{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VQJYFGGNR64XMLAYKY323GAYGS","short_pith_number":"pith:VQJYFGGN","canonical_record":{"source":{"id":"1811.11617","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-28T15:17:19Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"db22a6e4607c62ad20e89332d3e0fa060d05c5de62b751ac74503594881c7090","abstract_canon_sha256":"dbf66497bc6e803d9fcc6254807cbc674056611d7f429cdcf3587ab075b3316b"},"schema_version":"1.0"},"canonical_sha256":"ac138298cd8fb9762c185637ad981834857f36c78959c17c392a0f6375f4b960","source":{"kind":"arxiv","id":"1811.11617","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.11617","created_at":"2026-05-17T23:39:47Z"},{"alias_kind":"arxiv_version","alias_value":"1811.11617v1","created_at":"2026-05-17T23:39:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.11617","created_at":"2026-05-17T23:39:47Z"},{"alias_kind":"pith_short_12","alias_value":"VQJYFGGNR64X","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VQJYFGGNR64XMLAY","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VQJYFGGN","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VQJYFGGNR64XMLAYKY323GAYGS","target":"record","payload":{"canonical_record":{"source":{"id":"1811.11617","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-28T15:17:19Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"db22a6e4607c62ad20e89332d3e0fa060d05c5de62b751ac74503594881c7090","abstract_canon_sha256":"dbf66497bc6e803d9fcc6254807cbc674056611d7f429cdcf3587ab075b3316b"},"schema_version":"1.0"},"canonical_sha256":"ac138298cd8fb9762c185637ad981834857f36c78959c17c392a0f6375f4b960","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:47.866604Z","signature_b64":"hb3Bx6FKRXxhc0lJZmrm6+mp3k3TDefFLEZUhLuwozd9jt+kIA0i+49DY+L9XXfiaR3YvaX0bONagK+tRs6SAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac138298cd8fb9762c185637ad981834857f36c78959c17c392a0f6375f4b960","last_reissued_at":"2026-05-17T23:39:47.865997Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:47.865997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.11617","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":"2026-05-17T23:39:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CTjwdsSBLCMMl42QVrs8n1j9UEF1Cl8PnSklQjr5vSxo1/kBb5P3eE2tBmTJR84t3Q0aGB/aPMcHafFU198dDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:09:11.565131Z"},"content_sha256":"7544483ca7629137d4a09ed795ff16b13394096ba12b682fbd139a0f1e513314","schema_version":"1.0","event_id":"sha256:7544483ca7629137d4a09ed795ff16b13394096ba12b682fbd139a0f1e513314"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VQJYFGGNR64XMLAYKY323GAYGS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Majorization and dynamics of continuous distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Bruno G. da Costa, Ignacio S. Gomez, M. A. F. dos Santos","submitted_at":"2018-11-28T15:17:19Z","abstract_excerpt":"In this work we show how the concept of majorization in continuous distributions can be employed to characterize chaotic, diffusive and quantum dynamics. The key point lies in that majorization allows to define an intuitive arrow of time, within a continuous dynamics, along with an associated majorized Second Law which implies the standard Second Law of thermodynamics but not viceversa. Moreover, mixing dynamics, generalized Fokker-Planck equations and quantum evolutions are explored as majorized ordered chains along the time evolution, being the stationary states the infimum elements."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.11617","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:39:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9y6kLvS78YUEpOM3ekDgbYDNrV4JzFb4LyK4e7d9YqsD1iZf+EHnbgw3M7CBSVHD5VQAXVYxZBSmhqfik0clDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:09:11.565499Z"},"content_sha256":"50d203333b582697bdd980de6f28bafc24ec57c4e77488d74bf6f92c6b1f40fc","schema_version":"1.0","event_id":"sha256:50d203333b582697bdd980de6f28bafc24ec57c4e77488d74bf6f92c6b1f40fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VQJYFGGNR64XMLAYKY323GAYGS/bundle.json","state_url":"https://pith.science/pith/VQJYFGGNR64XMLAYKY323GAYGS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VQJYFGGNR64XMLAYKY323GAYGS/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":"2026-06-08T22:09:11Z","links":{"resolver":"https://pith.science/pith/VQJYFGGNR64XMLAYKY323GAYGS","bundle":"https://pith.science/pith/VQJYFGGNR64XMLAYKY323GAYGS/bundle.json","state":"https://pith.science/pith/VQJYFGGNR64XMLAYKY323GAYGS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VQJYFGGNR64XMLAYKY323GAYGS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VQJYFGGNR64XMLAYKY323GAYGS","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":"dbf66497bc6e803d9fcc6254807cbc674056611d7f429cdcf3587ab075b3316b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-28T15:17:19Z","title_canon_sha256":"db22a6e4607c62ad20e89332d3e0fa060d05c5de62b751ac74503594881c7090"},"schema_version":"1.0","source":{"id":"1811.11617","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.11617","created_at":"2026-05-17T23:39:47Z"},{"alias_kind":"arxiv_version","alias_value":"1811.11617v1","created_at":"2026-05-17T23:39:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.11617","created_at":"2026-05-17T23:39:47Z"},{"alias_kind":"pith_short_12","alias_value":"VQJYFGGNR64X","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VQJYFGGNR64XMLAY","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VQJYFGGN","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:50d203333b582697bdd980de6f28bafc24ec57c4e77488d74bf6f92c6b1f40fc","target":"graph","created_at":"2026-05-17T23:39:47Z","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":"In this work we show how the concept of majorization in continuous distributions can be employed to characterize chaotic, diffusive and quantum dynamics. The key point lies in that majorization allows to define an intuitive arrow of time, within a continuous dynamics, along with an associated majorized Second Law which implies the standard Second Law of thermodynamics but not viceversa. Moreover, mixing dynamics, generalized Fokker-Planck equations and quantum evolutions are explored as majorized ordered chains along the time evolution, being the stationary states the infimum elements.","authors_text":"Bruno G. da Costa, Ignacio S. Gomez, M. A. F. dos Santos","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-28T15:17:19Z","title":"Majorization and dynamics of continuous distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.11617","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":"sha256:7544483ca7629137d4a09ed795ff16b13394096ba12b682fbd139a0f1e513314","target":"record","created_at":"2026-05-17T23:39:47Z","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":"dbf66497bc6e803d9fcc6254807cbc674056611d7f429cdcf3587ab075b3316b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-28T15:17:19Z","title_canon_sha256":"db22a6e4607c62ad20e89332d3e0fa060d05c5de62b751ac74503594881c7090"},"schema_version":"1.0","source":{"id":"1811.11617","kind":"arxiv","version":1}},"canonical_sha256":"ac138298cd8fb9762c185637ad981834857f36c78959c17c392a0f6375f4b960","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac138298cd8fb9762c185637ad981834857f36c78959c17c392a0f6375f4b960","first_computed_at":"2026-05-17T23:39:47.865997Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:47.865997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hb3Bx6FKRXxhc0lJZmrm6+mp3k3TDefFLEZUhLuwozd9jt+kIA0i+49DY+L9XXfiaR3YvaX0bONagK+tRs6SAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:47.866604Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.11617","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7544483ca7629137d4a09ed795ff16b13394096ba12b682fbd139a0f1e513314","sha256:50d203333b582697bdd980de6f28bafc24ec57c4e77488d74bf6f92c6b1f40fc"],"state_sha256":"999a1385b795177ff6f0e6de481d55879e6c74e8232a64135584f0d04cc16ea9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E66G2SPKXy8D5DCkeirR1f3FFISeFEMcmcJMbx4YUua3QCP4EAwTKXqfTHWI6Da25OcjpSAyCu5rwgLmeLdmDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T22:09:11.567366Z","bundle_sha256":"5706fa714b41e7da19336f0ef157531ab51dbbfe1cc761764b7db2f5594e6124"}}