verdict, not on the agent's confidence. Each theorem carries its statement, proof, checker version and dependency set, and a later result can cite only admitted theorems.
How the wiring works
- Parse the candidate theorem into a canonical statement.
- Run the checker against the statement and proof in an isolated environment.
- Admit the theorem only on a positive verdict and record its dependencies.
- Re-check dependants when a checker or axiom set changes.
What is real today
LIBRARY Production code and tests exist in this repository; there is no hosted route for this exact use.
The checker gate is real for a bounded logic subset. No theorem-library agent is operated here.
| Component in this repository | What the module says it is |
|---|---|
cain/cain_z3_verifygate.py | CAIN Trust Fabric - Formal Z3 SMT Semantic Verification Gate (Phase 3) |
vericoding-gate/expr_compiler.py | Safe Python-subset -> Z3 compiler. |
cain/causality/graph.py | CAIN CAUSALITY — Causal Event Graph (Prompt CAUSALITY, Phase 3). |
Descriptions are the first line of each module's own docstring, read without importing it. A module path is a pointer into this repository, not a hosted endpoint. Its existence is checked by the test suite; its status for this use is the label above.
Check it yourself
- Run a live Z3 proof
/vericoding-keystone - Fire a live decision through the CAIN-42 pipeline
/fabric/try— the same enforcement path every product sits behind.
Commercial package
| Offer | Formal Artifact Review |
|---|---|
| Buyer | Formal-methods teams and proof-assistant vendors |
| Price (proposal) | $5,000–$12,000 per review |
| Bundle | Code & Proof — Prove the fix, not just the diff. |
| Operator stream | Stream 2 of the 10-stream operator playbook |
Platform engineering, AI coding-tool vendors, security engineering is the bundle buyer. The entry offer for this bundle is Fabrication audit or long-run engineering attestation; the range is $1,500–$6,000 per audit; $2,500–$4,000/month retainer. A price on this page is a proposal, not a validated rate, and no customer is claimed.
Buy this as a product or service
CAIN-A75-011 — Formal Artifact Review DELIVERABLE
A bounded engine run on the buyer's sample: findings, a written report, and a SHA-256 artifact manifest. The manifest is unsigned: it is not a signature and not an attestation.
Kind: Assessment · Price (proposal): $5,000–$12,000 per review · Lead time: 5 business days.
Open the product page · all 75 products
What this page does not claim
What this page is not. CAIN-42 is not affiliated with, endorsed by, integrated into, or shipped with the organisation named in the 2026 item. The item is public context; the page describes how CAIN-42 would govern that class of capability. No page here claims a customer, a partnership, a certification, a patent, or a production integration. Prices are proposals. Built by a three-person team.