DEFINITION

Proof Intelligence

Proof Intelligence is AI that proposes, formal methods that decide, and evidence anyone can check without trusting the vendor.

Ironproof Research · 17 October 2026

This page defines a term. Every result it points to is already published on this site; it adds no new figure.

Don’t trust the verdict. Verify the evidence.

AI now writes code, moves money, and changes critical systems faster than humans can review them. But speed without assurance is not enough.

Every critical action must be authorized before execution. Every migration must preserve the behavior that matters. Every claim must withstand independent verification. Proof Intelligence is the name for doing all three with a machine-checked answer instead of a confident one.

Three parts, one chain

01AI proposes. A model turns a written policy, a program or a question into a precise statement a machine can decide. It is fast, and it can be wrong, so it never has the last word.
02Formal methods decide. Solvers and model checkers (Z3, cvc5, CBMC) settle the statement over every case the model allows, not the cases someone thought to try.
03Evidence leaves with you. The decision, its justification and the proof result are sealed (Ed25519 + ML-DSA-65) into an artifact your own auditor can re-check offline, without an Ironproof dashboard.

AI proposes. Formal methods decide. The evidence travels.

Three verdicts, never two

A pass/fail system has a hidden third state. When a tool cannot decide, “pass” is usually where the case lands. Every Proof Intelligence result is one of three, always stated within the declared model:

01Proven. The property holds in every case the model allows.
02Refuted. The property fails, and the result carries the exact case that breaks it, so you can replay it yourself.
03Not demonstrated. We could not conclude, or the rule could not be modelled. It is reported as such, never folded into proven.

A result that cannot say “I don’t know” cannot be trusted when it says “yes”.

What it is not

01Not a confidence score. A probability that an answer is right is not a proof that it is.
02Not AI checking AI. The model proposes; a solver decides, and the solver’s result is what gets sealed.
03Not a dashboard you have to trust. The evidence verifies offline, without us.
04Not a proof about the world. A proof holds for the declared model and its assumptions. Here is exactly where ours stop.

Where Ironproof applies it today

01Critical actions. Authorization before execution for actions that cannot be undone — moving money, granting access, deleting records, changing production — whether an AI agent, a script, an API call or a person initiates them. How it works.
02Legacy modernization. COBOL to Python, checked for the same results, available now as a service. Send us a program.
03Software security. Proving that a fix to C code closes the flaw it targets. In research. What we have run.

We prove what holds. We show what breaks.

Others sell trust. We sell the right not to trust us.

SOURCES

Ironproof Research — What our proofs do not prove (16 October 2026)The three verdicts and the five places a proof is weaker than its word, restated in sections 2 and 3.
IRONPROOF: COBOL-to-Python Transpilation with SMT-Based Equivalence Checking (arXiv:2610.11073)The published method behind the modernization results.

This page introduces no figure that is not already published. When the definition changes, it changes here first.