{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:IYPRWGSQTGA6TV6GCVUM52DNEI","short_pith_number":"pith:IYPRWGSQ","canonical_record":{"source":{"id":"1901.09268","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-01-26T19:36:53Z","cross_cats_sorted":[],"title_canon_sha256":"bf6b7c97f9b490aacf4483a2a96ffc44374b325adae32b23e1d2efc5cb442298","abstract_canon_sha256":"935e736fb2713acafeae8dc588f56f70ac5c93b630bf37b81c9a1391ee83610d"},"schema_version":"1.0"},"canonical_sha256":"461f1b1a509981e9d7c61568cee86d222f116ddb57f99af3be4bb4b61f5502be","source":{"kind":"arxiv","id":"1901.09268","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.09268","created_at":"2026-05-17T23:55:25Z"},{"alias_kind":"arxiv_version","alias_value":"1901.09268v1","created_at":"2026-05-17T23:55:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.09268","created_at":"2026-05-17T23:55:25Z"},{"alias_kind":"pith_short_12","alias_value":"IYPRWGSQTGA6","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IYPRWGSQTGA6TV6G","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IYPRWGSQ","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:IYPRWGSQTGA6TV6GCVUM52DNEI","target":"record","payload":{"canonical_record":{"source":{"id":"1901.09268","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-01-26T19:36:53Z","cross_cats_sorted":[],"title_canon_sha256":"bf6b7c97f9b490aacf4483a2a96ffc44374b325adae32b23e1d2efc5cb442298","abstract_canon_sha256":"935e736fb2713acafeae8dc588f56f70ac5c93b630bf37b81c9a1391ee83610d"},"schema_version":"1.0"},"canonical_sha256":"461f1b1a509981e9d7c61568cee86d222f116ddb57f99af3be4bb4b61f5502be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:25.273023Z","signature_b64":"TYSZ9kzXRF/kb8AvdZQ2xdaXjJuM/sqBkd/O7rMG0THAkGS/FGFzzHkbg2SmesK1nUG87Pr4hgq7F7oVR8jOAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"461f1b1a509981e9d7c61568cee86d222f116ddb57f99af3be4bb4b61f5502be","last_reissued_at":"2026-05-17T23:55:25.272434Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:25.272434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.09268","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":"2026-05-17T23:55:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8ol6kgzatjdaUF0I25ut7kd7XXlfVReUdhtEftFL/V53gAYSejR7+ugbwUPLh9X2fQoLwqsFpaydf4r5sPhUAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:54:10.957846Z"},"content_sha256":"512c814a94c7bd94e862086335177c3d1bc2520f71cb771860549f0223b69ba7","schema_version":"1.0","event_id":"sha256:512c814a94c7bd94e862086335177c3d1bc2520f71cb771860549f0223b69ba7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:IYPRWGSQTGA6TV6GCVUM52DNEI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Godbillon-Vey sequence and Francoise algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dmitry Novikov, Jessie Pontigo-Herrera, Laura Ortiz-Bobadilla, Pavao Mardesic","submitted_at":"2019-01-26T19:36:53Z","abstract_excerpt":"We consider foliations given by deformations $dF+\\epsilon\\omega$ of exact forms $dF$ in $\\mathbb{C}^2$ in a neighborhood of a family of cycles $\\gamma(t)\\subset F^{-1}(t)$.\n  In 1996 Francoise gave an algorithm for calculating the first nonzero term of the displacement function $\\Delta$ along $\\gamma$ of such deformations. This algorithm recalls the well-known Godbillon-Vey sequences discovered in 1971 for investigation integrability of a form $\\omega$. In this paper, we establish the correspondence between the two approaches and translate some results by Casale relating types of integrability"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09268","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":"2026-05-17T23:55:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7nrE6iekVBNKfjUbD/qBcRUpZKf6xdeMlEwcgTpIPJOntjZ98OFgkACs3u5scrbV+riLjeo0TfapWzIqxDSRDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:54:10.958205Z"},"content_sha256":"321beae5eaf93e3d8761465373e489d85e546f72bf92f2031e59d897ccc33e61","schema_version":"1.0","event_id":"sha256:321beae5eaf93e3d8761465373e489d85e546f72bf92f2031e59d897ccc33e61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IYPRWGSQTGA6TV6GCVUM52DNEI/bundle.json","state_url":"https://pith.science/pith/IYPRWGSQTGA6TV6GCVUM52DNEI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IYPRWGSQTGA6TV6GCVUM52DNEI/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":"2026-05-27T11:54:10Z","links":{"resolver":"https://pith.science/pith/IYPRWGSQTGA6TV6GCVUM52DNEI","bundle":"https://pith.science/pith/IYPRWGSQTGA6TV6GCVUM52DNEI/bundle.json","state":"https://pith.science/pith/IYPRWGSQTGA6TV6GCVUM52DNEI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IYPRWGSQTGA6TV6GCVUM52DNEI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IYPRWGSQTGA6TV6GCVUM52DNEI","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":"935e736fb2713acafeae8dc588f56f70ac5c93b630bf37b81c9a1391ee83610d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-01-26T19:36:53Z","title_canon_sha256":"bf6b7c97f9b490aacf4483a2a96ffc44374b325adae32b23e1d2efc5cb442298"},"schema_version":"1.0","source":{"id":"1901.09268","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.09268","created_at":"2026-05-17T23:55:25Z"},{"alias_kind":"arxiv_version","alias_value":"1901.09268v1","created_at":"2026-05-17T23:55:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.09268","created_at":"2026-05-17T23:55:25Z"},{"alias_kind":"pith_short_12","alias_value":"IYPRWGSQTGA6","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IYPRWGSQTGA6TV6G","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IYPRWGSQ","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:321beae5eaf93e3d8761465373e489d85e546f72bf92f2031e59d897ccc33e61","target":"graph","created_at":"2026-05-17T23:55:25Z","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 consider foliations given by deformations $dF+\\epsilon\\omega$ of exact forms $dF$ in $\\mathbb{C}^2$ in a neighborhood of a family of cycles $\\gamma(t)\\subset F^{-1}(t)$.\n  In 1996 Francoise gave an algorithm for calculating the first nonzero term of the displacement function $\\Delta$ along $\\gamma$ of such deformations. This algorithm recalls the well-known Godbillon-Vey sequences discovered in 1971 for investigation integrability of a form $\\omega$. In this paper, we establish the correspondence between the two approaches and translate some results by Casale relating types of integrability","authors_text":"Dmitry Novikov, Jessie Pontigo-Herrera, Laura Ortiz-Bobadilla, Pavao Mardesic","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-01-26T19:36:53Z","title":"Godbillon-Vey sequence and Francoise algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09268","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":"sha256:512c814a94c7bd94e862086335177c3d1bc2520f71cb771860549f0223b69ba7","target":"record","created_at":"2026-05-17T23:55:25Z","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":"935e736fb2713acafeae8dc588f56f70ac5c93b630bf37b81c9a1391ee83610d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-01-26T19:36:53Z","title_canon_sha256":"bf6b7c97f9b490aacf4483a2a96ffc44374b325adae32b23e1d2efc5cb442298"},"schema_version":"1.0","source":{"id":"1901.09268","kind":"arxiv","version":1}},"canonical_sha256":"461f1b1a509981e9d7c61568cee86d222f116ddb57f99af3be4bb4b61f5502be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"461f1b1a509981e9d7c61568cee86d222f116ddb57f99af3be4bb4b61f5502be","first_computed_at":"2026-05-17T23:55:25.272434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:25.272434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TYSZ9kzXRF/kb8AvdZQ2xdaXjJuM/sqBkd/O7rMG0THAkGS/FGFzzHkbg2SmesK1nUG87Pr4hgq7F7oVR8jOAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:25.273023Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.09268","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:512c814a94c7bd94e862086335177c3d1bc2520f71cb771860549f0223b69ba7","sha256:321beae5eaf93e3d8761465373e489d85e546f72bf92f2031e59d897ccc33e61"],"state_sha256":"75bb561c6c0fb461fd1437cdc6c8829b76cae1da665fe59cba5da27e9f3e6efe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PjYzWAO5JoHg2yqHfTiQKvwrcGL4Bu7df/gjSVWfrbroctb4cqS9wRxq3gEdTPRliaGHaJA+t6ew/1w2hw3BBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:54:10.961185Z","bundle_sha256":"fbdf6f3ec11144189722ed73df31777b22d6ec14a3a75d2583e0af9b7cb7ed21"}}