{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JMGD2SSYBCNDNOJRTINEALULHZ","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":"df47ecddbd2088a9696880aa8350af371c992fbaf99ef9b666549d79f8f4efd0","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-11T15:50:12Z","title_canon_sha256":"abd9bb7604b57eea1691050cd5def1bd431ae2ee1247dc56b6bf72984fac6f96"},"schema_version":"1.0","source":{"id":"1111.2780","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2780","created_at":"2026-05-18T03:02:57Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2780v1","created_at":"2026-05-18T03:02:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2780","created_at":"2026-05-18T03:02:57Z"},{"alias_kind":"pith_short_12","alias_value":"JMGD2SSYBCND","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JMGD2SSYBCNDNOJR","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JMGD2SSY","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:bf381b353c458362f4d15ff5b0fc16b6b4ed3201b83740c717db6094e1980d81","target":"graph","created_at":"2026-05-18T03:02:57Z","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":"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.","authors_text":"Bernd Ammann, Emmanuel Humbert, Mattias Dahl","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-11T15:50:12Z","title":"Square-integrability of solutions of the Yamabe equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2780","kind":"arxiv","version":1},"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":"sha256:5ad7ff7fdb1d33f627c2cd4d0fba8058e10707c5c58428ba62a8a21d3e897c89","target":"record","created_at":"2026-05-18T03:02:57Z","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":"df47ecddbd2088a9696880aa8350af371c992fbaf99ef9b666549d79f8f4efd0","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-11T15:50:12Z","title_canon_sha256":"abd9bb7604b57eea1691050cd5def1bd431ae2ee1247dc56b6bf72984fac6f96"},"schema_version":"1.0","source":{"id":"1111.2780","kind":"arxiv","version":1}},"canonical_sha256":"4b0c3d4a58089a36b9319a1a402e8b3e4a51346163fcf6f267aec60f9b21be25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b0c3d4a58089a36b9319a1a402e8b3e4a51346163fcf6f267aec60f9b21be25","first_computed_at":"2026-05-18T03:02:57.549132Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:57.549132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FFSXSmkP784UClnHhK1w8MyIYFxg/MFTHHObfRw3wqysQC0d3D3tLjBl4RIWek0o71QAMSx8o+vlWOKopuvzCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:57.549846Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.2780","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ad7ff7fdb1d33f627c2cd4d0fba8058e10707c5c58428ba62a8a21d3e897c89","sha256:bf381b353c458362f4d15ff5b0fc16b6b4ed3201b83740c717db6094e1980d81"],"state_sha256":"4113c54d77138ae8d1ed709013f81ac4cfee1ee51b977edac948240d8c1a3d22"}