{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:HKJYJWXLQALERBZGHX2RGY4QTO","short_pith_number":"pith:HKJYJWXL","canonical_record":{"source":{"id":"1012.5356","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-12-24T07:52:42Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"2a4ebf0c22eca83354bbb2ed139a2540a5a9c444e805f3cf8a4644b32d0c9d99","abstract_canon_sha256":"d35d855f7f5f3066ac4d05628dcca74af52688b2f24dbc7bff29f95dee72fa88"},"schema_version":"1.0"},"canonical_sha256":"3a9384daeb80164887263df51363909ba848f22802ee7bd115781c555aee2f24","source":{"kind":"arxiv","id":"1012.5356","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5356","created_at":"2026-05-18T04:19:21Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5356v3","created_at":"2026-05-18T04:19:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5356","created_at":"2026-05-18T04:19:21Z"},{"alias_kind":"pith_short_12","alias_value":"HKJYJWXLQALE","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HKJYJWXLQALERBZG","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HKJYJWXL","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:HKJYJWXLQALERBZGHX2RGY4QTO","target":"record","payload":{"canonical_record":{"source":{"id":"1012.5356","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-12-24T07:52:42Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"2a4ebf0c22eca83354bbb2ed139a2540a5a9c444e805f3cf8a4644b32d0c9d99","abstract_canon_sha256":"d35d855f7f5f3066ac4d05628dcca74af52688b2f24dbc7bff29f95dee72fa88"},"schema_version":"1.0"},"canonical_sha256":"3a9384daeb80164887263df51363909ba848f22802ee7bd115781c555aee2f24","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:21.879083Z","signature_b64":"wuLNsgbkeLGOe8K5F6CIl/pMhoc3FASwjaHZU0zZRkQT7PhMgqY32LCVZ0pilJIvOOa/L0LAL7MIkDyljwexAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a9384daeb80164887263df51363909ba848f22802ee7bd115781c555aee2f24","last_reissued_at":"2026-05-18T04:19:21.878470Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:21.878470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.5356","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:19:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eYmbGD7QyArY0VDJka21l30MbQnVXiP3epm62MEuCP1dwffcOtKXpgUvmtKEGkoWMoRFJba8JQBmXQ6BextUAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:23:07.822191Z"},"content_sha256":"8b698edc0bb5ef488cf911b2417eb4987672b7263851eea74277568c63d715cf","schema_version":"1.0","event_id":"sha256:8b698edc0bb5ef488cf911b2417eb4987672b7263851eea74277568c63d715cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:HKJYJWXLQALERBZGHX2RGY4QTO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some general properties of unified entropies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Alexey E. Rastegin","submitted_at":"2010-12-24T07:52:42Z","abstract_excerpt":"Basic properties of the unified entropies are examined. The consideration is mainly restricted to the finite-dimensional quantum case. Bounds in terms of ensembles of quantum states are given. Both the continuity in Fannes' sense and stability in Lesche's sense are shown for wide ranges of parameters. In particular, uniform estimates are obtained for the quantum R\\'{e}nyi entropies. Stability properties in the thermodynamic limit are discussed as well. It is shown that the unified entropies enjoy both the subadditivity and triangle inequality for a certain range of parameters. Non-decreasing o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5356","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:19:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kQGu0bM92jwADaxu6RVEGAjFbO7VlisjeyIQVv115GLAusgZw6W45yyvhpZGSSKcIuYt4qRCpsqWcawgPQHyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:23:07.822989Z"},"content_sha256":"b44c31ea221a4bee72bc039cd90f290663d63c953679f4bc8670a2086936fa7c","schema_version":"1.0","event_id":"sha256:b44c31ea221a4bee72bc039cd90f290663d63c953679f4bc8670a2086936fa7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HKJYJWXLQALERBZGHX2RGY4QTO/bundle.json","state_url":"https://pith.science/pith/HKJYJWXLQALERBZGHX2RGY4QTO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HKJYJWXLQALERBZGHX2RGY4QTO/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":"2026-05-30T12:23:07Z","links":{"resolver":"https://pith.science/pith/HKJYJWXLQALERBZGHX2RGY4QTO","bundle":"https://pith.science/pith/HKJYJWXLQALERBZGHX2RGY4QTO/bundle.json","state":"https://pith.science/pith/HKJYJWXLQALERBZGHX2RGY4QTO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HKJYJWXLQALERBZGHX2RGY4QTO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HKJYJWXLQALERBZGHX2RGY4QTO","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":"d35d855f7f5f3066ac4d05628dcca74af52688b2f24dbc7bff29f95dee72fa88","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-12-24T07:52:42Z","title_canon_sha256":"2a4ebf0c22eca83354bbb2ed139a2540a5a9c444e805f3cf8a4644b32d0c9d99"},"schema_version":"1.0","source":{"id":"1012.5356","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5356","created_at":"2026-05-18T04:19:21Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5356v3","created_at":"2026-05-18T04:19:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5356","created_at":"2026-05-18T04:19:21Z"},{"alias_kind":"pith_short_12","alias_value":"HKJYJWXLQALE","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HKJYJWXLQALERBZG","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HKJYJWXL","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:b44c31ea221a4bee72bc039cd90f290663d63c953679f4bc8670a2086936fa7c","target":"graph","created_at":"2026-05-18T04:19:21Z","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"},"paper":{"abstract_excerpt":"Basic properties of the unified entropies are examined. The consideration is mainly restricted to the finite-dimensional quantum case. Bounds in terms of ensembles of quantum states are given. Both the continuity in Fannes' sense and stability in Lesche's sense are shown for wide ranges of parameters. In particular, uniform estimates are obtained for the quantum R\\'{e}nyi entropies. Stability properties in the thermodynamic limit are discussed as well. It is shown that the unified entropies enjoy both the subadditivity and triangle inequality for a certain range of parameters. Non-decreasing o","authors_text":"Alexey E. Rastegin","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-12-24T07:52:42Z","title":"Some general properties of unified entropies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5356","kind":"arxiv","version":3},"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":"sha256:8b698edc0bb5ef488cf911b2417eb4987672b7263851eea74277568c63d715cf","target":"record","created_at":"2026-05-18T04:19:21Z","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":"d35d855f7f5f3066ac4d05628dcca74af52688b2f24dbc7bff29f95dee72fa88","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-12-24T07:52:42Z","title_canon_sha256":"2a4ebf0c22eca83354bbb2ed139a2540a5a9c444e805f3cf8a4644b32d0c9d99"},"schema_version":"1.0","source":{"id":"1012.5356","kind":"arxiv","version":3}},"canonical_sha256":"3a9384daeb80164887263df51363909ba848f22802ee7bd115781c555aee2f24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a9384daeb80164887263df51363909ba848f22802ee7bd115781c555aee2f24","first_computed_at":"2026-05-18T04:19:21.878470Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:21.878470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wuLNsgbkeLGOe8K5F6CIl/pMhoc3FASwjaHZU0zZRkQT7PhMgqY32LCVZ0pilJIvOOa/L0LAL7MIkDyljwexAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:21.879083Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5356","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b698edc0bb5ef488cf911b2417eb4987672b7263851eea74277568c63d715cf","sha256:b44c31ea221a4bee72bc039cd90f290663d63c953679f4bc8670a2086936fa7c"],"state_sha256":"f5562dfa4866b49629f575fb43578d3b068b41b61877a57181996e3be80321cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ed36nb9GavMK6hrzu/oBGy2BB01K9GLFraTjEeH8L1HsBQG0B7i8idOFwZRL5WyQFhOJI932YSs7mwN6MOjKDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T12:23:07.827366Z","bundle_sha256":"2e761398203102f8965fae0a88fa2a78b35cc50ad393aa0ae9771c6033378a4d"}}