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The only assumption on the excited state is finiteness of its SRD relative to the vacuum.","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')."}},"verdict_id":"f95d56b3-dde6-490d-ab5c-8d6a55d5aa91"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:837ee544772de1b8c68aaf45ee50bc0e36282bb1cc5627c52dccc43d592cbd41","target":"record","created_at":"2026-05-20T00:00:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"83124c5c680d782dd32c9f4fde53c9634333a3544ce2d9674ab16c1a101eeb3f","cross_cats_sorted":["math-ph","math.MP","math.OA","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-05-14T18:00:02Z","title_canon_sha256":"898a08ddd8429294bfdad68b6bb6b834b0501f7f1fd63278590bcf9efd403320"},"schema_version":"1.0","source":{"id":"2605.15272","kind":"arxiv","version":1}},"canonical_sha256":"d221efc84c63aa817517df8cf136e1fc137c02502cb27e5c41eb5cef5c2984fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d221efc84c63aa817517df8cf136e1fc137c02502cb27e5c41eb5cef5c2984fe","first_computed_at":"2026-05-20T00:00:49.905337Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:00:49.905337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vNWPClzzU+KrnhGPWw4XelpndaeNPiS/dfGC4dSqXS0PUKiMcZlyOA3D8+Tdr8HBI3ifLqsIs/hA20/87Y3qAw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:00:49.905983Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.15272","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:837ee544772de1b8c68aaf45ee50bc0e36282bb1cc5627c52dccc43d592cbd41","sha256:0f27c4b77a897c9847c98ce4394ccbed649671f75c5fe67461a221bbb9b6cdd1"],"state_sha256":"89c549a432f1fa76ffa03e5fdd20410a5d79659e58294da06a997cf47d76da66"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rDSrepbvQkARXKt2+dpJiiziGrVuQ1zA+0+aipiumucHP4f1fLbQGPJGSCr9Oi08J7/4G71Eop9xkLZr1Lr5BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T12:26:27.159065Z","bundle_sha256":"5200bf5ff61c53bb126197bc4a7ccbafef216205113809c4070bfb56e2f0be02"}}