On July 1, 2026, the UK's Advanced Research and Invention Agency (ARIA) closed its £20 million 'Safeguarded AI' funding call, which explicitly funds AI tools that formally verify critical code. This has sparked a race among cybersecurity CTOs to build agentic pipelines that autonomously generate machine-checked mathematical proofs, shifting enterprise defense from reactive vulnerability patching to provable mathematical security.
Master Plan: Agentic AI Pipeline for Machine-Checked Mathematical Proofs in Cybersecurity in 2026
Automate formal verification of security-critical software using reasoning models and deterministic machine checkers.
The Problem
Security-critical software—such as cryptographic libraries, microkernels, and smart contracts—requires absolute guarantees of correctness that traditional unit testing cannot provide. Formal verification using machine-checked mathematical proofs (e.g., in Lean 4, Coq, or F*) offers mathematical certainty but is notoriously labor-intensive. It requires highly specialized proof engineers and months of manual effort per module. As codebases evolve, maintaining these proofs becomes a severe bottleneck, often forcing security teams to abandon formal methods entirely. This project introduces an agentic AI pipeline designed to automate the generation and iterative refinement of formal proofs. By tightly coupling a reasoning-focused LLM with a formal verification environment (the "machine checker"), the AI acts as an autonomous proof engineer. It proposes tactics, interprets compiler errors, and refines its approach until the proof is accepted by the checker. Crucially, because the output is mathematically verified by a deterministic compiler, the risk of AI hallucination is structurally mitigated—an invalid proof simply will not compile. However, to ensure the specification itself is correct and the proof strategy aligns with security requirements, the pipeline enforces a strict Human-in-the-Loop (HITL) validation gate where senior security engineers review the verified theorems before merging.
Who this is for: Principal Security Engineer / Formal Methods Researcher at Enterprise or Web3 scale
Head-to-Head: Why This Model Won
Formal proof generation requires exceptional complex reasoning, deep understanding of niche functional languages, and the ability to adapt to strict compiler feedback. Cost is secondary to reasoning capability, as a single successful proof saves days of human engineering time.
Primary workload evaluated: Iterative formal proof generation and refinement — costs below are for 10,000 tasks of this workload.
| Model | Cost / 10k tasks | Best feature | Biggest drawback | Verdict |
|---|---|---|---|---|
| claude-opus-4-8 Anthropic | $5000 | Unmatched adaptive thinking and historical dominance in niche formal languages like Lean and Coq. | High cost per token, which compounds quickly during deep iterative loops with the compiler. | Winner (Primary Role) |
| o3-pro OpenAI | $18000 | Exceptional raw reasoning capabilities and robust tool calling for interacting with the checker. | Prohibitively expensive at $20/$80 per million tokens for a highly iterative, multi-step agent loop. | Runner Up |
| deepseek-v4-pro DeepSeek | $304.5 | Provides near-flagship reasoning and thinking capabilities at a fraction of the cost. | Occasionally struggles with the highly specific syntax of obscure formal verification languages compared to Claude. | Budget Pick |
| grok-4-3 xAI | $875 | Strong agentic capabilities and fast execution for tool-heavy workflows. | Lacks the deep mathematical reasoning and specialized coding benchmarks required for formal proofs. | Rejected for Primary Role |
Recommended AI Stack
Proof Generation Agent (Primary) → claude-opus-4-8 (Anthropic)
Why: Claude Opus 4.8 provides the highest level of adaptive thinking and reasoning required to navigate complex mathematical proofs. Its deep knowledge of formal languages like Lean 4 ensures it can propose valid tactics and adjust its strategy based on strict compiler feedback.
~$0.5 / request
Math: Assume 5 iterations per task. Each iteration: 10k input tokens ($5/1M) + 2k output tokens ($25/1M) = $0.10. 5 * $0.10 = $0.50.
Alternatives considered: o3-pro was rejected due to its significantly higher cost ($20/$80) which makes deep iterative loops financially unviable at scale.
Error Parser & Linter → deepseek-v4-flash (DeepSeek)
Why: Acts as a fast, ultra-cheap intermediary that parses raw, verbose compiler errors from the machine checker and formats them into concise, actionable feedback for the primary agent. This saves expensive input tokens on the primary model.
~$0.0021 / request
Math: Assume 5 iterations. Each iteration: 2k input tokens ($0.14/1M) + 500 output tokens ($0.28/1M) = $0.00042. 5 * $0.00042 = $0.0021.
Alternatives considered: gpt-5-4-mini was considered but DeepSeek V4 Flash is significantly cheaper for high-volume parsing tasks while maintaining excellent formatting capabilities.
HITL Summarizer → claude-haiku-4-6 (Anthropic)
Why: Once a proof compiles, this model translates the formal mathematical logic into a plain-English summary of the security guarantees proven. This is critical for the Human-in-the-Loop (HITL) review gate, allowing security engineers to verify the specification intent.
~$0.001875 / request
Math: 1 run per successful proof: 5k input tokens ($0.25/1M) + 500 output tokens ($1.25/1M) = $0.00125 + $0.000625 = $0.001875.
Alternatives considered: gemini-3-1-flash-lite was considered, but keeping the summarizer in the Anthropic ecosystem allows for easier prompt sharing and consistent tone with the primary agent.
Compare migration costs
Run a live cost comparison before you commit:
System Architecture
Cost Breakdown
| Scenario | Cost |
|---|---|
| Per request (typical workload) | $0.5040 |
| Daily @ 100 req/day | $50.40 |
| Daily @ 1,000 req/day | $503.98 |
| Daily @ 10,000 req/day | $5039.75 |
| Monthly @ 1,000 req/day | $15119.40 |
| Monthly @ 10,000 req/day (at scale) | $151192.50 |
💰 Cost Optimization Strategies
Provider-specific tactics to cut the monthly bill above. Apply these AFTER you have a working baseline — premature optimization wastes engineering time.
claude-opus-4-8
Anthropic offers ~90% off cached read tokens via Prompt Caching. Cache the massive system prompt containing the formal language syntax rules, standard library lemmas, and project-specific axioms. Every iteration in the agent loop will hit this cache, drastically reducing the cost of the 10k+ input context.
Anthropic offers ~50% off via the Batch API. Use this for nightly regression runs where previously verified proofs are re-checked and re-generated against new codebase commits, as these do not require real-time latency.
deepseek-v4-flash
DeepSeek offers ~90% off cached input tokens. Cache the compiler error formatting instructions and few-shot error resolution examples to minimize the cost of the parsing step.
Not applicable — the error parser operates in the synchronous fast-feedback loop of the agent and requires real-time latency to unblock the primary model.
claude-haiku-4-6
Anthropic offers ~90% off cached read tokens. Cache the project's overarching security specification guidelines and terminology dictionary used for generating the HITL summaries.
Anthropic offers ~50% off via the Batch API. Use this for bulk-generating documentation summaries for the entire verified codebase during off-peak hours.
30-Day Implementation Plan
Week 1: Foundation
- Set up the formal verification environment (Lean 4 or Coq) inside isolated, sandboxed Docker containers.
- Define the formal specifications and theorems for a pilot cryptographic module.
- Establish the Human-in-the-Loop (HITL) review criteria and build the basic approval UI.
Week 2: Core Build
- Implement the primary agent loop using claude-opus-4-8.
- Build the tool-calling interface allowing the agent to write `.lean` files and execute the compiler.
- Implement state management to track the proof context across multiple compiler iterations.
Week 3: Production Hardening
- Integrate deepseek-v4-flash to parse and compress raw compiler errors before feeding them back to Opus.
- Implement circuit breakers and max-iteration limits to prevent infinite loops on unsolvable proofs.
- Integrate claude-haiku-4-6 to generate plain-English summaries of successful proofs for the HITL dashboard.
Week 4: Launch & Optimization
- Implement Anthropic Prompt Caching for the primary agent's system instructions and lemma libraries.
- Run automated regression tests on a suite of known solvable proofs to measure agent success rate.
- Deploy the pipeline to staging and conduct a dry-run with the security engineering team.
Pros / Cons / Risks
✓ Pros
- Provides mathematical certainty of code correctness, eliminating entire classes of vulnerabilities.
- Structurally mitigates AI hallucination risk, as the deterministic compiler acts as an absolute ground truth.
- Drastically reduces the manual labor required for formal verification, making it viable for faster-moving projects.
− Cons
- High token consumption due to the iterative nature of interacting with a strict compiler.
- The AI can still get stuck in infinite loops if it pursues a fundamentally flawed proof strategy.
- Requires highly specialized human engineers to write the initial specifications and perform the HITL review.
⚠ Risks
- The model may prove the wrong specification (e.g., proving a function is memory-safe but ignoring cryptographic timing leaks), which is why HITL validation of the specification is mandatory.
- Sandboxed execution environments for the machine checker must be strictly isolated to prevent malicious code execution if the agent is compromised via prompt injection.
Recommended Infrastructure
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