What was already known
Earlier unconditional schemes had inverse-polynomial security loss or inefficient encryption or decryption, according to the paper.
AI involvement
The authors credit independent Codex GPT-5.6 Sol Ultra conversations with the construction and proof. They supplied harness ideas, merged drafts, verified and substantially revised the argument.
The authors explicitly assign discovery of the central construction and proof to Codex across separate extended conversations, with human harness design and later revision.
Importance
The construction combines unconditional security, efficiency and exponentially small cloning advantage for one-bit messages.
Limitations
The reported Lean proof covers Theorem 4.1 correctness and security, not efficiency or later arbitrary-message applications. Those extensions are separate human-led work.
Technical verification
The paper reports careful author verification of the complete proof and says the public Lean repository proves all correctness and security claims in Theorem 4.1. The Lean scope excludes efficiency and downstream applications, which rest on the paper's separate human exposition and prior reductions. Neither check was rerun here.
Formal checking
Formalization of the operational scheme and complete Pauli security bound
- Checker
- Lean 4 on the authors' Pauli construction repository
- Scope
- Theorem 4.1 correctness and one-bit unclonable-indistinguishability security, excluding efficiency
- Basis
- Reported by the linked checker
Formal checking
Authors report careful verification and substantial cleanup of model-generated drafts
- Checker
- Prabhanjan Ananth, Seyoon Ragavan and Amit Sahai
- Scope
- The one-bit Pauli construction and proof of its security bound
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain why expanding the key set to all nonidentity Paulis enables the negligible advantage and how operator bounds and disagreement terms complete the security proof.
Correction and publication history
The construction combines unconditional security, efficiency and exponentially small cloning advantage for one-bit messages.
Read this published revision