{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:QOEZ5OL4IHFQ3AEXQQ42ULBUS4","short_pith_number":"pith:QOEZ5OL4","schema_version":"1.0","canonical_sha256":"83899eb97c41cb0d80978439aa2c349725e242101787e6e6b1c05a14d4e0dff2","source":{"kind":"arxiv","id":"1402.7287","version":1},"attestation_state":"computed","paper":{"title":"On the long-time asymptotics of quantum dynamical semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Guido A. Raggio, Pablo R. Zangara","submitted_at":"2014-02-28T15:46:59Z","abstract_excerpt":"We consider semigroups $\\{\\alpha_t: \\; t\\geq 0\\}$ of normal, unital, completely positive maps $\\alpha_t$ on a von Neumann algebra ${\\mathcal M}$. The (predual) semigroup $\\nu_t (\\rho):= \\rho \\circ \\alpha_t$ on normal states $\\rho$ of $\\mathcal M$ leaves invariant the face ${\\mathcal F}_p:= \\{\\rho : \\; \\rho (p)=1\\}$ supported by the projection $p\\in {\\mathcal M}$, if and only if $\\alpha_t(p)\\geq p$ (i.e., $p$ is sub-harmonic). We complete the arguments showing that the sub-harmonic projections form a complete lattice. We then consider $r_o$, the smallest projection which is larger than each sup"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1402.7287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-28T15:46:59Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"97ccfe8e5af310d6c54bfcf23a5077e4e4f272176bf1372bdc5d0ad62baf1d6a","abstract_canon_sha256":"0570416ee32a6b8277bca451ecb30fc07b697df9ee3d34124534a81cb2c844d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:02.088440Z","signature_b64":"bHf3ZW+RjfRh4UsL/taz60kn0N+NNHh4n/luYrEua3Y/LzbfozFR1iIP/tILaUEvMrJTl26Ca/xUMVKk1EliDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83899eb97c41cb0d80978439aa2c349725e242101787e6e6b1c05a14d4e0dff2","last_reissued_at":"2026-05-18T00:37:02.087682Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:02.087682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the long-time asymptotics of quantum dynamical semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Guido A. Raggio, Pablo R. Zangara","submitted_at":"2014-02-28T15:46:59Z","abstract_excerpt":"We consider semigroups $\\{\\alpha_t: \\; t\\geq 0\\}$ of normal, unital, completely positive maps $\\alpha_t$ on a von Neumann algebra ${\\mathcal M}$. The (predual) semigroup $\\nu_t (\\rho):= \\rho \\circ \\alpha_t$ on normal states $\\rho$ of $\\mathcal M$ leaves invariant the face ${\\mathcal F}_p:= \\{\\rho : \\; \\rho (p)=1\\}$ supported by the projection $p\\in {\\mathcal M}$, if and only if $\\alpha_t(p)\\geq p$ (i.e., $p$ is sub-harmonic). We complete the arguments showing that the sub-harmonic projections form a complete lattice. We then consider $r_o$, the smallest projection which is larger than each sup"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.7287","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1402.7287","created_at":"2026-05-18T00:37:02.087798+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.7287v1","created_at":"2026-05-18T00:37:02.087798+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.7287","created_at":"2026-05-18T00:37:02.087798+00:00"},{"alias_kind":"pith_short_12","alias_value":"QOEZ5OL4IHFQ","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"QOEZ5OL4IHFQ3AEX","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"QOEZ5OL4","created_at":"2026-05-18T12:28:46.137349+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.18392","citing_title":"Precision limits for time-dependent quantum metrology under Markovian noise","ref_index":16,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QOEZ5OL4IHFQ3AEXQQ42ULBUS4","json":"https://pith.science/pith/QOEZ5OL4IHFQ3AEXQQ42ULBUS4.json","graph_json":"https://pith.science/api/pith-number/QOEZ5OL4IHFQ3AEXQQ42ULBUS4/graph.json","events_json":"https://pith.science/api/pith-number/QOEZ5OL4IHFQ3AEXQQ42ULBUS4/events.json","paper":"https://pith.science/paper/QOEZ5OL4"},"agent_actions":{"view_html":"https://pith.science/pith/QOEZ5OL4IHFQ3AEXQQ42ULBUS4","download_json":"https://pith.science/pith/QOEZ5OL4IHFQ3AEXQQ42ULBUS4.json","view_paper":"https://pith.science/paper/QOEZ5OL4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.7287&json=true","fetch_graph":"https://pith.science/api/pith-number/QOEZ5OL4IHFQ3AEXQQ42ULBUS4/graph.json","fetch_events":"https://pith.science/api/pith-number/QOEZ5OL4IHFQ3AEXQQ42ULBUS4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QOEZ5OL4IHFQ3AEXQQ42ULBUS4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QOEZ5OL4IHFQ3AEXQQ42ULBUS4/action/storage_attestation","attest_author":"https://pith.science/pith/QOEZ5OL4IHFQ3AEXQQ42ULBUS4/action/author_attestation","sign_citation":"https://pith.science/pith/QOEZ5OL4IHFQ3AEXQQ42ULBUS4/action/citation_signature","submit_replication":"https://pith.science/pith/QOEZ5OL4IHFQ3AEXQQ42ULBUS4/action/replication_record"}},"created_at":"2026-05-18T00:37:02.087798+00:00","updated_at":"2026-05-18T00:37:02.087798+00:00"}