{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:TSXRKW5FRO4KGIKGQYSPNKOR54","short_pith_number":"pith:TSXRKW5F","canonical_record":{"source":{"id":"1401.3932","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-16T08:43:13Z","cross_cats_sorted":[],"title_canon_sha256":"46b58d4c6570c6192befa288f1f7f4f21649cd12ec06eeacd02e36b4acaae5aa","abstract_canon_sha256":"7c2bf443d5bc67ef10b5416a84a35b31a48c64d9d8f44be4af026b947c6020aa"},"schema_version":"1.0"},"canonical_sha256":"9caf155ba58bb8a321468624f6a9d1ef26f051eeb04ceeb50916fff1d5ee50fa","source":{"kind":"arxiv","id":"1401.3932","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.3932","created_at":"2026-05-18T00:16:16Z"},{"alias_kind":"arxiv_version","alias_value":"1401.3932v2","created_at":"2026-05-18T00:16:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.3932","created_at":"2026-05-18T00:16:16Z"},{"alias_kind":"pith_short_12","alias_value":"TSXRKW5FRO4K","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TSXRKW5FRO4KGIKG","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TSXRKW5F","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:TSXRKW5FRO4KGIKGQYSPNKOR54","target":"record","payload":{"canonical_record":{"source":{"id":"1401.3932","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-16T08:43:13Z","cross_cats_sorted":[],"title_canon_sha256":"46b58d4c6570c6192befa288f1f7f4f21649cd12ec06eeacd02e36b4acaae5aa","abstract_canon_sha256":"7c2bf443d5bc67ef10b5416a84a35b31a48c64d9d8f44be4af026b947c6020aa"},"schema_version":"1.0"},"canonical_sha256":"9caf155ba58bb8a321468624f6a9d1ef26f051eeb04ceeb50916fff1d5ee50fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:16.344992Z","signature_b64":"yoROEKm6ujHOGEYf+Z3CLp5pq/jtdWG+vdpt66+z7idn0MsLa1B8aj3a78rUI3tu3n0Z0Dxp8+UI1DWh5PE4BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9caf155ba58bb8a321468624f6a9d1ef26f051eeb04ceeb50916fff1d5ee50fa","last_reissued_at":"2026-05-18T00:16:16.344264Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:16.344264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.3932","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":"2026-05-18T00:16:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DyIrud71VPWTINZsEUyi68I+I6x0ag2gSZu26GVc+vFCwIPfLDBATtSVSTPL9E2RFLo5LaguciDnrrRZYnoIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T20:28:09.398066Z"},"content_sha256":"39a16eac35fbea68633500b407d29aecc1c282db9074c3110b5231d1cefeb24c","schema_version":"1.0","event_id":"sha256:39a16eac35fbea68633500b407d29aecc1c282db9074c3110b5231d1cefeb24c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:TSXRKW5FRO4KGIKGQYSPNKOR54","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial normal forms of Constrained Differential Equations with three parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Henk Broer, H. Jard\\'on-Kojakhmetov","submitted_at":"2014-01-16T08:43:13Z","abstract_excerpt":"We study generic constrained differential equations (CDEs) with three parameters, thereby extending Takens's classification of singularities of such equations. In this approach, the singularities analyzed are the Swallowtail, the Hyperbolic, and the Elliptic Umbilics. We provide polynomial local normal forms of CDEs under topological equivalence. Generic CDEs are important in the study of slow-fast (SF) systems. Many properties and the characteristic behavior of the solutions of SF systems can be inferred from the corresponding CDE. Therefore, the results of this paper show a first approximati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3932","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":"2026-05-18T00:16:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oBgF159x/tb1a8mguETxk1Wiead/g7PCLJ1Co2iiHuFl64DZCIMRXErnQbeJfQEabmXb2Ql9hHzBLXPWzkF0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T20:28:09.398430Z"},"content_sha256":"b4cec9e62c9ab260dd914d8a70cebabf30267a6fff6dab5bce867532258c546e","schema_version":"1.0","event_id":"sha256:b4cec9e62c9ab260dd914d8a70cebabf30267a6fff6dab5bce867532258c546e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TSXRKW5FRO4KGIKGQYSPNKOR54/bundle.json","state_url":"https://pith.science/pith/TSXRKW5FRO4KGIKGQYSPNKOR54/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TSXRKW5FRO4KGIKGQYSPNKOR54/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":"2026-06-23T20:28:09Z","links":{"resolver":"https://pith.science/pith/TSXRKW5FRO4KGIKGQYSPNKOR54","bundle":"https://pith.science/pith/TSXRKW5FRO4KGIKGQYSPNKOR54/bundle.json","state":"https://pith.science/pith/TSXRKW5FRO4KGIKGQYSPNKOR54/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TSXRKW5FRO4KGIKGQYSPNKOR54/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TSXRKW5FRO4KGIKGQYSPNKOR54","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":"7c2bf443d5bc67ef10b5416a84a35b31a48c64d9d8f44be4af026b947c6020aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-16T08:43:13Z","title_canon_sha256":"46b58d4c6570c6192befa288f1f7f4f21649cd12ec06eeacd02e36b4acaae5aa"},"schema_version":"1.0","source":{"id":"1401.3932","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.3932","created_at":"2026-05-18T00:16:16Z"},{"alias_kind":"arxiv_version","alias_value":"1401.3932v2","created_at":"2026-05-18T00:16:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.3932","created_at":"2026-05-18T00:16:16Z"},{"alias_kind":"pith_short_12","alias_value":"TSXRKW5FRO4K","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TSXRKW5FRO4KGIKG","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TSXRKW5F","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:b4cec9e62c9ab260dd914d8a70cebabf30267a6fff6dab5bce867532258c546e","target":"graph","created_at":"2026-05-18T00:16:16Z","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 study generic constrained differential equations (CDEs) with three parameters, thereby extending Takens's classification of singularities of such equations. In this approach, the singularities analyzed are the Swallowtail, the Hyperbolic, and the Elliptic Umbilics. We provide polynomial local normal forms of CDEs under topological equivalence. Generic CDEs are important in the study of slow-fast (SF) systems. Many properties and the characteristic behavior of the solutions of SF systems can be inferred from the corresponding CDE. Therefore, the results of this paper show a first approximati","authors_text":"Henk Broer, H. Jard\\'on-Kojakhmetov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-16T08:43:13Z","title":"Polynomial normal forms of Constrained Differential Equations with three parameters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3932","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":"sha256:39a16eac35fbea68633500b407d29aecc1c282db9074c3110b5231d1cefeb24c","target":"record","created_at":"2026-05-18T00:16:16Z","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":"7c2bf443d5bc67ef10b5416a84a35b31a48c64d9d8f44be4af026b947c6020aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-16T08:43:13Z","title_canon_sha256":"46b58d4c6570c6192befa288f1f7f4f21649cd12ec06eeacd02e36b4acaae5aa"},"schema_version":"1.0","source":{"id":"1401.3932","kind":"arxiv","version":2}},"canonical_sha256":"9caf155ba58bb8a321468624f6a9d1ef26f051eeb04ceeb50916fff1d5ee50fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9caf155ba58bb8a321468624f6a9d1ef26f051eeb04ceeb50916fff1d5ee50fa","first_computed_at":"2026-05-18T00:16:16.344264Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:16.344264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yoROEKm6ujHOGEYf+Z3CLp5pq/jtdWG+vdpt66+z7idn0MsLa1B8aj3a78rUI3tu3n0Z0Dxp8+UI1DWh5PE4BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:16.344992Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.3932","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39a16eac35fbea68633500b407d29aecc1c282db9074c3110b5231d1cefeb24c","sha256:b4cec9e62c9ab260dd914d8a70cebabf30267a6fff6dab5bce867532258c546e"],"state_sha256":"ab9cfca879e10c9c44cfe548432fd7c27d1da28c96d8389c3c59d39b425e5841"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oJZDQ0GDDHp2tG7HZRMqkBfyPqm4jKGwu0iwnDCvQhzSBvYpT29J3G5ylW/R7V3kujCJEJwfoj56xXLyNHYwDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T20:28:09.400361Z","bundle_sha256":"0e796a390bcb53745aa4d7bb670fb08f0db0eee5b1130ff6a2dd46dbc9f3c21c"}}