{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:VZTMLNZMHYZ47RAKJYWRBLEQXL","short_pith_number":"pith:VZTMLNZM","schema_version":"1.0","canonical_sha256":"ae66c5b72c3e33cfc40a4e2d10ac90badc3346cbfbf893d15fb22b0bff536a78","source":{"kind":"arxiv","id":"1606.02605","version":1},"attestation_state":"computed","paper":{"title":"Non-commutative integrable systems on $b$-symplectic manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Anna Kiesenhofer, Eva Miranda","submitted_at":"2016-06-08T15:28:38Z","abstract_excerpt":"In this paper we study non-commutative integrable systems on $b$-Poisson manifolds. One important source of examples (and motivation) of such systems comes from considering non-commutative systems on manifolds with boundary having the right asymptotics on the boundary. In this paper we describe this and other examples and we prove an action-angle theorem for non-commutative integrable systems on a $b$-symplectic manifold in a neighbourhood of a Liouville torus inside the critical set of the Poisson structure associated to the $b$-symplectic structure."},"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":"1606.02605","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-06-08T15:28:38Z","cross_cats_sorted":[],"title_canon_sha256":"d05f6b6115278c26a144745fa250c7f8e5f23192f07b3586d1673c9f79ee0bd1","abstract_canon_sha256":"fdaffda81ffaab12e36abef73cceb240e89fb4d902b8606439019b72858a233a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:57.169763Z","signature_b64":"Zr4IJrZEXAFfv6XKzxHvJNSjgFaUzH7fcuDmeYfExfu7GZJpjPxGiFrd4OdfdbJ3ct+tPmmCQv9GXCWMfZIaCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae66c5b72c3e33cfc40a4e2d10ac90badc3346cbfbf893d15fb22b0bff536a78","last_reissued_at":"2026-05-18T00:23:57.169284Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:57.169284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-commutative integrable systems on $b$-symplectic manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Anna Kiesenhofer, Eva Miranda","submitted_at":"2016-06-08T15:28:38Z","abstract_excerpt":"In this paper we study non-commutative integrable systems on $b$-Poisson manifolds. One important source of examples (and motivation) of such systems comes from considering non-commutative systems on manifolds with boundary having the right asymptotics on the boundary. In this paper we describe this and other examples and we prove an action-angle theorem for non-commutative integrable systems on a $b$-symplectic manifold in a neighbourhood of a Liouville torus inside the critical set of the Poisson structure associated to the $b$-symplectic structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02605","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":"1606.02605","created_at":"2026-05-18T00:23:57.169361+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.02605v1","created_at":"2026-05-18T00:23:57.169361+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02605","created_at":"2026-05-18T00:23:57.169361+00:00"},{"alias_kind":"pith_short_12","alias_value":"VZTMLNZMHYZ4","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"VZTMLNZMHYZ47RAK","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"VZTMLNZM","created_at":"2026-05-18T12:30:48.956258+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VZTMLNZMHYZ47RAKJYWRBLEQXL","json":"https://pith.science/pith/VZTMLNZMHYZ47RAKJYWRBLEQXL.json","graph_json":"https://pith.science/api/pith-number/VZTMLNZMHYZ47RAKJYWRBLEQXL/graph.json","events_json":"https://pith.science/api/pith-number/VZTMLNZMHYZ47RAKJYWRBLEQXL/events.json","paper":"https://pith.science/paper/VZTMLNZM"},"agent_actions":{"view_html":"https://pith.science/pith/VZTMLNZMHYZ47RAKJYWRBLEQXL","download_json":"https://pith.science/pith/VZTMLNZMHYZ47RAKJYWRBLEQXL.json","view_paper":"https://pith.science/paper/VZTMLNZM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.02605&json=true","fetch_graph":"https://pith.science/api/pith-number/VZTMLNZMHYZ47RAKJYWRBLEQXL/graph.json","fetch_events":"https://pith.science/api/pith-number/VZTMLNZMHYZ47RAKJYWRBLEQXL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VZTMLNZMHYZ47RAKJYWRBLEQXL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VZTMLNZMHYZ47RAKJYWRBLEQXL/action/storage_attestation","attest_author":"https://pith.science/pith/VZTMLNZMHYZ47RAKJYWRBLEQXL/action/author_attestation","sign_citation":"https://pith.science/pith/VZTMLNZMHYZ47RAKJYWRBLEQXL/action/citation_signature","submit_replication":"https://pith.science/pith/VZTMLNZMHYZ47RAKJYWRBLEQXL/action/replication_record"}},"created_at":"2026-05-18T00:23:57.169361+00:00","updated_at":"2026-05-18T00:23:57.169361+00:00"}