{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:O2JHGVC2JUATPPMTOB4UW3IO5Q","short_pith_number":"pith:O2JHGVC2","schema_version":"1.0","canonical_sha256":"769273545a4d0137bd9370794b6d0eec27f495b13a11789e57561198bbe9be47","source":{"kind":"arxiv","id":"1802.07184","version":1},"attestation_state":"computed","paper":{"title":"Comment on the Bekenstein bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-th","math.MP","math.OA"],"primary_cat":"math-ph","authors_text":"Feng Xu, Roberto Longo","submitted_at":"2018-02-20T16:23:22Z","abstract_excerpt":"We propose a rigorous derivation of the Bekenstein upper limit for the entropy/information that can be contained by a physical system in a given finite region of space with given finite energy. The starting point is the observation that the derivation of such a bound provided by Casini [6] is similar to the description of the black hole incremental free energy that had been given by the first named author [23]. The approach here is different but close in the spirit to [6]. Our bound is obtained by operator algebraic methods, in particular Connes' bimodules, Tomita-Takesaki modular theory and J"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1802.07184","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-02-20T16:23:22Z","cross_cats_sorted":["gr-qc","hep-th","math.MP","math.OA"],"title_canon_sha256":"c6490735b984d20e91c5018f346e8cf9e85b01845fa5e4ee5b8abab96de57c34","abstract_canon_sha256":"257030f69e046c72d0fefc7c03ecd4b06b59109b51b06431090d545acfe60b4d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:25.648737Z","signature_b64":"LYDijAABUs7FitZN6wNojKohb4Iw8427NeJOQU3sqs2yndhDkX3sKmi3usEXdWnTLZ+3iYPgL9QX7PSDT23zDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"769273545a4d0137bd9370794b6d0eec27f495b13a11789e57561198bbe9be47","last_reissued_at":"2026-05-18T00:16:25.648248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:25.648248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Comment on the Bekenstein bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-th","math.MP","math.OA"],"primary_cat":"math-ph","authors_text":"Feng Xu, Roberto Longo","submitted_at":"2018-02-20T16:23:22Z","abstract_excerpt":"We propose a rigorous derivation of the Bekenstein upper limit for the entropy/information that can be contained by a physical system in a given finite region of space with given finite energy. The starting point is the observation that the derivation of such a bound provided by Casini [6] is similar to the description of the black hole incremental free energy that had been given by the first named author [23]. The approach here is different but close in the spirit to [6]. Our bound is obtained by operator algebraic methods, in particular Connes' bimodules, Tomita-Takesaki modular theory and J"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07184","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1802.07184","created_at":"2026-05-18T00:16:25.648325+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.07184v1","created_at":"2026-05-18T00:16:25.648325+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.07184","created_at":"2026-05-18T00:16:25.648325+00:00"},{"alias_kind":"pith_short_12","alias_value":"O2JHGVC2JUAT","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_16","alias_value":"O2JHGVC2JUATPPMT","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_8","alias_value":"O2JHGVC2","created_at":"2026-05-18T12:32:40.477152+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.18383","citing_title":"Bounding relative entropy for non-unitary excitations in quantum field theory","ref_index":29,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/O2JHGVC2JUATPPMTOB4UW3IO5Q","json":"https://pith.science/pith/O2JHGVC2JUATPPMTOB4UW3IO5Q.json","graph_json":"https://pith.science/api/pith-number/O2JHGVC2JUATPPMTOB4UW3IO5Q/graph.json","events_json":"https://pith.science/api/pith-number/O2JHGVC2JUATPPMTOB4UW3IO5Q/events.json","paper":"https://pith.science/paper/O2JHGVC2"},"agent_actions":{"view_html":"https://pith.science/pith/O2JHGVC2JUATPPMTOB4UW3IO5Q","download_json":"https://pith.science/pith/O2JHGVC2JUATPPMTOB4UW3IO5Q.json","view_paper":"https://pith.science/paper/O2JHGVC2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.07184&json=true","fetch_graph":"https://pith.science/api/pith-number/O2JHGVC2JUATPPMTOB4UW3IO5Q/graph.json","fetch_events":"https://pith.science/api/pith-number/O2JHGVC2JUATPPMTOB4UW3IO5Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O2JHGVC2JUATPPMTOB4UW3IO5Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O2JHGVC2JUATPPMTOB4UW3IO5Q/action/storage_attestation","attest_author":"https://pith.science/pith/O2JHGVC2JUATPPMTOB4UW3IO5Q/action/author_attestation","sign_citation":"https://pith.science/pith/O2JHGVC2JUATPPMTOB4UW3IO5Q/action/citation_signature","submit_replication":"https://pith.science/pith/O2JHGVC2JUATPPMTOB4UW3IO5Q/action/replication_record"}},"created_at":"2026-05-18T00:16:25.648325+00:00","updated_at":"2026-05-18T00:16:25.648325+00:00"}