{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:ZK7VOFDLF4KZ5IEY3RFIGOKZ4I","short_pith_number":"pith:ZK7VOFDL","canonical_record":{"source":{"id":"math/0411202","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2004-11-09T16:29:41Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"b4d5f353bda6830f77d6af02c9dc87deb7b1a2cac6a047262b0e51408cf02f67","abstract_canon_sha256":"19b5fe9777992a389a9aae5c67a75452944231837dbbfa957c277ec60c30cdfe"},"schema_version":"1.0"},"canonical_sha256":"cabf57146b2f159ea098dc4a833959e225465ae7cb83ebcfe09d17b9a0c991ac","source":{"kind":"arxiv","id":"math/0411202","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0411202","created_at":"2026-07-04T14:39:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0411202v1","created_at":"2026-07-04T14:39:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0411202","created_at":"2026-07-04T14:39:21Z"},{"alias_kind":"pith_short_12","alias_value":"ZK7VOFDLF4KZ","created_at":"2026-07-04T14:39:21Z"},{"alias_kind":"pith_short_16","alias_value":"ZK7VOFDLF4KZ5IEY","created_at":"2026-07-04T14:39:21Z"},{"alias_kind":"pith_short_8","alias_value":"ZK7VOFDL","created_at":"2026-07-04T14:39:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:ZK7VOFDLF4KZ5IEY3RFIGOKZ4I","target":"record","payload":{"canonical_record":{"source":{"id":"math/0411202","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2004-11-09T16:29:41Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"b4d5f353bda6830f77d6af02c9dc87deb7b1a2cac6a047262b0e51408cf02f67","abstract_canon_sha256":"19b5fe9777992a389a9aae5c67a75452944231837dbbfa957c277ec60c30cdfe"},"schema_version":"1.0"},"canonical_sha256":"cabf57146b2f159ea098dc4a833959e225465ae7cb83ebcfe09d17b9a0c991ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:39:21.145839Z","signature_b64":"WddPnb/kx4yYE+EnhMoSxEgo6Aw+4LDQt+vaNaP/8GbwS6vm7y25M+Uwk1/nIbG7+p2WT/PRNrsnw5Oc4jauBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cabf57146b2f159ea098dc4a833959e225465ae7cb83ebcfe09d17b9a0c991ac","last_reissued_at":"2026-07-04T14:39:21.145412Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:39:21.145412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0411202","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":"2026-07-04T14:39:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/UGoEl/IptWSwaQkNMkZLgtzbc5uSHOHOFkXsriFVnW5ZX3MEciEMd+WIXTO7jX8k18PjoRjjA72LZYtBlaMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T19:19:57.257613Z"},"content_sha256":"11ebac6e5a9514f78c1afd1a4a76cc888224966232bcbbbaf876defdb4c57196","schema_version":"1.0","event_id":"sha256:11ebac6e5a9514f78c1afd1a4a76cc888224966232bcbbbaf876defdb4c57196"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:ZK7VOFDLF4KZ5IEY3RFIGOKZ4I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinite dimensional entangled Markov chains","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OA","authors_text":"Francesco Fidaleo","submitted_at":"2004-11-09T16:29:41Z","abstract_excerpt":"We continue the analysis of nontrivial examples of quantum Markov processes. This is done by applying the construction of entangled Markov chains obtained from classical Markov chains with infinite state--space. The formula giving the joint correlations arises from the corresponding classical formula by replacing the usual matrix multiplication by the Schur multiplication. In this way, we provide nontrivial examples of entangled Markov chains on $\\bar{\\cup_{J\\subset Z} \\bar{\\otimes}_{J}F}^{C^{*}}$, $F$ being any infinite dimensional type $I$ factor, $J$ a finite interval of $Z$, and the bar th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411202","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/math/0411202/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":"2026-07-04T14:39:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NjV/Nj8iNGTi8uOjCV9mZd2YG79p4130kIVIx/bjZp4mvfjvG2b3BGU93PSHRMYUUuAlvXUqzDFmKye9zOLtCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T19:19:57.257990Z"},"content_sha256":"dc4a1d3e4bf576c42d061828f76355dfb306ae3396c9f48dc491aca384c72c7c","schema_version":"1.0","event_id":"sha256:dc4a1d3e4bf576c42d061828f76355dfb306ae3396c9f48dc491aca384c72c7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZK7VOFDLF4KZ5IEY3RFIGOKZ4I/bundle.json","state_url":"https://pith.science/pith/ZK7VOFDLF4KZ5IEY3RFIGOKZ4I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZK7VOFDLF4KZ5IEY3RFIGOKZ4I/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":"2026-07-04T19:19:57Z","links":{"resolver":"https://pith.science/pith/ZK7VOFDLF4KZ5IEY3RFIGOKZ4I","bundle":"https://pith.science/pith/ZK7VOFDLF4KZ5IEY3RFIGOKZ4I/bundle.json","state":"https://pith.science/pith/ZK7VOFDLF4KZ5IEY3RFIGOKZ4I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZK7VOFDLF4KZ5IEY3RFIGOKZ4I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:ZK7VOFDLF4KZ5IEY3RFIGOKZ4I","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":"19b5fe9777992a389a9aae5c67a75452944231837dbbfa957c277ec60c30cdfe","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"math.OA","submitted_at":"2004-11-09T16:29:41Z","title_canon_sha256":"b4d5f353bda6830f77d6af02c9dc87deb7b1a2cac6a047262b0e51408cf02f67"},"schema_version":"1.0","source":{"id":"math/0411202","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0411202","created_at":"2026-07-04T14:39:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0411202v1","created_at":"2026-07-04T14:39:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0411202","created_at":"2026-07-04T14:39:21Z"},{"alias_kind":"pith_short_12","alias_value":"ZK7VOFDLF4KZ","created_at":"2026-07-04T14:39:21Z"},{"alias_kind":"pith_short_16","alias_value":"ZK7VOFDLF4KZ5IEY","created_at":"2026-07-04T14:39:21Z"},{"alias_kind":"pith_short_8","alias_value":"ZK7VOFDL","created_at":"2026-07-04T14:39:21Z"}],"graph_snapshots":[{"event_id":"sha256:dc4a1d3e4bf576c42d061828f76355dfb306ae3396c9f48dc491aca384c72c7c","target":"graph","created_at":"2026-07-04T14:39:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0411202/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We continue the analysis of nontrivial examples of quantum Markov processes. This is done by applying the construction of entangled Markov chains obtained from classical Markov chains with infinite state--space. The formula giving the joint correlations arises from the corresponding classical formula by replacing the usual matrix multiplication by the Schur multiplication. In this way, we provide nontrivial examples of entangled Markov chains on $\\bar{\\cup_{J\\subset Z} \\bar{\\otimes}_{J}F}^{C^{*}}$, $F$ being any infinite dimensional type $I$ factor, $J$ a finite interval of $Z$, and the bar th","authors_text":"Francesco Fidaleo","cross_cats":["math.PR"],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"2004-11-09T16:29:41Z","title":"Infinite dimensional entangled Markov chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411202","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":"sha256:11ebac6e5a9514f78c1afd1a4a76cc888224966232bcbbbaf876defdb4c57196","target":"record","created_at":"2026-07-04T14:39:21Z","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":"19b5fe9777992a389a9aae5c67a75452944231837dbbfa957c277ec60c30cdfe","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"math.OA","submitted_at":"2004-11-09T16:29:41Z","title_canon_sha256":"b4d5f353bda6830f77d6af02c9dc87deb7b1a2cac6a047262b0e51408cf02f67"},"schema_version":"1.0","source":{"id":"math/0411202","kind":"arxiv","version":1}},"canonical_sha256":"cabf57146b2f159ea098dc4a833959e225465ae7cb83ebcfe09d17b9a0c991ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cabf57146b2f159ea098dc4a833959e225465ae7cb83ebcfe09d17b9a0c991ac","first_computed_at":"2026-07-04T14:39:21.145412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:39:21.145412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WddPnb/kx4yYE+EnhMoSxEgo6Aw+4LDQt+vaNaP/8GbwS6vm7y25M+Uwk1/nIbG7+p2WT/PRNrsnw5Oc4jauBg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:39:21.145839Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0411202","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11ebac6e5a9514f78c1afd1a4a76cc888224966232bcbbbaf876defdb4c57196","sha256:dc4a1d3e4bf576c42d061828f76355dfb306ae3396c9f48dc491aca384c72c7c"],"state_sha256":"255ef21fd6e68fea5e87c5735babb64eedef13e6c5192baedb244d2de6d3953b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C61ffn3ulQuyOPe0Dsx5/AE/2HLhsI2c/ukUvyQk8KdI6YRuDK61MxzEKiRQTWFSgg7t0atJeNV0ZR3kcJYpBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T19:19:57.260113Z","bundle_sha256":"022b530a4449e03a817cc0feed1e35dc2f11a58425f1e78b2acf7d0c5c63ab8a"}}