{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VZTMLNZMHYZ47RAKJYWRBLEQXL","short_pith_number":"pith:VZTMLNZM","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"},"canonical_sha256":"ae66c5b72c3e33cfc40a4e2d10ac90badc3346cbfbf893d15fb22b0bff536a78","source":{"kind":"arxiv","id":"1606.02605","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02605","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02605v1","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02605","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"pith_short_12","alias_value":"VZTMLNZMHYZ4","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VZTMLNZMHYZ47RAK","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VZTMLNZM","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VZTMLNZMHYZ47RAKJYWRBLEQXL","target":"record","payload":{"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"},"canonical_sha256":"ae66c5b72c3e33cfc40a4e2d10ac90badc3346cbfbf893d15fb22b0bff536a78","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"},"source_kind":"arxiv","source_id":"1606.02605","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":"2026-05-18T00:23:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n45EFCzZGB6VwpSWKrUJ9mFNcjdbA9uo0mBlFH4huhdRHAYbWeBRWM7rDyACDZVxxmcz2aUtCP6fgfRcyuAlBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:58:19.982045Z"},"content_sha256":"c7a14bfc1911c6b737cab21391c8fdaa5ed55c4597a41e106d0655336b0f6fbf","schema_version":"1.0","event_id":"sha256:c7a14bfc1911c6b737cab21391c8fdaa5ed55c4597a41e106d0655336b0f6fbf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VZTMLNZMHYZ47RAKJYWRBLEQXL","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RhF9Cvvt9rXlS10yHAOl5yqaMh588jnOkN6nljCF2ox/Q7cN3n8My4PxUQQFriz9wX+9UvEwgV19GNFa9A5RBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:58:19.982796Z"},"content_sha256":"55c188d06f4bd378a92e6f1926a016622a2bed32f438eddcb84a1a56325244f3","schema_version":"1.0","event_id":"sha256:55c188d06f4bd378a92e6f1926a016622a2bed32f438eddcb84a1a56325244f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VZTMLNZMHYZ47RAKJYWRBLEQXL/bundle.json","state_url":"https://pith.science/pith/VZTMLNZMHYZ47RAKJYWRBLEQXL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VZTMLNZMHYZ47RAKJYWRBLEQXL/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":"2026-05-31T10:58:19Z","links":{"resolver":"https://pith.science/pith/VZTMLNZMHYZ47RAKJYWRBLEQXL","bundle":"https://pith.science/pith/VZTMLNZMHYZ47RAKJYWRBLEQXL/bundle.json","state":"https://pith.science/pith/VZTMLNZMHYZ47RAKJYWRBLEQXL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VZTMLNZMHYZ47RAKJYWRBLEQXL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VZTMLNZMHYZ47RAKJYWRBLEQXL","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":"fdaffda81ffaab12e36abef73cceb240e89fb4d902b8606439019b72858a233a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-06-08T15:28:38Z","title_canon_sha256":"d05f6b6115278c26a144745fa250c7f8e5f23192f07b3586d1673c9f79ee0bd1"},"schema_version":"1.0","source":{"id":"1606.02605","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02605","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02605v1","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02605","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"pith_short_12","alias_value":"VZTMLNZMHYZ4","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VZTMLNZMHYZ47RAK","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VZTMLNZM","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:55c188d06f4bd378a92e6f1926a016622a2bed32f438eddcb84a1a56325244f3","target":"graph","created_at":"2026-05-18T00:23:57Z","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":"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.","authors_text":"Anna Kiesenhofer, Eva Miranda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-06-08T15:28:38Z","title":"Non-commutative integrable systems on $b$-symplectic manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02605","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:c7a14bfc1911c6b737cab21391c8fdaa5ed55c4597a41e106d0655336b0f6fbf","target":"record","created_at":"2026-05-18T00:23:57Z","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":"fdaffda81ffaab12e36abef73cceb240e89fb4d902b8606439019b72858a233a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-06-08T15:28:38Z","title_canon_sha256":"d05f6b6115278c26a144745fa250c7f8e5f23192f07b3586d1673c9f79ee0bd1"},"schema_version":"1.0","source":{"id":"1606.02605","kind":"arxiv","version":1}},"canonical_sha256":"ae66c5b72c3e33cfc40a4e2d10ac90badc3346cbfbf893d15fb22b0bff536a78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae66c5b72c3e33cfc40a4e2d10ac90badc3346cbfbf893d15fb22b0bff536a78","first_computed_at":"2026-05-18T00:23:57.169284Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:57.169284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zr4IJrZEXAFfv6XKzxHvJNSjgFaUzH7fcuDmeYfExfu7GZJpjPxGiFrd4OdfdbJ3ct+tPmmCQv9GXCWMfZIaCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:57.169763Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.02605","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7a14bfc1911c6b737cab21391c8fdaa5ed55c4597a41e106d0655336b0f6fbf","sha256:55c188d06f4bd378a92e6f1926a016622a2bed32f438eddcb84a1a56325244f3"],"state_sha256":"d4b78f3ae144b5a75710e98267efa518a4cbc62f6664d672bb204892747811e5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RJwm7tis+V+yb4MoC9Obw02nVhYmobGbUHEDij5ywyMqQmyUufYvvfdu8154Aa7ZV/24lT3k4PkzFMvui9PaDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:58:19.986493Z","bundle_sha256":"6ea7c99713a3a03233587dc0d47c9739e3664469c2b95e81acadca0298f7d071"}}