{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GMJWMJ3IZDCFPCXTDAK5TP7PU7","short_pith_number":"pith:GMJWMJ3I","schema_version":"1.0","canonical_sha256":"3313662768c8c4578af31815d9bfefa7d171537d97844adc6b1a8606c616bacb","source":{"kind":"arxiv","id":"1703.08417","version":1},"attestation_state":"computed","paper":{"title":"Rabinowitz alternative for non-cooperative elliptic systems on geodesic balls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Naoki Shioji, Piotr Stefaniak, S{\\l}awomir Rybicki","submitted_at":"2017-03-24T14:20:53Z","abstract_excerpt":"The purpose of this paper is to study properties of continua (closed connected sets) of nontrivial solutions of non-cooperative elliptic systems considered on geodesic balls in $S^n$. In particular, we have shown that if the geodesic ball is a hemisphere, then these continua are unbounded. It is also shown that the phenomenon of global symmetry-breaking bifurcation of such solutions occurs. Since the problem is variational and SO(n)-symmetric, we apply the techniques of equivariant bifurcation theory to prove the main results of this article. As the topological tool we use the degree theory fo"},"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":"1703.08417","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-24T14:20:53Z","cross_cats_sorted":[],"title_canon_sha256":"3d35541ea29352c1ce6daf6faa13e9adbf80f01de278993bb9cd6a21c25a2b91","abstract_canon_sha256":"b4c1c5d2c7b1c36b003f872741af4cdde685becc9e5aec1dfbca71c0d693cb01"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:59.984131Z","signature_b64":"hkT+Y9hjeeYp8opRTskgiFANRgTWx7d/Tj3+fYkAQUFsQnCx93dkob31rH4DKX9aDPG2aaCWKLt2R3oCjAiFBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3313662768c8c4578af31815d9bfefa7d171537d97844adc6b1a8606c616bacb","last_reissued_at":"2026-05-18T00:47:59.983576Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:59.983576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rabinowitz alternative for non-cooperative elliptic systems on geodesic balls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Naoki Shioji, Piotr Stefaniak, S{\\l}awomir Rybicki","submitted_at":"2017-03-24T14:20:53Z","abstract_excerpt":"The purpose of this paper is to study properties of continua (closed connected sets) of nontrivial solutions of non-cooperative elliptic systems considered on geodesic balls in $S^n$. In particular, we have shown that if the geodesic ball is a hemisphere, then these continua are unbounded. It is also shown that the phenomenon of global symmetry-breaking bifurcation of such solutions occurs. Since the problem is variational and SO(n)-symmetric, we apply the techniques of equivariant bifurcation theory to prove the main results of this article. As the topological tool we use the degree theory fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08417","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":"1703.08417","created_at":"2026-05-18T00:47:59.983658+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.08417v1","created_at":"2026-05-18T00:47:59.983658+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08417","created_at":"2026-05-18T00:47:59.983658+00:00"},{"alias_kind":"pith_short_12","alias_value":"GMJWMJ3IZDCF","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"GMJWMJ3IZDCFPCXT","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"GMJWMJ3I","created_at":"2026-05-18T12:31:18.294218+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/GMJWMJ3IZDCFPCXTDAK5TP7PU7","json":"https://pith.science/pith/GMJWMJ3IZDCFPCXTDAK5TP7PU7.json","graph_json":"https://pith.science/api/pith-number/GMJWMJ3IZDCFPCXTDAK5TP7PU7/graph.json","events_json":"https://pith.science/api/pith-number/GMJWMJ3IZDCFPCXTDAK5TP7PU7/events.json","paper":"https://pith.science/paper/GMJWMJ3I"},"agent_actions":{"view_html":"https://pith.science/pith/GMJWMJ3IZDCFPCXTDAK5TP7PU7","download_json":"https://pith.science/pith/GMJWMJ3IZDCFPCXTDAK5TP7PU7.json","view_paper":"https://pith.science/paper/GMJWMJ3I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.08417&json=true","fetch_graph":"https://pith.science/api/pith-number/GMJWMJ3IZDCFPCXTDAK5TP7PU7/graph.json","fetch_events":"https://pith.science/api/pith-number/GMJWMJ3IZDCFPCXTDAK5TP7PU7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GMJWMJ3IZDCFPCXTDAK5TP7PU7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GMJWMJ3IZDCFPCXTDAK5TP7PU7/action/storage_attestation","attest_author":"https://pith.science/pith/GMJWMJ3IZDCFPCXTDAK5TP7PU7/action/author_attestation","sign_citation":"https://pith.science/pith/GMJWMJ3IZDCFPCXTDAK5TP7PU7/action/citation_signature","submit_replication":"https://pith.science/pith/GMJWMJ3IZDCFPCXTDAK5TP7PU7/action/replication_record"}},"created_at":"2026-05-18T00:47:59.983658+00:00","updated_at":"2026-05-18T00:47:59.983658+00:00"}