{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MI5ZBICINJ2QF6WWQACUYU2PK5","short_pith_number":"pith:MI5ZBICI","canonical_record":{"source":{"id":"1512.05303","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-12-16T19:53:17Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"165f4e67a6cc9a413346e801b0e5a5a0a18e265fad1cfd5aedc4fe7cacabf77b","abstract_canon_sha256":"9f461ad064b9ecc7911337e8e177879e6399cbb9fdaa16821cf7b3dae01ee0c1"},"schema_version":"1.0"},"canonical_sha256":"623b90a0486a7502fad680054c534f5771db36a5777715ebb2185e92648e0217","source":{"kind":"arxiv","id":"1512.05303","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05303","created_at":"2026-05-18T00:12:01Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05303v2","created_at":"2026-05-18T00:12:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05303","created_at":"2026-05-18T00:12:01Z"},{"alias_kind":"pith_short_12","alias_value":"MI5ZBICINJ2Q","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MI5ZBICINJ2QF6WW","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MI5ZBICI","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MI5ZBICINJ2QF6WWQACUYU2PK5","target":"record","payload":{"canonical_record":{"source":{"id":"1512.05303","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-12-16T19:53:17Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"165f4e67a6cc9a413346e801b0e5a5a0a18e265fad1cfd5aedc4fe7cacabf77b","abstract_canon_sha256":"9f461ad064b9ecc7911337e8e177879e6399cbb9fdaa16821cf7b3dae01ee0c1"},"schema_version":"1.0"},"canonical_sha256":"623b90a0486a7502fad680054c534f5771db36a5777715ebb2185e92648e0217","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:01.040600Z","signature_b64":"88aT2hfS5wuplXKsPIgEE6gmrknzzwKotSAHaw4gXaAAPvAsMklITE3yR90XBtNeY/u4YvHomTYq3qrWfPvXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"623b90a0486a7502fad680054c534f5771db36a5777715ebb2185e92648e0217","last_reissued_at":"2026-05-18T00:12:01.040029Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:01.040029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.05303","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:12:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kyanQh5JlaS5NYiZpI1mD8DN0b7kvk7PymjJAhpMKOqtlU/NUfFaUoKNLZ14A8wdyFHS3Nl4vsH/2d/Qn2MdDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:19:12.995375Z"},"content_sha256":"065fcc269dd4cff0b4aa9c5e58e127f4ed3b0484754e5e043326174c13428089","schema_version":"1.0","event_id":"sha256:065fcc269dd4cff0b4aa9c5e58e127f4ed3b0484754e5e043326174c13428089"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MI5ZBICINJ2QF6WWQACUYU2PK5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Desingularizing $b^m$-symplectic structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Eva Miranda, Jonathan Weitsman, Victor Guillemin","submitted_at":"2015-12-16T19:53:17Z","abstract_excerpt":"A $2n$-dimensional Poisson manifold $(M ,\\Pi)$ is said to be $b^m$-symplectic if it is symplectic on the complement of a hypersurface $Z$ and has a simple Darboux canonical form at points of $Z$ which we will describe below. In this paper we will discuss a desingularization procedure which, for $m$ even, converts $\\Pi$ into a family of symplectic forms $\\omega_{\\epsilon}$ having the property that $\\omega_{\\epsilon}$ is equal to the $b^m$-symplectic form dual to $\\Pi$ outside an $\\epsilon$-neighborhood of $Z$ and, in addition, converges to this form as $\\epsilon$ tends to zero in a sense that w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05303","kind":"arxiv","version":2},"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":"2026-05-18T00:12:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RWw92oMqVpxltdP9xGB5ezVe8UX40YZGtAt56OTrw7LUk1UG8iUu2RYzNuHL0DutLRqp3dAv7lsdYoIyWy1GBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:19:12.995758Z"},"content_sha256":"daff99ccc04daacbd458771449eac9dfc618ee4e283ab915b985bb690ba56e1f","schema_version":"1.0","event_id":"sha256:daff99ccc04daacbd458771449eac9dfc618ee4e283ab915b985bb690ba56e1f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MI5ZBICINJ2QF6WWQACUYU2PK5/bundle.json","state_url":"https://pith.science/pith/MI5ZBICINJ2QF6WWQACUYU2PK5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MI5ZBICINJ2QF6WWQACUYU2PK5/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":"2026-05-31T08:19:12Z","links":{"resolver":"https://pith.science/pith/MI5ZBICINJ2QF6WWQACUYU2PK5","bundle":"https://pith.science/pith/MI5ZBICINJ2QF6WWQACUYU2PK5/bundle.json","state":"https://pith.science/pith/MI5ZBICINJ2QF6WWQACUYU2PK5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MI5ZBICINJ2QF6WWQACUYU2PK5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MI5ZBICINJ2QF6WWQACUYU2PK5","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":"9f461ad064b9ecc7911337e8e177879e6399cbb9fdaa16821cf7b3dae01ee0c1","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-12-16T19:53:17Z","title_canon_sha256":"165f4e67a6cc9a413346e801b0e5a5a0a18e265fad1cfd5aedc4fe7cacabf77b"},"schema_version":"1.0","source":{"id":"1512.05303","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05303","created_at":"2026-05-18T00:12:01Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05303v2","created_at":"2026-05-18T00:12:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05303","created_at":"2026-05-18T00:12:01Z"},{"alias_kind":"pith_short_12","alias_value":"MI5ZBICINJ2Q","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MI5ZBICINJ2QF6WW","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MI5ZBICI","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:daff99ccc04daacbd458771449eac9dfc618ee4e283ab915b985bb690ba56e1f","target":"graph","created_at":"2026-05-18T00:12:01Z","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":"A $2n$-dimensional Poisson manifold $(M ,\\Pi)$ is said to be $b^m$-symplectic if it is symplectic on the complement of a hypersurface $Z$ and has a simple Darboux canonical form at points of $Z$ which we will describe below. In this paper we will discuss a desingularization procedure which, for $m$ even, converts $\\Pi$ into a family of symplectic forms $\\omega_{\\epsilon}$ having the property that $\\omega_{\\epsilon}$ is equal to the $b^m$-symplectic form dual to $\\Pi$ outside an $\\epsilon$-neighborhood of $Z$ and, in addition, converges to this form as $\\epsilon$ tends to zero in a sense that w","authors_text":"Eva Miranda, Jonathan Weitsman, Victor Guillemin","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-12-16T19:53:17Z","title":"Desingularizing $b^m$-symplectic structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05303","kind":"arxiv","version":2},"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":"sha256:065fcc269dd4cff0b4aa9c5e58e127f4ed3b0484754e5e043326174c13428089","target":"record","created_at":"2026-05-18T00:12:01Z","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":"9f461ad064b9ecc7911337e8e177879e6399cbb9fdaa16821cf7b3dae01ee0c1","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-12-16T19:53:17Z","title_canon_sha256":"165f4e67a6cc9a413346e801b0e5a5a0a18e265fad1cfd5aedc4fe7cacabf77b"},"schema_version":"1.0","source":{"id":"1512.05303","kind":"arxiv","version":2}},"canonical_sha256":"623b90a0486a7502fad680054c534f5771db36a5777715ebb2185e92648e0217","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"623b90a0486a7502fad680054c534f5771db36a5777715ebb2185e92648e0217","first_computed_at":"2026-05-18T00:12:01.040029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:01.040029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"88aT2hfS5wuplXKsPIgEE6gmrknzzwKotSAHaw4gXaAAPvAsMklITE3yR90XBtNeY/u4YvHomTYq3qrWfPvXDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:01.040600Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.05303","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:065fcc269dd4cff0b4aa9c5e58e127f4ed3b0484754e5e043326174c13428089","sha256:daff99ccc04daacbd458771449eac9dfc618ee4e283ab915b985bb690ba56e1f"],"state_sha256":"acfe59ec31c8b49517becb1528c235162dd706327c8058e7be44777b2d6c6042"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GVSxGVCZFpQ1TTjlCtjFF25rOBCtkIcXsLFclYAXMlbz1WtkYxQA9IkdyaMl69qAgJZte9nMk7WbPupAZP6SBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:19:12.998867Z","bundle_sha256":"f72498b624c7fa62e0f21f9fa2dec772c7c6c158ea5bf59b83d0319ab28e28b2"}}