{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:F4YMVTGAVNEUWXZRJSKHRPY3LG","short_pith_number":"pith:F4YMVTGA","canonical_record":{"source":{"id":"2308.13359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-08-25T13:10:26Z","cross_cats_sorted":["math.AP","math.DG","math.GT"],"title_canon_sha256":"b78f7804cdf5fd1a7b995992a4626775ff19b270cfe4d47141cf6df2836508d2","abstract_canon_sha256":"8a8477782c2e35d70c2ebcf239f4a493c96a9a8d5e6eec7e97a2ea655e5f2ed1"},"schema_version":"1.0"},"canonical_sha256":"2f30caccc0ab494b5f314c9478bf1b599d877104819b2577b31e26ee4805a48e","source":{"kind":"arxiv","id":"2308.13359","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.13359","created_at":"2026-07-05T06:44:42Z"},{"alias_kind":"arxiv_version","alias_value":"2308.13359v1","created_at":"2026-07-05T06:44:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.13359","created_at":"2026-07-05T06:44:42Z"},{"alias_kind":"pith_short_12","alias_value":"F4YMVTGAVNEU","created_at":"2026-07-05T06:44:42Z"},{"alias_kind":"pith_short_16","alias_value":"F4YMVTGAVNEUWXZR","created_at":"2026-07-05T06:44:42Z"},{"alias_kind":"pith_short_8","alias_value":"F4YMVTGA","created_at":"2026-07-05T06:44:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:F4YMVTGAVNEUWXZRJSKHRPY3LG","target":"record","payload":{"canonical_record":{"source":{"id":"2308.13359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-08-25T13:10:26Z","cross_cats_sorted":["math.AP","math.DG","math.GT"],"title_canon_sha256":"b78f7804cdf5fd1a7b995992a4626775ff19b270cfe4d47141cf6df2836508d2","abstract_canon_sha256":"8a8477782c2e35d70c2ebcf239f4a493c96a9a8d5e6eec7e97a2ea655e5f2ed1"},"schema_version":"1.0"},"canonical_sha256":"2f30caccc0ab494b5f314c9478bf1b599d877104819b2577b31e26ee4805a48e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:44:42.783617Z","signature_b64":"M8y6uDqCWU90Roo9AVoQKQaYJbY+3y2BsLlmOzjZihTveh4ASlJ/0RPeNKYDP4Cp0iPL4FHKd8cSZ5Iw+/4kBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f30caccc0ab494b5f314c9478bf1b599d877104819b2577b31e26ee4805a48e","last_reissued_at":"2026-07-05T06:44:42.783112Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:44:42.783112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2308.13359","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":"2026-07-05T06:44:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tmJgnWmPs7cSuUfa1piILibu6d4PVaEaX1OFdpw0X5lgXGRrMtXLUyx1ktXgfYFcpWeRv5kMC/dLyBkwr/t2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T12:28:36.271012Z"},"content_sha256":"790cf4eb33de9319ad81d7a98f782c22c86360d2b76e5afa91e708d2b1729338","schema_version":"1.0","event_id":"sha256:790cf4eb33de9319ad81d7a98f782c22c86360d2b76e5afa91e708d2b1729338"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:F4YMVTGAVNEUWXZRJSKHRPY3LG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topology of first integrals via Milnor fibrations II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG","math.GT"],"primary_cat":"math.DS","authors_text":"Euripedes da Silva, Fernando Reis, Maico Ribeiro","submitted_at":"2023-08-25T13:10:26Z","abstract_excerpt":"This survey is the continuation of a series of works aimed at applying tools from Singularity Theory to Differential Equations. More precisely, we utilize the powerfull Milnor's Fibration Theory to give geometric-topological classifications of first integrals of differential systems. In the previous paper, systems of first-order quasilinear partial differential equations were examined, focusing on the case of an isolated singularity. Now, we address both cases of isolated and \\textit{non-isolated singularities} for more general dynamical systems (namely, \\textit{foliations}) that admit at leas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.13359","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.13359/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:44:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tc2I8QsJPOU/4+SxpnFPTvgvWyZk9F0ilcd/0H+TmV/d+EeiPQzLwPRil1fCOggyyOKDdw4W6zKGyU2x0OYyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T12:28:36.271394Z"},"content_sha256":"86c972e2d06229c0fd8a898227146714f551fbdda21298f79abb571aa7b1aba6","schema_version":"1.0","event_id":"sha256:86c972e2d06229c0fd8a898227146714f551fbdda21298f79abb571aa7b1aba6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F4YMVTGAVNEUWXZRJSKHRPY3LG/bundle.json","state_url":"https://pith.science/pith/F4YMVTGAVNEUWXZRJSKHRPY3LG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F4YMVTGAVNEUWXZRJSKHRPY3LG/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":"2026-07-06T12:28:36Z","links":{"resolver":"https://pith.science/pith/F4YMVTGAVNEUWXZRJSKHRPY3LG","bundle":"https://pith.science/pith/F4YMVTGAVNEUWXZRJSKHRPY3LG/bundle.json","state":"https://pith.science/pith/F4YMVTGAVNEUWXZRJSKHRPY3LG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F4YMVTGAVNEUWXZRJSKHRPY3LG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:F4YMVTGAVNEUWXZRJSKHRPY3LG","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":"8a8477782c2e35d70c2ebcf239f4a493c96a9a8d5e6eec7e97a2ea655e5f2ed1","cross_cats_sorted":["math.AP","math.DG","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-08-25T13:10:26Z","title_canon_sha256":"b78f7804cdf5fd1a7b995992a4626775ff19b270cfe4d47141cf6df2836508d2"},"schema_version":"1.0","source":{"id":"2308.13359","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.13359","created_at":"2026-07-05T06:44:42Z"},{"alias_kind":"arxiv_version","alias_value":"2308.13359v1","created_at":"2026-07-05T06:44:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.13359","created_at":"2026-07-05T06:44:42Z"},{"alias_kind":"pith_short_12","alias_value":"F4YMVTGAVNEU","created_at":"2026-07-05T06:44:42Z"},{"alias_kind":"pith_short_16","alias_value":"F4YMVTGAVNEUWXZR","created_at":"2026-07-05T06:44:42Z"},{"alias_kind":"pith_short_8","alias_value":"F4YMVTGA","created_at":"2026-07-05T06:44:42Z"}],"graph_snapshots":[{"event_id":"sha256:86c972e2d06229c0fd8a898227146714f551fbdda21298f79abb571aa7b1aba6","target":"graph","created_at":"2026-07-05T06:44:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2308.13359/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This survey is the continuation of a series of works aimed at applying tools from Singularity Theory to Differential Equations. More precisely, we utilize the powerfull Milnor's Fibration Theory to give geometric-topological classifications of first integrals of differential systems. In the previous paper, systems of first-order quasilinear partial differential equations were examined, focusing on the case of an isolated singularity. Now, we address both cases of isolated and \\textit{non-isolated singularities} for more general dynamical systems (namely, \\textit{foliations}) that admit at leas","authors_text":"Euripedes da Silva, Fernando Reis, Maico Ribeiro","cross_cats":["math.AP","math.DG","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-08-25T13:10:26Z","title":"Topology of first integrals via Milnor fibrations II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.13359","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":"sha256:790cf4eb33de9319ad81d7a98f782c22c86360d2b76e5afa91e708d2b1729338","target":"record","created_at":"2026-07-05T06:44:42Z","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":"8a8477782c2e35d70c2ebcf239f4a493c96a9a8d5e6eec7e97a2ea655e5f2ed1","cross_cats_sorted":["math.AP","math.DG","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-08-25T13:10:26Z","title_canon_sha256":"b78f7804cdf5fd1a7b995992a4626775ff19b270cfe4d47141cf6df2836508d2"},"schema_version":"1.0","source":{"id":"2308.13359","kind":"arxiv","version":1}},"canonical_sha256":"2f30caccc0ab494b5f314c9478bf1b599d877104819b2577b31e26ee4805a48e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f30caccc0ab494b5f314c9478bf1b599d877104819b2577b31e26ee4805a48e","first_computed_at":"2026-07-05T06:44:42.783112Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:44:42.783112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M8y6uDqCWU90Roo9AVoQKQaYJbY+3y2BsLlmOzjZihTveh4ASlJ/0RPeNKYDP4Cp0iPL4FHKd8cSZ5Iw+/4kBg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:44:42.783617Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.13359","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:790cf4eb33de9319ad81d7a98f782c22c86360d2b76e5afa91e708d2b1729338","sha256:86c972e2d06229c0fd8a898227146714f551fbdda21298f79abb571aa7b1aba6"],"state_sha256":"75c9906254d4c7b3c783b3053ad2abd078a7ab49c45f648fb2380d978237bb67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xpve6ZYeJipx0GKpppmoYCAOsbGC1WAlCegN04aSFbfM9J8tfq6dojrXCod1uZ7Wlx0hDtgNH2sGOo6Un/8WBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T12:28:36.273292Z","bundle_sha256":"c7f5ea9350b68c391a78de189a0bce0f4cc7ed86ff8e1da2e30d0325e978d0c9"}}