{"paper":{"title":"A general proof of integer R\\'enyi QNEC","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The sandwiched Rényi divergence obeys a null energy condition for every integer order two and higher in algebras equipped with half-sided modular inclusions.","cross_cats":["math-ph","math.MP","math.OA","quant-ph"],"primary_cat":"hep-th","authors_text":"Pratik Roy, Tanay Kibe","submitted_at":"2026-05-14T18:00:02Z","abstract_excerpt":"The R\\'enyi quantum null energy condition conjectures that the second null shape variation of the sandwiched R\\'enyi divergence (SRD) of an excited state relative to the vacuum is non-negative in local Poincar\\'e-invariant quantum field theory, giving a one-parameter generalization of the quantum null energy condition (QNEC). We prove R\\'enyi QNEC for all integer R\\'enyi parameters $n\\geq 2$ for von Neumann algebras carrying a half-sided modular inclusion structure. The only assumption on the excited state is finiteness of its SRD relative to the vacuum. Concretely, for any $\\sigma$-finite von"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove Rényi QNEC for all integer Rényi parameters n≥2 for von Neumann algebras carrying a half-sided modular inclusion structure. The only assumption on the excited state is finiteness of its SRD relative to the vacuum.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The algebra must carry a half-sided modular inclusion that generates the null-translation semigroup; without this structure the log-convexity argument does not apply (abstract, paragraph beginning 'Concretely, for any σ-finite von Neumann algebra').","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Proves integer Rényi QNEC by establishing log-convexity of Kosaki L^n norms under null-translation semigroups for σ-finite von Neumann algebras with half-sided modular inclusions, assuming only finite sandwiched Rényi divergence to the vacuum.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The sandwiched Rényi divergence obeys a null energy condition for every integer order two and higher in algebras equipped with half-sided modular inclusions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"900d80af9be67834204a69c3f7420afbb344455c144b411d5763332421219458"},"source":{"id":"2605.15272","kind":"arxiv","version":1},"verdict":{"id":"f95d56b3-dde6-490d-ab5c-8d6a55d5aa91","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T15:45:35.863442Z","strongest_claim":"We prove Rényi QNEC for all integer Rényi parameters n≥2 for von Neumann algebras carrying a half-sided modular inclusion structure. The only assumption on the excited state is finiteness of its SRD relative to the vacuum.","one_line_summary":"Proves integer Rényi QNEC by establishing log-convexity of Kosaki L^n norms under null-translation semigroups for σ-finite von Neumann algebras with half-sided modular inclusions, assuming only finite sandwiched Rényi divergence to the vacuum.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The algebra must carry a half-sided modular inclusion that generates the null-translation semigroup; without this structure the log-convexity argument does not apply (abstract, paragraph beginning 'Concretely, for any σ-finite von Neumann algebra').","pith_extraction_headline":"The sandwiched Rényi divergence obeys a null energy condition for every integer order two and higher in algebras equipped with half-sided modular inclusions."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15272/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T16:01:18.195014Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T15:54:53.026490Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T14:41:54.262755Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T13:33:22.801906Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"6cb524daffe7333acb62d778770d81a3450c6be6b5b61814ffc848345cfe6eae"},"references":{"count":63,"sample":[{"doi":"","year":2016,"title":"A Quantum Focussing Conjecture","work_id":"22982099-5fda-45a9-89e7-54f7cf711183","ref_index":1,"cited_arxiv_id":"1506.02669","is_internal_anchor":true},{"doi":"","year":2016,"title":"Proof of the Quantum Null Energy Condition","work_id":"1dc03798-9ae8-4481-9ac6-b39f42a3d723","ref_index":2,"cited_arxiv_id":"1509.02542","is_internal_anchor":true},{"doi":"","year":2020,"title":"T.A. Malik and R. Lopez-Mobilia,Proof of the quantum null energy condition for free fermionic field theories,Phys. Rev. D101(2020) 066028 [1910.07594]","work_id":"9e7e3b09-030a-4964-ab75-84e429abc55d","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"Holographic Proof of the Quantum Null Energy Condition","work_id":"910d6062-0501-4491-9d0a-01dd659a8288","ref_index":4,"cited_arxiv_id":"1512.06109","is_internal_anchor":true},{"doi":"","year":2019,"title":"S. Balakrishnan, T. Faulkner, Z.U. Khandker and H. Wang,A General Proof of the Quantum Null Energy Condition,JHEP09(2019) 020 [1706.09432]","work_id":"9f0108e1-d3eb-4ad0-8dc1-6307ad56d257","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":63,"snapshot_sha256":"5f174db9bcdef055735bfb9ffe0f2a5f185a4c6e648aa47a5ca7077450ae1c96","internal_anchors":18},"formal_canon":{"evidence_count":2,"snapshot_sha256":"d9de2a4ff74f4f77ebf231fd3d95b9b9905aa5e1d1a96e5abd9a0ec98f55190a"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}