{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:PAABD2DMKMEIC2PWLSYJHV4SKK","short_pith_number":"pith:PAABD2DM","schema_version":"1.0","canonical_sha256":"780011e86c53088169f65cb093d79252b605139ca16f7e5b03b6b988469b413d","source":{"kind":"arxiv","id":"1503.06176","version":1},"attestation_state":"computed","paper":{"title":"Functions on the sphere with critical points in pairs and orthogonal geodesic chords","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"F. Giannoni, P. Piccione, R. Giamb\\`o","submitted_at":"2015-03-20T17:42:54Z","abstract_excerpt":"Using an estimate on the number of critical points for a Morse-even function on the sphere $\\mathbb S^m$, $m\\ge1$, we prove a multiplicity result for orthogonal geodesic chords in Riemannian manifolds with boundary that are diffeomorphic to Euclidean balls. This yields also a multiplicity result for brake orbits in a potential well."},"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":"1503.06176","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-20T17:42:54Z","cross_cats_sorted":[],"title_canon_sha256":"ecb2195efbb2a96f0dcb4403746bd0ae0ef6cbb10dcc6ae4df511791a88913e2","abstract_canon_sha256":"e479d5ccf8eae5e43dcb61a295d71e95b7444998f5906bb4098528c7ee65fb33"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:48.408109Z","signature_b64":"E08qzcc3mxGC14AvcXkg30gUd9WIWlQXYQgCRIfopBuAM8GD12oBLcrGVOmrfPG3FC53geILYI0fGOqAQKZIAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"780011e86c53088169f65cb093d79252b605139ca16f7e5b03b6b988469b413d","last_reissued_at":"2026-05-18T02:20:48.407408Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:48.407408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Functions on the sphere with critical points in pairs and orthogonal geodesic chords","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"F. Giannoni, P. Piccione, R. Giamb\\`o","submitted_at":"2015-03-20T17:42:54Z","abstract_excerpt":"Using an estimate on the number of critical points for a Morse-even function on the sphere $\\mathbb S^m$, $m\\ge1$, we prove a multiplicity result for orthogonal geodesic chords in Riemannian manifolds with boundary that are diffeomorphic to Euclidean balls. This yields also a multiplicity result for brake orbits in a potential well."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06176","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":"1503.06176","created_at":"2026-05-18T02:20:48.407506+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.06176v1","created_at":"2026-05-18T02:20:48.407506+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06176","created_at":"2026-05-18T02:20:48.407506+00:00"},{"alias_kind":"pith_short_12","alias_value":"PAABD2DMKMEI","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"PAABD2DMKMEIC2PW","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"PAABD2DM","created_at":"2026-05-18T12:29:34.919912+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/PAABD2DMKMEIC2PWLSYJHV4SKK","json":"https://pith.science/pith/PAABD2DMKMEIC2PWLSYJHV4SKK.json","graph_json":"https://pith.science/api/pith-number/PAABD2DMKMEIC2PWLSYJHV4SKK/graph.json","events_json":"https://pith.science/api/pith-number/PAABD2DMKMEIC2PWLSYJHV4SKK/events.json","paper":"https://pith.science/paper/PAABD2DM"},"agent_actions":{"view_html":"https://pith.science/pith/PAABD2DMKMEIC2PWLSYJHV4SKK","download_json":"https://pith.science/pith/PAABD2DMKMEIC2PWLSYJHV4SKK.json","view_paper":"https://pith.science/paper/PAABD2DM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.06176&json=true","fetch_graph":"https://pith.science/api/pith-number/PAABD2DMKMEIC2PWLSYJHV4SKK/graph.json","fetch_events":"https://pith.science/api/pith-number/PAABD2DMKMEIC2PWLSYJHV4SKK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PAABD2DMKMEIC2PWLSYJHV4SKK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PAABD2DMKMEIC2PWLSYJHV4SKK/action/storage_attestation","attest_author":"https://pith.science/pith/PAABD2DMKMEIC2PWLSYJHV4SKK/action/author_attestation","sign_citation":"https://pith.science/pith/PAABD2DMKMEIC2PWLSYJHV4SKK/action/citation_signature","submit_replication":"https://pith.science/pith/PAABD2DMKMEIC2PWLSYJHV4SKK/action/replication_record"}},"created_at":"2026-05-18T02:20:48.407506+00:00","updated_at":"2026-05-18T02:20:48.407506+00:00"}