{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:CS5PIOTUH4Z7JXNZKHDNUNQFNV","short_pith_number":"pith:CS5PIOTU","schema_version":"1.0","canonical_sha256":"14baf43a743f33f4ddb951c6da36056d47815c1244ac1cdd5d6dd669698a5a45","source":{"kind":"arxiv","id":"1902.07833","version":1},"attestation_state":"computed","paper":{"title":"Validated computations for connecting orbits in polynomial vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jan Bouwe van den Berg, Ray Sheombarsing","submitted_at":"2019-02-21T01:27:56Z","abstract_excerpt":"In this paper we present a computer-assisted procedure for proving the existence of transverse heteroclinic orbits connecting hyperbolic equilibria of polynomial vector fields. The idea is to compute high-order Taylor approximations of local charts on the (un)stable manifolds by using the Parameterization Method and to use Chebyshev series to parameterize the orbit in between, which solves a boundary value problem. The existence of a heteroclinic orbit can then be established by setting up an appropriate fixed-point problem amenable to computer-assisted analysis. The fixed point problem simult"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1902.07833","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-02-21T01:27:56Z","cross_cats_sorted":[],"title_canon_sha256":"982f2fe1e45e0f41599fea35d1db97a9326245893214a13ebc08be45895a60f8","abstract_canon_sha256":"ccc81285393a33f416665698bd45a3ad86b9dcc82ed4289c10a4d3728fd0f574"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:03.739005Z","signature_b64":"PbC8br3CwuCxrtKug4AcodUb6Kphy4aQ2h8SwaYwfFPxgxnxHBD5mgpNSzYZHxRstq1Zzi+jVEoQ7c3hOnkcAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14baf43a743f33f4ddb951c6da36056d47815c1244ac1cdd5d6dd669698a5a45","last_reissued_at":"2026-05-17T23:53:03.738482Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:03.738482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Validated computations for connecting orbits in polynomial vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jan Bouwe van den Berg, Ray Sheombarsing","submitted_at":"2019-02-21T01:27:56Z","abstract_excerpt":"In this paper we present a computer-assisted procedure for proving the existence of transverse heteroclinic orbits connecting hyperbolic equilibria of polynomial vector fields. The idea is to compute high-order Taylor approximations of local charts on the (un)stable manifolds by using the Parameterization Method and to use Chebyshev series to parameterize the orbit in between, which solves a boundary value problem. The existence of a heteroclinic orbit can then be established by setting up an appropriate fixed-point problem amenable to computer-assisted analysis. The fixed point problem simult"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.07833","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1902.07833","created_at":"2026-05-17T23:53:03.738543+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.07833v1","created_at":"2026-05-17T23:53:03.738543+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.07833","created_at":"2026-05-17T23:53:03.738543+00:00"},{"alias_kind":"pith_short_12","alias_value":"CS5PIOTUH4Z7","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"CS5PIOTUH4Z7JXNZ","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"CS5PIOTU","created_at":"2026-05-18T12:33:15.570797+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CS5PIOTUH4Z7JXNZKHDNUNQFNV","json":"https://pith.science/pith/CS5PIOTUH4Z7JXNZKHDNUNQFNV.json","graph_json":"https://pith.science/api/pith-number/CS5PIOTUH4Z7JXNZKHDNUNQFNV/graph.json","events_json":"https://pith.science/api/pith-number/CS5PIOTUH4Z7JXNZKHDNUNQFNV/events.json","paper":"https://pith.science/paper/CS5PIOTU"},"agent_actions":{"view_html":"https://pith.science/pith/CS5PIOTUH4Z7JXNZKHDNUNQFNV","download_json":"https://pith.science/pith/CS5PIOTUH4Z7JXNZKHDNUNQFNV.json","view_paper":"https://pith.science/paper/CS5PIOTU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.07833&json=true","fetch_graph":"https://pith.science/api/pith-number/CS5PIOTUH4Z7JXNZKHDNUNQFNV/graph.json","fetch_events":"https://pith.science/api/pith-number/CS5PIOTUH4Z7JXNZKHDNUNQFNV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CS5PIOTUH4Z7JXNZKHDNUNQFNV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CS5PIOTUH4Z7JXNZKHDNUNQFNV/action/storage_attestation","attest_author":"https://pith.science/pith/CS5PIOTUH4Z7JXNZKHDNUNQFNV/action/author_attestation","sign_citation":"https://pith.science/pith/CS5PIOTUH4Z7JXNZKHDNUNQFNV/action/citation_signature","submit_replication":"https://pith.science/pith/CS5PIOTUH4Z7JXNZKHDNUNQFNV/action/replication_record"}},"created_at":"2026-05-17T23:53:03.738543+00:00","updated_at":"2026-05-17T23:53:03.738543+00:00"}