{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FDUHAL37QBBVY2SJFZY6VWHV5M","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"880775c470bfde3445988e6e21627a001a2864452bc9e478240f6afd24f3301c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-17T15:59:04Z","title_canon_sha256":"e3a1878f85ec2a53ad4adba7aede3b8ebe54d33f70014bfadb1fd3b4919e66bf"},"schema_version":"1.0","source":{"id":"1606.05573","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.05573","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"arxiv_version","alias_value":"1606.05573v2","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.05573","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"pith_short_12","alias_value":"FDUHAL37QBBV","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FDUHAL37QBBVY2SJ","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FDUHAL37","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:20e8e866101265e59e7a9e985f58362e584f060e30c89e0b91450b9a194642c4","target":"graph","created_at":"2026-05-18T01:04:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $(M^m,g_M)$ be a closed, connected manifold with positive scalar curvature and $(T^k,g)$ some flat $k$-Torus of unit volume. By a result of F. Dobarro and E. Lami Dozo, there exists a unique $f: M \\rightarrow \\mathbf{R}_{>0}$ such that the warped product $M\\times_f T^k$ has constant scalar curvature and unit volume. We study the Yamabe equation on these spaces. We use techniques from bifurcation theory, along with spectral theory for warped products, to prove multiplicity results for the Yamabe problem.","authors_text":"Juan Miguel Ruiz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-17T15:59:04Z","title":"Multiplicity of constant scalar curvature metrics on warped products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05573","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ede2ef8d7ecbbe58e852d0d6a8599ea24bee6c7bddf65c32ca9ef068655d7622","target":"record","created_at":"2026-05-18T01:04:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"880775c470bfde3445988e6e21627a001a2864452bc9e478240f6afd24f3301c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-17T15:59:04Z","title_canon_sha256":"e3a1878f85ec2a53ad4adba7aede3b8ebe54d33f70014bfadb1fd3b4919e66bf"},"schema_version":"1.0","source":{"id":"1606.05573","kind":"arxiv","version":2}},"canonical_sha256":"28e8702f7f80435c6a492e71ead8f5eb39723726969d7f33c299d65a17e00212","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28e8702f7f80435c6a492e71ead8f5eb39723726969d7f33c299d65a17e00212","first_computed_at":"2026-05-18T01:04:27.467374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:27.467374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hz/X4+jhB7Z//Vkl8JB4MV4ES9kvb9stQqpVYEbxDXo2AC6jHaH69Rn2vrtaRhvCAdpW8Qmuo1e4WWa8NYwjAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:27.467901Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.05573","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ede2ef8d7ecbbe58e852d0d6a8599ea24bee6c7bddf65c32ca9ef068655d7622","sha256:20e8e866101265e59e7a9e985f58362e584f060e30c89e0b91450b9a194642c4"],"state_sha256":"c87bd9f32d1ba1166dc52e8d85a063401bd5ee7f504cecca59f073ef1b6e30ad"}