{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:3RJITUKMPHCMTXHLND4KPBRFHZ","short_pith_number":"pith:3RJITUKM","schema_version":"1.0","canonical_sha256":"dc5289d14c79c4c9dceb68f8a786253e759fefb26b73d4b134cb6539db5697ab","source":{"kind":"arxiv","id":"1809.09950","version":1},"attestation_state":"computed","paper":{"title":"Global bifurcation index of critical orbit of strongly indefinite functional","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anna Go{\\l}\\k{e}biewska, Piotr Stefaniak","submitted_at":"2018-09-26T13:02:26Z","abstract_excerpt":"In this paper we study an index of a critical orbit, defined in terms of the degree for invariant strongly indefinite functionals. We establish a relationship of this index with the index of a critical point of the mapping restricted to the space normal to the orbit. The second aim of the article is to use the index of a critical orbit to prove the bifurcation of nontrivial solutions of nonlinear elliptic systems with Neumann boundary conditions. We consider also the existence of unbounded sets of solutions of such systems."},"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":"1809.09950","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-26T13:02:26Z","cross_cats_sorted":[],"title_canon_sha256":"f1730d4c6010dcb11bd667d5d448cbf865591d0c68fae4da0a207bf438623038","abstract_canon_sha256":"4d5a68ed9a989f22775c6f962ae60cc0f8d226584c3d364be41d7afea1caef40"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:43.144163Z","signature_b64":"Q2K/pYGrHg38ejfFCiV0MalltXV/ZpvoBpJd6g1K7bknkku1IFqI0WYJlyJNg7XZZPiIbphSlulf3uD2M04XCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc5289d14c79c4c9dceb68f8a786253e759fefb26b73d4b134cb6539db5697ab","last_reissued_at":"2026-05-18T00:04:43.143441Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:43.143441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global bifurcation index of critical orbit of strongly indefinite functional","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anna Go{\\l}\\k{e}biewska, Piotr Stefaniak","submitted_at":"2018-09-26T13:02:26Z","abstract_excerpt":"In this paper we study an index of a critical orbit, defined in terms of the degree for invariant strongly indefinite functionals. We establish a relationship of this index with the index of a critical point of the mapping restricted to the space normal to the orbit. The second aim of the article is to use the index of a critical orbit to prove the bifurcation of nontrivial solutions of nonlinear elliptic systems with Neumann boundary conditions. We consider also the existence of unbounded sets of solutions of such systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09950","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":"1809.09950","created_at":"2026-05-18T00:04:43.143594+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.09950v1","created_at":"2026-05-18T00:04:43.143594+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09950","created_at":"2026-05-18T00:04:43.143594+00:00"},{"alias_kind":"pith_short_12","alias_value":"3RJITUKMPHCM","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"3RJITUKMPHCMTXHL","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"3RJITUKM","created_at":"2026-05-18T12:32:02.567920+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/3RJITUKMPHCMTXHLND4KPBRFHZ","json":"https://pith.science/pith/3RJITUKMPHCMTXHLND4KPBRFHZ.json","graph_json":"https://pith.science/api/pith-number/3RJITUKMPHCMTXHLND4KPBRFHZ/graph.json","events_json":"https://pith.science/api/pith-number/3RJITUKMPHCMTXHLND4KPBRFHZ/events.json","paper":"https://pith.science/paper/3RJITUKM"},"agent_actions":{"view_html":"https://pith.science/pith/3RJITUKMPHCMTXHLND4KPBRFHZ","download_json":"https://pith.science/pith/3RJITUKMPHCMTXHLND4KPBRFHZ.json","view_paper":"https://pith.science/paper/3RJITUKM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.09950&json=true","fetch_graph":"https://pith.science/api/pith-number/3RJITUKMPHCMTXHLND4KPBRFHZ/graph.json","fetch_events":"https://pith.science/api/pith-number/3RJITUKMPHCMTXHLND4KPBRFHZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3RJITUKMPHCMTXHLND4KPBRFHZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3RJITUKMPHCMTXHLND4KPBRFHZ/action/storage_attestation","attest_author":"https://pith.science/pith/3RJITUKMPHCMTXHLND4KPBRFHZ/action/author_attestation","sign_citation":"https://pith.science/pith/3RJITUKMPHCMTXHLND4KPBRFHZ/action/citation_signature","submit_replication":"https://pith.science/pith/3RJITUKMPHCMTXHLND4KPBRFHZ/action/replication_record"}},"created_at":"2026-05-18T00:04:43.143594+00:00","updated_at":"2026-05-18T00:04:43.143594+00:00"}