{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GXFJICQBGCY4PKIT42TTG3ITAT","short_pith_number":"pith:GXFJICQB","canonical_record":{"source":{"id":"1102.4318","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-02-21T20:13:53Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"74886ccdac410adabe0892a7dce6ce9e3e2962c5dcb111799a6e022bc0f8b431","abstract_canon_sha256":"20abcc3a5a097800f49c3374a51453276a72dbd340be0c641a1d532d430e3fbd"},"schema_version":"1.0"},"canonical_sha256":"35ca940a0130b1c7a913e6a7336d1304d6c144a694d46ecd39539234e5d7441c","source":{"kind":"arxiv","id":"1102.4318","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4318","created_at":"2026-05-18T04:20:50Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4318v2","created_at":"2026-05-18T04:20:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4318","created_at":"2026-05-18T04:20:50Z"},{"alias_kind":"pith_short_12","alias_value":"GXFJICQBGCY4","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GXFJICQBGCY4PKIT","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GXFJICQB","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GXFJICQBGCY4PKIT42TTG3ITAT","target":"record","payload":{"canonical_record":{"source":{"id":"1102.4318","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-02-21T20:13:53Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"74886ccdac410adabe0892a7dce6ce9e3e2962c5dcb111799a6e022bc0f8b431","abstract_canon_sha256":"20abcc3a5a097800f49c3374a51453276a72dbd340be0c641a1d532d430e3fbd"},"schema_version":"1.0"},"canonical_sha256":"35ca940a0130b1c7a913e6a7336d1304d6c144a694d46ecd39539234e5d7441c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:50.922682Z","signature_b64":"DclztHYfAAgRx5TA5o9oc2nPPsK0llzxSpkS30k06VizAj746a1ssk+jlw7SlJyqpg0JITddBnu3jQGw4wI1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35ca940a0130b1c7a913e6a7336d1304d6c144a694d46ecd39539234e5d7441c","last_reissued_at":"2026-05-18T04:20:50.921997Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:50.921997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.4318","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:20:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I32P6yTxVs7vqLZEpmjlGC16Ie3MA0gZpIUBtQGYAm3WBOPKs6Hdm9/jA5BpKJkV4Qt/UiIigYvPFGQ8U9LSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:58:02.004646Z"},"content_sha256":"e69729dac01c3dc9addd2016e079dab355e2b6aa1386485db5c8f01e1657b714","schema_version":"1.0","event_id":"sha256:e69729dac01c3dc9addd2016e079dab355e2b6aa1386485db5c8f01e1657b714"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GXFJICQBGCY4PKIT42TTG3ITAT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On measures of non-Markovianity: divisibility vs. backflow of information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Andrzej Kossakowski, \\'Angel Rivas, Dariusz Chru\\'sci\\'nski","submitted_at":"2011-02-21T20:13:53Z","abstract_excerpt":"We analyze two recently proposed measures of non-Markovianity: one based on the concept of divisibility of the dynamical map and the other one based on distinguishability of quantum states. We provide a toy model to show that these two measures need not agree. In addition, we discuss possible generalizations and intricate relations between these measures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4318","kind":"arxiv","version":2},"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":"2026-05-18T04:20:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SCPTNk4S4HII6mQQj88k3dEPOmc1bkL46mipUmzfleYalT4VAZ73U99JBgAR5xLlQYw9EQQIHNV5Mgc1x2MCDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:58:02.005422Z"},"content_sha256":"88038cb129d84dce397a3b5e9c5eddb5add2e0b4bb3379df18bae4e57adb4a44","schema_version":"1.0","event_id":"sha256:88038cb129d84dce397a3b5e9c5eddb5add2e0b4bb3379df18bae4e57adb4a44"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GXFJICQBGCY4PKIT42TTG3ITAT/bundle.json","state_url":"https://pith.science/pith/GXFJICQBGCY4PKIT42TTG3ITAT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GXFJICQBGCY4PKIT42TTG3ITAT/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":"2026-05-31T12:58:02Z","links":{"resolver":"https://pith.science/pith/GXFJICQBGCY4PKIT42TTG3ITAT","bundle":"https://pith.science/pith/GXFJICQBGCY4PKIT42TTG3ITAT/bundle.json","state":"https://pith.science/pith/GXFJICQBGCY4PKIT42TTG3ITAT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GXFJICQBGCY4PKIT42TTG3ITAT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GXFJICQBGCY4PKIT42TTG3ITAT","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":"20abcc3a5a097800f49c3374a51453276a72dbd340be0c641a1d532d430e3fbd","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-02-21T20:13:53Z","title_canon_sha256":"74886ccdac410adabe0892a7dce6ce9e3e2962c5dcb111799a6e022bc0f8b431"},"schema_version":"1.0","source":{"id":"1102.4318","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4318","created_at":"2026-05-18T04:20:50Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4318v2","created_at":"2026-05-18T04:20:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4318","created_at":"2026-05-18T04:20:50Z"},{"alias_kind":"pith_short_12","alias_value":"GXFJICQBGCY4","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GXFJICQBGCY4PKIT","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GXFJICQB","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:88038cb129d84dce397a3b5e9c5eddb5add2e0b4bb3379df18bae4e57adb4a44","target":"graph","created_at":"2026-05-18T04:20:50Z","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":"We analyze two recently proposed measures of non-Markovianity: one based on the concept of divisibility of the dynamical map and the other one based on distinguishability of quantum states. We provide a toy model to show that these two measures need not agree. In addition, we discuss possible generalizations and intricate relations between these measures.","authors_text":"Andrzej Kossakowski, \\'Angel Rivas, Dariusz Chru\\'sci\\'nski","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-02-21T20:13:53Z","title":"On measures of non-Markovianity: divisibility vs. backflow of information"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4318","kind":"arxiv","version":2},"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:e69729dac01c3dc9addd2016e079dab355e2b6aa1386485db5c8f01e1657b714","target":"record","created_at":"2026-05-18T04:20:50Z","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":"20abcc3a5a097800f49c3374a51453276a72dbd340be0c641a1d532d430e3fbd","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-02-21T20:13:53Z","title_canon_sha256":"74886ccdac410adabe0892a7dce6ce9e3e2962c5dcb111799a6e022bc0f8b431"},"schema_version":"1.0","source":{"id":"1102.4318","kind":"arxiv","version":2}},"canonical_sha256":"35ca940a0130b1c7a913e6a7336d1304d6c144a694d46ecd39539234e5d7441c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35ca940a0130b1c7a913e6a7336d1304d6c144a694d46ecd39539234e5d7441c","first_computed_at":"2026-05-18T04:20:50.921997Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:50.921997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DclztHYfAAgRx5TA5o9oc2nPPsK0llzxSpkS30k06VizAj746a1ssk+jlw7SlJyqpg0JITddBnu3jQGw4wI1DA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:50.922682Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4318","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e69729dac01c3dc9addd2016e079dab355e2b6aa1386485db5c8f01e1657b714","sha256:88038cb129d84dce397a3b5e9c5eddb5add2e0b4bb3379df18bae4e57adb4a44"],"state_sha256":"e8c5c5cb85eefbe9302194bebd26c6c7fa99e8671ae9b19840dbaeda56dc3960"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S3IzeM/BX4pBCXZaFIIfefmK/mFqgi2WhE4adVOLmRH4lO6ftlqS9O4FBXvpNOimdzgorLkKgpbJBLCfzHtbDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T12:58:02.009234Z","bundle_sha256":"807de5be50c5c896cf9b6a5646539c2e1ebd43b68b406e0cead34d6242fa04fe"}}