{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:JMGD2SSYBCNDNOJRTINEALULHZ","short_pith_number":"pith:JMGD2SSY","schema_version":"1.0","canonical_sha256":"4b0c3d4a58089a36b9319a1a402e8b3e4a51346163fcf6f267aec60f9b21be25","source":{"kind":"arxiv","id":"1111.2780","version":1},"attestation_state":"computed","paper":{"title":"Square-integrability of solutions of the Yamabe equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Bernd Ammann, Emmanuel Humbert, Mattias Dahl","submitted_at":"2011-11-11T15:50:12Z","abstract_excerpt":"We show that solutions of the Yamabe equation on certain n-dimensional non-compact Riemannian manifolds which are bounded and L^p for p=2n/(n-2) are also L^2. This L^p-L^2-implication provides explicit constants in the surgery-monotonicity formula for the smooth Yamabe invariant in a previous article of the authors. As an application we see that the smooth Yamabe invariant of any 2-connected compact 7-dimensional manifold is at least 74.5. Similar conclusions follow in dimension 8 and in dimensions at least 11."},"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":"1111.2780","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-11T15:50:12Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"abd9bb7604b57eea1691050cd5def1bd431ae2ee1247dc56b6bf72984fac6f96","abstract_canon_sha256":"df47ecddbd2088a9696880aa8350af371c992fbaf99ef9b666549d79f8f4efd0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:57.549846Z","signature_b64":"FFSXSmkP784UClnHhK1w8MyIYFxg/MFTHHObfRw3wqysQC0d3D3tLjBl4RIWek0o71QAMSx8o+vlWOKopuvzCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b0c3d4a58089a36b9319a1a402e8b3e4a51346163fcf6f267aec60f9b21be25","last_reissued_at":"2026-05-18T03:02:57.549132Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:57.549132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Square-integrability of solutions of the Yamabe equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Bernd Ammann, Emmanuel Humbert, Mattias Dahl","submitted_at":"2011-11-11T15:50:12Z","abstract_excerpt":"We show that solutions of the Yamabe equation on certain n-dimensional non-compact Riemannian manifolds which are bounded and L^p for p=2n/(n-2) are also L^2. This L^p-L^2-implication provides explicit constants in the surgery-monotonicity formula for the smooth Yamabe invariant in a previous article of the authors. As an application we see that the smooth Yamabe invariant of any 2-connected compact 7-dimensional manifold is at least 74.5. Similar conclusions follow in dimension 8 and in dimensions at least 11."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2780","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":"1111.2780","created_at":"2026-05-18T03:02:57.549246+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.2780v1","created_at":"2026-05-18T03:02:57.549246+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2780","created_at":"2026-05-18T03:02:57.549246+00:00"},{"alias_kind":"pith_short_12","alias_value":"JMGD2SSYBCND","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"JMGD2SSYBCNDNOJR","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"JMGD2SSY","created_at":"2026-05-18T12:26:32.869790+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/JMGD2SSYBCNDNOJRTINEALULHZ","json":"https://pith.science/pith/JMGD2SSYBCNDNOJRTINEALULHZ.json","graph_json":"https://pith.science/api/pith-number/JMGD2SSYBCNDNOJRTINEALULHZ/graph.json","events_json":"https://pith.science/api/pith-number/JMGD2SSYBCNDNOJRTINEALULHZ/events.json","paper":"https://pith.science/paper/JMGD2SSY"},"agent_actions":{"view_html":"https://pith.science/pith/JMGD2SSYBCNDNOJRTINEALULHZ","download_json":"https://pith.science/pith/JMGD2SSYBCNDNOJRTINEALULHZ.json","view_paper":"https://pith.science/paper/JMGD2SSY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.2780&json=true","fetch_graph":"https://pith.science/api/pith-number/JMGD2SSYBCNDNOJRTINEALULHZ/graph.json","fetch_events":"https://pith.science/api/pith-number/JMGD2SSYBCNDNOJRTINEALULHZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JMGD2SSYBCNDNOJRTINEALULHZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JMGD2SSYBCNDNOJRTINEALULHZ/action/storage_attestation","attest_author":"https://pith.science/pith/JMGD2SSYBCNDNOJRTINEALULHZ/action/author_attestation","sign_citation":"https://pith.science/pith/JMGD2SSYBCNDNOJRTINEALULHZ/action/citation_signature","submit_replication":"https://pith.science/pith/JMGD2SSYBCNDNOJRTINEALULHZ/action/replication_record"}},"created_at":"2026-05-18T03:02:57.549246+00:00","updated_at":"2026-05-18T03:02:57.549246+00:00"}