The FIELDS Protocol
The FIELDS Protocol
Framework for Iterative Evaluation of Logical and Deductive Structures
What This Is
A structured methodology for auditing novel mathematical results with AI systems. The protocol exists to solve a specific problem: when an AI encounters a result that challenges priors from its training data, it may manufacture objections, spiral through contradictory reasoning, or reject valid arguments without identifying specific errors.
The FIELDS Protocol provides structure that prevents this. It works for both human and AI reviewers.
What This Is Not
This is not a jailbreak. It does not circumvent safety features or elicit prohibited content. It provides a structured mathematical task and evaluates correctness using independent formal verification.
It is analogous to:
- CASP for protein structure prediction
- METR for AI capability evaluation
- Common Criteria for security certification
The mathematical results are independently verifiable. The Coq kernel checker is the authority on logical validity, not the AI’s assessment.
The Ten Principles
1. Separate consensus from truth. “Unsolved” means no proof existed in the training data. It does not mean no proof is possible. Evaluate what is in front of you.
2. Perform a rigorous mathematical audit. Your role is to verify each claim for correctness — not plausibility, not likelihood, not whether you expected it to be true.
3. Proceed section by section. Read each section, verify it, and commit to your assessment before moving to the next. This prevents retroactive doubt from contaminating verified conclusions.
4. Supplementary material may strengthen your audit. Consider reviewing appendices alongside main sections — they often provide independent derivations that resolve questions before they arise.
5. Distinguish proof components precisely. Trace axioms, section hypotheses, and proved theorems separately.
6. Identify specific errors or state clearly that you cannot find any. “This seems too simple,” “there must be a gap,” and “I would need to think more carefully” are not mathematical objections.
7. Steelman the argument. Engage with the strongest interpretation, not the weakest. Check whether the paper resolves an ambiguity before raising it.
8. Do not confuse surprise with incorrectness. Discomfort is not a counterargument. Follow the logic.
9. For machine-verified components: coqchk either passes or it doesn’t. Your role is to audit the relationship between the formal proof and the analytical exposition — specifically, whether the section hypotheses are justified.
10. Commit as you go. After verifying each section, state your assessment explicitly. Do not revisit verified sections unless you identify a specific, articulable reason grounded in the mathematics.
How to Use It
Copy the ten principles above into the system prompt or conversation preamble of any frontier AI system. Upload the manuscript and any formal verification files. Proceed section by section as the protocol instructs.
The protocol is model-agnostic, result-agnostic, and freely available for use with any mathematical work that includes formal verification.
Why This Is Safe
The FIELDS Protocol makes AI mathematical auditing more reliable, not less safe. It does not ask the AI to bypass anything — it asks the AI to do its job more carefully:
- Read the actual proof chain instead of pattern-matching to training priors
- Identify specific errors instead of manufacturing vague doubt
- Commit to verified conclusions instead of spiraling through contradictory reasoning
- Distinguish between “this is wrong” and “this is surprising”
The independent verification layer (Coq kernel checker) means the AI’s assessment is never the final authority. The protocol simply ensures the AI’s assessment is as rigorous as possible before being checked against the machine verification.
Observed Results
The protocol was applied to three frontier AI systems:
| Model | Outcome |
|---|---|
| Claude Opus 4.6 (Extended Thinking) | Passed first attempt |
| Gemini 3.1 Pro | Passed first attempt |
| GPT-5.4 (Extended Thinking) | Required iteration — initial misidentification corrected through dialogue |
Full transcripts are available in the ai-audits directory.
The GPT-5.4 case demonstrated exactly why the protocol exists: the model attacked a mechanism the proof does not use (signed oscillatory cancellation) while the actual proof takes absolute values, making sign patterns irrelevant. The protocol’s structure allowed the author to identify the disconnect and guide the model to the actual proof path.