Proof-Carrying Numbers (PCN): A Protocol for Trustworthy Numeric Answers from LLMs via Claim Verification
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908525036306432 |
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| author | Solatorio, Aivin V. |
| author_facet | Solatorio, Aivin V. |
| contents | Large Language Models (LLMs) as stochastic systems may generate numbers that deviate from available data, a failure known as \emph{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 \emph{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 \emph{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: \emph{trust is earned only by proof}, while the absence of a mark communicates uncertainty. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_06902 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Proof-Carrying Numbers (PCN): A Protocol for Trustworthy Numeric Answers from LLMs via Claim Verification Solatorio, Aivin V. Computation and Language Cryptography and Security Databases Machine Learning Large Language Models (LLMs) as stochastic systems may generate numbers that deviate from available data, a failure known as \emph{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 \emph{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 \emph{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: \emph{trust is earned only by proof}, while the absence of a mark communicates uncertainty. |
| title | Proof-Carrying Numbers (PCN): A Protocol for Trustworthy Numeric Answers from LLMs via Claim Verification |
| topic | Computation and Language Cryptography and Security Databases Machine Learning |
| url | https://arxiv.org/abs/2509.06902 |