{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MGM7CLJUSYOYR2CJSMJDEQCJTD","short_pith_number":"pith:MGM7CLJU","canonical_record":{"source":{"id":"1509.04849","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-16T08:28:51Z","cross_cats_sorted":["math.DS","math.MP","math.PR","quant-ph"],"title_canon_sha256":"5b3b1c7426582743f07f63039aa511c34c196a95f791f74356d5a8c5a3386d88","abstract_canon_sha256":"55e890489bb835cc2e95f224bba9180dac2c4434773272305ef5ff1762ad30e9"},"schema_version":"1.0"},"canonical_sha256":"6199f12d34961d88e849931232404998c412ac6442bfc8a2bf78aa41802ad85e","source":{"kind":"arxiv","id":"1509.04849","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.04849","created_at":"2026-05-18T01:32:51Z"},{"alias_kind":"arxiv_version","alias_value":"1509.04849v1","created_at":"2026-05-18T01:32:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04849","created_at":"2026-05-18T01:32:51Z"},{"alias_kind":"pith_short_12","alias_value":"MGM7CLJUSYOY","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MGM7CLJUSYOYR2CJ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MGM7CLJU","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MGM7CLJUSYOYR2CJSMJDEQCJTD","target":"record","payload":{"canonical_record":{"source":{"id":"1509.04849","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-16T08:28:51Z","cross_cats_sorted":["math.DS","math.MP","math.PR","quant-ph"],"title_canon_sha256":"5b3b1c7426582743f07f63039aa511c34c196a95f791f74356d5a8c5a3386d88","abstract_canon_sha256":"55e890489bb835cc2e95f224bba9180dac2c4434773272305ef5ff1762ad30e9"},"schema_version":"1.0"},"canonical_sha256":"6199f12d34961d88e849931232404998c412ac6442bfc8a2bf78aa41802ad85e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:51.497386Z","signature_b64":"C/lb5UPk/B1UH4ueNthw1jFd0MRvdMITaBdtlyHWtG2+kxkM6/d4taPbuXW2BhcOG2eCI0tEdmBVAJHunvGkDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6199f12d34961d88e849931232404998c412ac6442bfc8a2bf78aa41802ad85e","last_reissued_at":"2026-05-18T01:32:51.496755Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:51.496755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.04849","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":"2026-05-18T01:32:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F7Ao3Gf0FE1BfOESiODG6efWxHYQ35aBXreLy4oVY7hrf0kI6vjzTzhB2W92RxBNg0j8pdo5pMZrE6oF2dsFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:00:22.622732Z"},"content_sha256":"f7ee94acfffe153dd0941df7bc9e43ba6db7d47a2e3877d68d0145dc5ac02b93","schema_version":"1.0","event_id":"sha256:f7ee94acfffe153dd0941df7bc9e43ba6db7d47a2e3877d68d0145dc5ac02b93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MGM7CLJUSYOYR2CJSMJDEQCJTD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum extensions of dynamical systems and of Markov semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP","math.PR","quant-ph"],"primary_cat":"math-ph","authors_text":"Ivan Bardet","submitted_at":"2015-09-16T08:28:51Z","abstract_excerpt":"We investigate some particular completely positive maps which admit a stable commutative Von Neumann subalgebra. The restriction of such maps to the stable algebra is then a Markov operator. In the first part of this article, we propose a recipe in order to find a quantum extension of a given Markov operator in the above sense. We show that the existence of such an extension is linked with the existence of a special form of dilation for the Markov operator studied by Attal in \\cite{Att1}, reducing the problem to the extension of dynamical system. We then apply our method to the same problem in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04849","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":"2026-05-18T01:32:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C7PRx40cfIwnVWVSSWOv9cfLp+MoqCZ5ZdTg3BDyx97zHn+hlNStXXFbyOzfGROT6JnazJgF9fJSeXo6GP/qBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:00:22.623308Z"},"content_sha256":"2b58e399e016c770ba8a93826cbb95f365661fb348d5da4c41924b7ce97b7caa","schema_version":"1.0","event_id":"sha256:2b58e399e016c770ba8a93826cbb95f365661fb348d5da4c41924b7ce97b7caa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MGM7CLJUSYOYR2CJSMJDEQCJTD/bundle.json","state_url":"https://pith.science/pith/MGM7CLJUSYOYR2CJSMJDEQCJTD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MGM7CLJUSYOYR2CJSMJDEQCJTD/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":"2026-06-07T06:00:22Z","links":{"resolver":"https://pith.science/pith/MGM7CLJUSYOYR2CJSMJDEQCJTD","bundle":"https://pith.science/pith/MGM7CLJUSYOYR2CJSMJDEQCJTD/bundle.json","state":"https://pith.science/pith/MGM7CLJUSYOYR2CJSMJDEQCJTD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MGM7CLJUSYOYR2CJSMJDEQCJTD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MGM7CLJUSYOYR2CJSMJDEQCJTD","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":"55e890489bb835cc2e95f224bba9180dac2c4434773272305ef5ff1762ad30e9","cross_cats_sorted":["math.DS","math.MP","math.PR","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-16T08:28:51Z","title_canon_sha256":"5b3b1c7426582743f07f63039aa511c34c196a95f791f74356d5a8c5a3386d88"},"schema_version":"1.0","source":{"id":"1509.04849","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.04849","created_at":"2026-05-18T01:32:51Z"},{"alias_kind":"arxiv_version","alias_value":"1509.04849v1","created_at":"2026-05-18T01:32:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04849","created_at":"2026-05-18T01:32:51Z"},{"alias_kind":"pith_short_12","alias_value":"MGM7CLJUSYOY","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MGM7CLJUSYOYR2CJ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MGM7CLJU","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:2b58e399e016c770ba8a93826cbb95f365661fb348d5da4c41924b7ce97b7caa","target":"graph","created_at":"2026-05-18T01:32:51Z","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 investigate some particular completely positive maps which admit a stable commutative Von Neumann subalgebra. The restriction of such maps to the stable algebra is then a Markov operator. In the first part of this article, we propose a recipe in order to find a quantum extension of a given Markov operator in the above sense. We show that the existence of such an extension is linked with the existence of a special form of dilation for the Markov operator studied by Attal in \\cite{Att1}, reducing the problem to the extension of dynamical system. We then apply our method to the same problem in","authors_text":"Ivan Bardet","cross_cats":["math.DS","math.MP","math.PR","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-16T08:28:51Z","title":"Quantum extensions of dynamical systems and of Markov semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04849","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:f7ee94acfffe153dd0941df7bc9e43ba6db7d47a2e3877d68d0145dc5ac02b93","target":"record","created_at":"2026-05-18T01:32:51Z","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":"55e890489bb835cc2e95f224bba9180dac2c4434773272305ef5ff1762ad30e9","cross_cats_sorted":["math.DS","math.MP","math.PR","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-16T08:28:51Z","title_canon_sha256":"5b3b1c7426582743f07f63039aa511c34c196a95f791f74356d5a8c5a3386d88"},"schema_version":"1.0","source":{"id":"1509.04849","kind":"arxiv","version":1}},"canonical_sha256":"6199f12d34961d88e849931232404998c412ac6442bfc8a2bf78aa41802ad85e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6199f12d34961d88e849931232404998c412ac6442bfc8a2bf78aa41802ad85e","first_computed_at":"2026-05-18T01:32:51.496755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:51.496755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C/lb5UPk/B1UH4ueNthw1jFd0MRvdMITaBdtlyHWtG2+kxkM6/d4taPbuXW2BhcOG2eCI0tEdmBVAJHunvGkDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:51.497386Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.04849","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7ee94acfffe153dd0941df7bc9e43ba6db7d47a2e3877d68d0145dc5ac02b93","sha256:2b58e399e016c770ba8a93826cbb95f365661fb348d5da4c41924b7ce97b7caa"],"state_sha256":"14b2813ead235a12a26a53653831687fc75a4915f99bf31d6e153d828d65d11e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Leljnp0tIM12hSQvh61zTGIWzUBhW5Rhej6rFmUJpoDmFwkw/r6kURGtnTnsO/YhEFnKXG5dUe1JPeySyAidDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T06:00:22.626436Z","bundle_sha256":"bcdbac64f1f246447209de8035a5a6bb3bb0c9fe59accdb390b7254daf1f709f"}}