{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:LMLYSIVUMS6ULCGXBULHWEVJEF","short_pith_number":"pith:LMLYSIVU","schema_version":"1.0","canonical_sha256":"5b178922b464bd4588d70d167b12a921539e62f57eef60f1f29a310ea10273da","source":{"kind":"arxiv","id":"1607.02746","version":2},"attestation_state":"computed","paper":{"title":"Resonance identity and multiplicity of non-contractible closed geodesics on Finsler $\\mathbb{R}P^{n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SG"],"primary_cat":"math.DS","authors_text":"Hui Liu, Yuming Xiao","submitted_at":"2016-07-10T13:44:36Z","abstract_excerpt":"In this paper, we establish first the resonance identity for non-contractible homologically visible prime closed geodesics on Finsler $n$-dimensional real projective space $(\\mathbb{R}P^n,F)$ when there exist only finitely many distinct non-contractible closed geodesics on $(\\mathbb{R}P^n,F)$, where the integer $n\\geq2$. Then as an application of this resonance identity, we prove the existence of at least two distinct non-contractible closed geodesics on $\\mathbb{R}P^{n}$ with a bumpy and irreversible Finsler metric. Together with two previous results on bumpy and reversible Finsler metrics in"},"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":"1607.02746","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-10T13:44:36Z","cross_cats_sorted":["math.DG","math.SG"],"title_canon_sha256":"0c58747f0cef73230b0261e0d2b5b1f26a3f4d857bd684d3e91cd1023952af39","abstract_canon_sha256":"3416b8370d402424ffdf291865a49b75605da80943ed4a481e3f57fcccf0eb95"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:13.390760Z","signature_b64":"Ve8OcSw9StSJP/7eMdfkdlaCA+0V9IQV+Zf9uw79w44wB2DUXFzyUftFLAcLb/ogwlPVEPDGLMx9RE6AaErZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b178922b464bd4588d70d167b12a921539e62f57eef60f1f29a310ea10273da","last_reissued_at":"2026-05-18T00:39:13.389966Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:13.389966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Resonance identity and multiplicity of non-contractible closed geodesics on Finsler $\\mathbb{R}P^{n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SG"],"primary_cat":"math.DS","authors_text":"Hui Liu, Yuming Xiao","submitted_at":"2016-07-10T13:44:36Z","abstract_excerpt":"In this paper, we establish first the resonance identity for non-contractible homologically visible prime closed geodesics on Finsler $n$-dimensional real projective space $(\\mathbb{R}P^n,F)$ when there exist only finitely many distinct non-contractible closed geodesics on $(\\mathbb{R}P^n,F)$, where the integer $n\\geq2$. Then as an application of this resonance identity, we prove the existence of at least two distinct non-contractible closed geodesics on $\\mathbb{R}P^{n}$ with a bumpy and irreversible Finsler metric. Together with two previous results on bumpy and reversible Finsler metrics in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02746","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1607.02746","created_at":"2026-05-18T00:39:13.390080+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.02746v2","created_at":"2026-05-18T00:39:13.390080+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02746","created_at":"2026-05-18T00:39:13.390080+00:00"},{"alias_kind":"pith_short_12","alias_value":"LMLYSIVUMS6U","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"LMLYSIVUMS6ULCGX","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"LMLYSIVU","created_at":"2026-05-18T12:30:29.479603+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/LMLYSIVUMS6ULCGXBULHWEVJEF","json":"https://pith.science/pith/LMLYSIVUMS6ULCGXBULHWEVJEF.json","graph_json":"https://pith.science/api/pith-number/LMLYSIVUMS6ULCGXBULHWEVJEF/graph.json","events_json":"https://pith.science/api/pith-number/LMLYSIVUMS6ULCGXBULHWEVJEF/events.json","paper":"https://pith.science/paper/LMLYSIVU"},"agent_actions":{"view_html":"https://pith.science/pith/LMLYSIVUMS6ULCGXBULHWEVJEF","download_json":"https://pith.science/pith/LMLYSIVUMS6ULCGXBULHWEVJEF.json","view_paper":"https://pith.science/paper/LMLYSIVU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.02746&json=true","fetch_graph":"https://pith.science/api/pith-number/LMLYSIVUMS6ULCGXBULHWEVJEF/graph.json","fetch_events":"https://pith.science/api/pith-number/LMLYSIVUMS6ULCGXBULHWEVJEF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LMLYSIVUMS6ULCGXBULHWEVJEF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LMLYSIVUMS6ULCGXBULHWEVJEF/action/storage_attestation","attest_author":"https://pith.science/pith/LMLYSIVUMS6ULCGXBULHWEVJEF/action/author_attestation","sign_citation":"https://pith.science/pith/LMLYSIVUMS6ULCGXBULHWEVJEF/action/citation_signature","submit_replication":"https://pith.science/pith/LMLYSIVUMS6ULCGXBULHWEVJEF/action/replication_record"}},"created_at":"2026-05-18T00:39:13.390080+00:00","updated_at":"2026-05-18T00:39:13.390080+00:00"}