{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:TIKY6NATWABK5S7IOYZFVAWZKU","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":"07b4ea5696878e26423dbcc0c8e41a15e3ceb865d112f5c8a787c47d8d0b3032","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-11-01T17:06:51Z","title_canon_sha256":"e30835ca3a52f735f2d4f454be3a73b9ede19d1ac59853f9ed8678b077d2979a"},"schema_version":"1.0","source":{"id":"0911.0182","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.0182","created_at":"2026-05-18T04:15:04Z"},{"alias_kind":"arxiv_version","alias_value":"0911.0182v3","created_at":"2026-05-18T04:15:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.0182","created_at":"2026-05-18T04:15:04Z"},{"alias_kind":"pith_short_12","alias_value":"TIKY6NATWABK","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"TIKY6NATWABK5S7I","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"TIKY6NAT","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:91044b79595f83cc3fd1ff2a84d0d1c433d9c776e5e1314c71a12edff8827270","target":"graph","created_at":"2026-05-18T04:15:04Z","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 describe some basic results for Quantum Stochastic Processes and present some new results about a certain class of processes which are associated to Quantum Iterated Function Systems (QIFS). We discuss questions related to the Markov property and we present a definition of entropy which is induced by a QIFS. This definition is a natural generalization of the Shannon-Kolmogorov entropy from Ergodic Theory. This definition is different from the one in the paper \"A Thermodynamic Formalism for density matrices in Quantum Information\" by the same authors.","authors_text":"A. Baraviera, Artur O. Lopes, C. F. Lardizabal, M. Terra Cunha","cross_cats":["math-ph","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-11-01T17:06:51Z","title":"Quantum Stochastic Processes, Quantum Iterated Function Systems and Entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0182","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":"sha256:3d134cb0df3acb893e2c6a60caec7c084268b63ae74d2db9711cd495c78ae0c1","target":"record","created_at":"2026-05-18T04:15:04Z","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":"07b4ea5696878e26423dbcc0c8e41a15e3ceb865d112f5c8a787c47d8d0b3032","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-11-01T17:06:51Z","title_canon_sha256":"e30835ca3a52f735f2d4f454be3a73b9ede19d1ac59853f9ed8678b077d2979a"},"schema_version":"1.0","source":{"id":"0911.0182","kind":"arxiv","version":3}},"canonical_sha256":"9a158f3413b002aecbe876325a82d9553df22f75edcc0b176b10e4945713acdb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a158f3413b002aecbe876325a82d9553df22f75edcc0b176b10e4945713acdb","first_computed_at":"2026-05-18T04:15:04.712200Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:04.712200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FIJDIMhvS0wqAY+yK0ChonAkhy3aZ4TfVg5MNLD8JwcZ2wWBIwNWlpxjFRIhqzwMdANUj6BWU9TwL723fhAjCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:04.712958Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.0182","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d134cb0df3acb893e2c6a60caec7c084268b63ae74d2db9711cd495c78ae0c1","sha256:91044b79595f83cc3fd1ff2a84d0d1c433d9c776e5e1314c71a12edff8827270"],"state_sha256":"5d99a7d87033f1d3630640fb2ca9c996a1b7da490f1181ded19acab4bcde90c8"}