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We prove that the set of Riemannian metrics in the conformal class $[g_0]$ that are isospectral to $g_1$ is compact in the $C^\\infty$ topology."},"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":"1606.02070","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-06-07T09:11:15Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"c2b60bea3f18c13442b84b8248040b337449221f1232b6afd54674fa8bec6cc4","abstract_canon_sha256":"a2bda1f0999ba4c75414bc37a104f31eb8ced1c8e31d57ad41cbfcce5a3f22cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:39.712268Z","signature_b64":"ULowhPVBVu9k4VTw1lDEipOLobaOHJBNa9Oz3CZu2GH0whCtPJw3FEYrAaYaYtkA36SUVWnVj6hoi2TppT/FAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9672a151a7d4384fd2251f1ea746132b36ab1201ec5db7c5c72614ed99a4894d","last_reissued_at":"2026-05-18T00:43:39.711816Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:39.711816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Isospectral compactness in conformal class for 4-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SP","authors_text":"Xianfu Liu, Zuoqin Wang","submitted_at":"2016-06-07T09:11:15Z","abstract_excerpt":"Let $(M, g_0)$ be a closed 4-manifold with positive Yamabe invariant and with $L^2$-small Weyl curvature tensor. Let $g_1 \\in [g_0]$ be any metric in the conformal class of $g_0$ whose scalar curvature is $L^2$-close to a constant. We prove that the set of Riemannian metrics in the conformal class $[g_0]$ that are isospectral to $g_1$ is compact in the $C^\\infty$ topology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02070","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":"1606.02070","created_at":"2026-05-18T00:43:39.711884+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.02070v2","created_at":"2026-05-18T00:43:39.711884+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02070","created_at":"2026-05-18T00:43:39.711884+00:00"},{"alias_kind":"pith_short_12","alias_value":"SZZKCUNH2Q4E","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"SZZKCUNH2Q4E7URF","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"SZZKCUNH","created_at":"2026-05-18T12:30:44.179134+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/SZZKCUNH2Q4E7URFD4PKORQTFM","json":"https://pith.science/pith/SZZKCUNH2Q4E7URFD4PKORQTFM.json","graph_json":"https://pith.science/api/pith-number/SZZKCUNH2Q4E7URFD4PKORQTFM/graph.json","events_json":"https://pith.science/api/pith-number/SZZKCUNH2Q4E7URFD4PKORQTFM/events.json","paper":"https://pith.science/paper/SZZKCUNH"},"agent_actions":{"view_html":"https://pith.science/pith/SZZKCUNH2Q4E7URFD4PKORQTFM","download_json":"https://pith.science/pith/SZZKCUNH2Q4E7URFD4PKORQTFM.json","view_paper":"https://pith.science/paper/SZZKCUNH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.02070&json=true","fetch_graph":"https://pith.science/api/pith-number/SZZKCUNH2Q4E7URFD4PKORQTFM/graph.json","fetch_events":"https://pith.science/api/pith-number/SZZKCUNH2Q4E7URFD4PKORQTFM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SZZKCUNH2Q4E7URFD4PKORQTFM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SZZKCUNH2Q4E7URFD4PKORQTFM/action/storage_attestation","attest_author":"https://pith.science/pith/SZZKCUNH2Q4E7URFD4PKORQTFM/action/author_attestation","sign_citation":"https://pith.science/pith/SZZKCUNH2Q4E7URFD4PKORQTFM/action/citation_signature","submit_replication":"https://pith.science/pith/SZZKCUNH2Q4E7URFD4PKORQTFM/action/replication_record"}},"created_at":"2026-05-18T00:43:39.711884+00:00","updated_at":"2026-05-18T00:43:39.711884+00:00"}