Proof-Carrying Numbers (PCN): A Protocol for Trustworthy Numeric Answers from LLMs via Claim Verification

ICLR 2026 Conference Submission20916 Authors

Keywords: Proof-Carrying Numbers, PCN, LLM, Trustworthiness

TL;DR: We introduce Proof-Carrying Numbers (PCN), a renderer-based protocol that enforces verified numeric claims in LLM outputs, ensuring fail-closed, spoof-proof fidelity: only proven numbers are trusted, others remain visibly uncertain.

Abstract: Large Language Models (LLMs) as stochastic systems may generate numbers that deviate from available data, a failure known as $\textit{numeric hallucination}$. Existing safeguards—retrieval-augmented generation, citations, and uncertainty estimation—improve transparency but cannot guarantee fidelity: fabricated or misquoted values may still be displayed as if correct. We propose $\textbf{Proof-Carrying Numbers (PCN)}$, a presentation-layer protocol that enforces numeric fidelity through mechanical verification. Under PCN, numeric spans are emitted as $\textit{claim-bound tokens}$ tied to structured claims, and a verifier checks each token under a declared policy (e.g., exact equality, rounding, aliases, or tolerance with qualifiers). Crucially, PCN places verification in the $\textit{renderer}$, not the model: only claim-checked numbers are marked as verified, and all others default to unverified. This separation prevents spoofing and guarantees fail-closed behavior. We formalize PCN and prove soundness, completeness under honest tokens, fail-closed behavior, and monotonicity under policy refinement. PCN is lightweight and model-agnostic, integrates seamlessly into existing applications, and can be extended with cryptographic commitments. By enforcing verification as a mandatory step before display, PCN establishes a simple contract for numerically sensitive settings: $\textit{trust is earned only by proof}$, while the absence of a mark communicates uncertainty.

Primary Area: alignment, fairness, safety, privacy, and societal considerations

Submission Number: 20916