{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:AU5HZVQWDXHAJJK5HK2R2X2Z2V","short_pith_number":"pith:AU5HZVQW","canonical_record":{"source":{"id":"2202.03357","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2022-02-07T17:01:45Z","cross_cats_sorted":["hep-th","math.MP","math.OA"],"title_canon_sha256":"f0ab7641031d5c5a3bac8de6d0f46e72f245cf637c3ac611ac031bcf3d08d0d2","abstract_canon_sha256":"b9a78df995db8023a4ed0289bcaef64da43359b203d779c9c62bc47d317046b1"},"schema_version":"1.0"},"canonical_sha256":"053a7cd6161dce04a55d3ab51d5f59d562eb20dc57078f987dd3503dcec2d973","source":{"kind":"arxiv","id":"2202.03357","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.03357","created_at":"2026-07-05T03:54:38Z"},{"alias_kind":"arxiv_version","alias_value":"2202.03357v1","created_at":"2026-07-05T03:54:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.03357","created_at":"2026-07-05T03:54:38Z"},{"alias_kind":"pith_short_12","alias_value":"AU5HZVQWDXHA","created_at":"2026-07-05T03:54:38Z"},{"alias_kind":"pith_short_16","alias_value":"AU5HZVQWDXHAJJK5","created_at":"2026-07-05T03:54:38Z"},{"alias_kind":"pith_short_8","alias_value":"AU5HZVQW","created_at":"2026-07-05T03:54:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:AU5HZVQWDXHAJJK5HK2R2X2Z2V","target":"record","payload":{"canonical_record":{"source":{"id":"2202.03357","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2022-02-07T17:01:45Z","cross_cats_sorted":["hep-th","math.MP","math.OA"],"title_canon_sha256":"f0ab7641031d5c5a3bac8de6d0f46e72f245cf637c3ac611ac031bcf3d08d0d2","abstract_canon_sha256":"b9a78df995db8023a4ed0289bcaef64da43359b203d779c9c62bc47d317046b1"},"schema_version":"1.0"},"canonical_sha256":"053a7cd6161dce04a55d3ab51d5f59d562eb20dc57078f987dd3503dcec2d973","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:54:38.101295Z","signature_b64":"IhHP+MWiTRMAe0tpvAPVlSIkwXZ9Pm6rxA3cOiFKjPO1xjoV9S30tMe/Ook6jxlRxSq3eacyB44WpFd+ZeBEAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"053a7cd6161dce04a55d3ab51d5f59d562eb20dc57078f987dd3503dcec2d973","last_reissued_at":"2026-07-05T03:54:38.100827Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:54:38.100827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2202.03357","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:54:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"esQ3Q265uAPCKjk0O5/MXjqg7trPKX1q1+qy2Tkuq3ox9CHA42I4M1fZdGwxcPnH8l0u0BkWGWbaSIbL5Io7BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T11:27:48.303762Z"},"content_sha256":"64c7f343c131aa38fe8bb52be23672b7455ba829d7f57ad32df2d418ca5cfd14","schema_version":"1.0","event_id":"sha256:64c7f343c131aa38fe8bb52be23672b7455ba829d7f57ad32df2d418ca5cfd14"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:AU5HZVQWDXHAJJK5HK2R2X2Z2V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on continuous entropy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.MP","math.OA"],"primary_cat":"math-ph","authors_text":"Edward Witten, Roberto Longo","submitted_at":"2022-02-07T17:01:45Z","abstract_excerpt":"Von Neumann entropy has a natural extension to the case of an arbitrary semifinite von Neumann algebra, as was considered by I. E. Segal. We relate this entropy to the relative entropy and show that the entropy increase for an inclusion of von Neumann factors is bounded by the logarithm of the Jones index. The bound is optimal if the factors are infinite dimensional."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.03357","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2202.03357/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:54:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6FF/6am1tBTvrWJ9NHDwqTRIUqzZymN1V/9fBdW98/YGLt/7qamn1zj5isNgiD8LR/pV4m67WGz3vhzu6M1DDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T11:27:48.304300Z"},"content_sha256":"c1fcc1434e6a8dc7cbc912b8fc99edda36f913c15adf3a18e3473c859946e815","schema_version":"1.0","event_id":"sha256:c1fcc1434e6a8dc7cbc912b8fc99edda36f913c15adf3a18e3473c859946e815"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AU5HZVQWDXHAJJK5HK2R2X2Z2V/bundle.json","state_url":"https://pith.science/pith/AU5HZVQWDXHAJJK5HK2R2X2Z2V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AU5HZVQWDXHAJJK5HK2R2X2Z2V/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-10T11:27:48Z","links":{"resolver":"https://pith.science/pith/AU5HZVQWDXHAJJK5HK2R2X2Z2V","bundle":"https://pith.science/pith/AU5HZVQWDXHAJJK5HK2R2X2Z2V/bundle.json","state":"https://pith.science/pith/AU5HZVQWDXHAJJK5HK2R2X2Z2V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AU5HZVQWDXHAJJK5HK2R2X2Z2V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:AU5HZVQWDXHAJJK5HK2R2X2Z2V","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b9a78df995db8023a4ed0289bcaef64da43359b203d779c9c62bc47d317046b1","cross_cats_sorted":["hep-th","math.MP","math.OA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2022-02-07T17:01:45Z","title_canon_sha256":"f0ab7641031d5c5a3bac8de6d0f46e72f245cf637c3ac611ac031bcf3d08d0d2"},"schema_version":"1.0","source":{"id":"2202.03357","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.03357","created_at":"2026-07-05T03:54:38Z"},{"alias_kind":"arxiv_version","alias_value":"2202.03357v1","created_at":"2026-07-05T03:54:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.03357","created_at":"2026-07-05T03:54:38Z"},{"alias_kind":"pith_short_12","alias_value":"AU5HZVQWDXHA","created_at":"2026-07-05T03:54:38Z"},{"alias_kind":"pith_short_16","alias_value":"AU5HZVQWDXHAJJK5","created_at":"2026-07-05T03:54:38Z"},{"alias_kind":"pith_short_8","alias_value":"AU5HZVQW","created_at":"2026-07-05T03:54:38Z"}],"graph_snapshots":[{"event_id":"sha256:c1fcc1434e6a8dc7cbc912b8fc99edda36f913c15adf3a18e3473c859946e815","target":"graph","created_at":"2026-07-05T03:54:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2202.03357/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Von Neumann entropy has a natural extension to the case of an arbitrary semifinite von Neumann algebra, as was considered by I. E. Segal. We relate this entropy to the relative entropy and show that the entropy increase for an inclusion of von Neumann factors is bounded by the logarithm of the Jones index. The bound is optimal if the factors are infinite dimensional.","authors_text":"Edward Witten, Roberto Longo","cross_cats":["hep-th","math.MP","math.OA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2022-02-07T17:01:45Z","title":"A note on continuous entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.03357","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:64c7f343c131aa38fe8bb52be23672b7455ba829d7f57ad32df2d418ca5cfd14","target":"record","created_at":"2026-07-05T03:54:38Z","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":"b9a78df995db8023a4ed0289bcaef64da43359b203d779c9c62bc47d317046b1","cross_cats_sorted":["hep-th","math.MP","math.OA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2022-02-07T17:01:45Z","title_canon_sha256":"f0ab7641031d5c5a3bac8de6d0f46e72f245cf637c3ac611ac031bcf3d08d0d2"},"schema_version":"1.0","source":{"id":"2202.03357","kind":"arxiv","version":1}},"canonical_sha256":"053a7cd6161dce04a55d3ab51d5f59d562eb20dc57078f987dd3503dcec2d973","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"053a7cd6161dce04a55d3ab51d5f59d562eb20dc57078f987dd3503dcec2d973","first_computed_at":"2026-07-05T03:54:38.100827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:54:38.100827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IhHP+MWiTRMAe0tpvAPVlSIkwXZ9Pm6rxA3cOiFKjPO1xjoV9S30tMe/Ook6jxlRxSq3eacyB44WpFd+ZeBEAg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:54:38.101295Z","signed_message":"canonical_sha256_bytes"},"source_id":"2202.03357","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64c7f343c131aa38fe8bb52be23672b7455ba829d7f57ad32df2d418ca5cfd14","sha256:c1fcc1434e6a8dc7cbc912b8fc99edda36f913c15adf3a18e3473c859946e815"],"state_sha256":"d7e15f4e84a7fcc1d7931ff2e0a8f97115c9855496d6dfc5b19a855958ae5e95"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nTqWdnXOWhgAWGBmN//vA9us7PLcHwFgB0G2C6s/x1KE73ZF7KvLj8+Dzp+QCnwUKg69W6yR0/Z/bcNi1ZIhAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T11:27:48.308568Z","bundle_sha256":"3f498cb821d282bde9b03f82c439efe17481bff1109f50dcc8991f4fa9548493"}}