FORMAL VERIFICATION
Stop hoping your rules work. Prove it.
Mathematical proofs. Cryptographic certificates. Counterexamples when something's wrong.
PROVEN before deploy. FAILED with exact counterexample.
80%
QA time eliminated
Proofs replace manual testing
$1.5M
Incident costs avoided
Edge cases caught before production
30s
Audit question answered
"Prove it" → certificate
THE PAIN YOU KNOW
Testing isn't proof.
Tests pass. Production fails. Sound familiar?
CURRENT PAIN
WITH PROOFS
| Metric | Before | After | Δ |
|---|
WHAT AUDITORS SEE
"Prove it."
Here's the certificate.
Auditors don't want to read test logs. They want proof certificates — cryptographically signed, mathematically verified, with counterexamples when something fails.
Graxon Proof Certificate Viewer
All Verifications Passed
5 of 5 properties proven • Certificate valid until Jan 24, 2026
ARTIFACT
Decision Table
kyc-risk-scoring
Version 2.4.1
sha256:a7f3b2c4d5e6...
CERTIFICATE
Certificate ID
cert_7f3a9b2c-4d5e-6f7a-8b9c-0d1e2f3a4b5c
Issued: Jan 24, 2025
Issuer: graxon-verification-engine
VERIFIED PROPERTIES
✓ PROVEN COMPLETENESS
0.847s ✓ PROVEN MUTUAL_EXCLUSION
1.203s ✓ PROVEN OUTPUT_CONFORMANCE
0.156s ✓ PROVEN POSTCONDITION: high_risk → edd_required
0.432s ✓ PROVEN INVARIANT: monotonic(score → tier)
0.891s WHAT YOU GET
Mathematical certainty.
Not statistical confidence.
TESTING
"All 2,000 tests passed"
"Coverage: 94%"
"Confidence: high"
Test #2,001 finds the bug in production.
PROOF
"PROVEN for all 850,000,000 possible inputs"
"Coverage: 100% (mathematical)"
"Certainty: absolute"
No counterexample exists. We checked.
When we say PROVEN
The property holds for every possible valid input. Not most. Not sampled. All of them. Mathematically.
When we say FAILED
You get the exact input that breaks it. Not "assertion failed on line 47" — the concrete case you can reproduce and fix.
WHAT WE CAN PROVE
Completeness
Every valid input gets a decision
Determinism
Same input always gives same output
Constraints
If X then always Y
Boundaries
No gaps, no overlaps
Equivalence
New system = old system
Compliance
Required rules are implemented
Our verification engine uses formal methods — the same class of mathematical techniques used to verify aircraft systems, cryptographic protocols, and chip designs. This isn't testing at scale. It's proof.
UNDERSTANDING FORMAL VERIFICATION
"Wait, this is actually possible?"
Yes. Here's the 60-year backstory and why it finally works for business rules.
Formal verification is mathematical proof that software behaves correctly — not for some inputs, but for ALL possible inputs.
Instead of writing tests and hoping you covered everything, you describe what "correct" means, and a theorem prover exhaustively checks every possibility.
If it says PROVEN, there is no counterexample. Not "we couldn't find one" — mathematically, one cannot exist.
You probably have, just in different contexts:
• Intel uses it to verify chip designs (after the $475M Pentium FDIV bug)
• Airbus uses it for flight control software
• AWS uses it internally for security policies
• Cryptographers use it to verify protocols
The catch: until recently, it required PhD-level expertise, months of manual effort, and only worked on small, critical systems.
For business rules? Nobody thought it was worth the investment. Testing was "good enough."
Three things converged:
1. Solver breakthroughs (2005-2015)
SAT and SMT solvers got exponentially faster. Problems that took hours now take milliseconds. The same algorithms that seemed impractical in 2000 now run on your laptop.
2. Cloud compute (2010s)
When a proof needs more power, we can throw 1000 cores at it for 30 seconds. The economics changed completely.
3. Domain restriction (our insight)
General program verification is still hard. But decision tables, business rules, workflow logic? They're a constrained domain. We're not proving arbitrary code — we're proving finite, structured logic. That's tractable.
SMT stands for "Satisfiability Modulo Theories" — it's the mathematical framework underneath.
Think of it like this: we translate your decision table into a logic puzzle, then ask "is there ANY input that breaks this property?"
If the answer is "no such input exists" (unsatisfiable), the property is PROVEN.
If the answer is "yes, here's one" (satisfiable), you get the exact COUNTEREXAMPLE.
The SMT-LIB language you see in proof details is the standard format for these logic puzzles. It's been peer-reviewed for decades and can be independently verified by any SMT solver.
No — almost the opposite.
AI/ML testing: Run many examples, measure statistical accuracy, hope edge cases are covered.
Formal verification: Mathematically prove properties hold for ALL inputs, with zero exceptions.
We use formal methods precisely because business rules need certainty, not confidence intervals. When the rule says "high-risk customers require EDD," you need that to be TRUE, not "true 99.7% of the time."
We're honest about limits:
• Undecidable properties: Some questions are mathematically impossible to answer in general (Gödel, Turing, etc.). We'll tell you "UNKNOWN" rather than guess.
• External dependencies: We can prove your rules are correct, not that your data is accurate or your upstream systems behave.
• Infinite domains: If your input space is truly unbounded, we apply reasonable bounds and prove within those bounds.
• Timeout: Complex proofs may exceed time limits. We return "UNKNOWN," not a wrong answer.
The key guarantee: if we say PROVEN, it's proven. We never give false positives.
Yes — that's the point of using standard formats.
The SMT-LIB encoding in each certificate can be checked by any independent SMT solver. Your auditor (or their technical team) can:
1. Download the certificate
2. Extract the formal encoding
3. Run it through their own solver
4. Confirm the result matches
This is reproducible mathematics, not "trust us." The proof is the proof.
For business rules and decision tables? As a product?
We don't know of anyone.
AWS built internal tools (Zelkova for IAM policies). Academic researchers publish papers. Security companies verify smart contracts.
But "upload your DMN table, get a proof certificate" as a commercial product for compliance teams? That's new. That's us.
WHAT THIS MEANS FOR YOU
Concrete outcomes.
Not theoretical benefits.
📋
For Compliance Teams
- ✓ GDPR audit? Hand them a proof certificate showing all Article 17 erasure rules are implemented. Not test logs — mathematical proof.
- ✓ Regulation changes? Re-verify in minutes. Know immediately if you're still compliant.
- ✓ "Prove high-risk always triggers EDD" — answered in 30 seconds with a certificate, not 2 weeks of evidence gathering.
Buy the GDPR pack → verify against your data model → receive proof certificate → audit-ready.
🧪
For QA & Engineering
- ✓ Replace 80% of edge case testing. Proofs cover ALL inputs, not just the ones you thought of.
- ✓ CI/CD gate. PROVEN badge required before deploy. Catch rule gaps before production.
- ✓ Regression confidence. Refactor rules knowing you haven't broken anything — mathematically.
6-week QA cycles → 1 week. 2,000 manual tests → 50 tests + proofs. 4-hour regression suite → 10 minutes.
📊
For Product & Business
- ✓ Ship faster. Rules verified in seconds, not weeks. Deploy with confidence.
- ✓ Zero edge-case incidents. $500K average incident cost → $0. Insurance, not hope.
- ✓ Customer trust. "Our pricing rules are mathematically verified" — a differentiator.
3 incidents/year @ $500K = $1.5M. Proof system cost: fraction of one incident.
🔄
For Migration Teams
- ✓ Skip the parallel run. Prove equivalence mathematically. 6 months of dual-running → 0.
- ✓ Find divergence instantly. Counterexample shows exact input where old ≠ new. Debug in minutes, not weeks.
- ✓ Confident cutover. Board asks "are you sure?" — show them the proof certificate.
18-month migration → 6 months. $2M parallel run cost → $0. $5M divergence incident risk → eliminated.
🤖
For AI Agent Teams
- ✓ Prove guardrails work. Not "we tested 10,000 prompts" — mathematical proof the agent CAN'T violate constraints.
- ✓ Answer the hard questions. "Can this agent ever approve a loan without income verification?" — PROVEN: No.
- ✓ Ship to production. Compliance, legal, and security sign off because you have proof, not promises.
"Our AI agent is mathematically guaranteed to never..." — say that to your CISO and watch their face.
THE BOTTOM LINE
80%
QA time eliminated
$1.5M+
Incident costs avoided
95%
Audit prep reduced
100%
Input coverage
MATHEMATICALLY VERIFIED
Stop testing.
Start proving.
You're in.
We'll reach out within 48 hours with verification access.