{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:EBODRZFIUJBKNOMC65MI3JQUOM","short_pith_number":"pith:EBODRZFI","schema_version":"1.0","canonical_sha256":"205c38e4a8a242a6b982f7588da614730f4f25401c8d8cc5cf80a91ddc3f9bba","source":{"kind":"arxiv","id":"1704.03802","version":1},"attestation_state":"computed","paper":{"title":"Sharp one-sided curvature estimates for fully nonlinear curvature flows and applications to ancient solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mat Langford, Stephen Lynch","submitted_at":"2017-04-12T15:41:45Z","abstract_excerpt":"We prove several sharp one-sided pinching estimates for immersed and embedded hypersurfaces evolving by various fully nonlinear, one-homogeneous curvature flows by the method of Stampacchia iteration. These include sharp estimates for the largest principal curvature and the inscribed curvature ('cylindrical estimates') for flows by concave speeds and a sharp estimate for the exscribed curvature for flows by convex speeds. Making use of a recent idea of Huisken and Sinestrari, we then obtain corresponding estimates for ancient solutions. In particular, this leads to various characterisations of"},"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":"1704.03802","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-04-12T15:41:45Z","cross_cats_sorted":[],"title_canon_sha256":"d5edd107c9178ed2dc5251bb7a1b9ff95e0dc8e1ed4dfa3361bbb41fa5c1d767","abstract_canon_sha256":"be33a81df752b11050475e3bbf39575627b3df2c0c3479b8ec1631e8d04ef2d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:26.839624Z","signature_b64":"upbqdANYtvbjxrSztoM1xPJ2O+GD+bSLixsZVlf5sFe/cksnDsR+6UfKFjJ8ohu/JXAx4EzPvPgiEVI3cikHBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"205c38e4a8a242a6b982f7588da614730f4f25401c8d8cc5cf80a91ddc3f9bba","last_reissued_at":"2026-05-18T00:46:26.838996Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:26.838996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp one-sided curvature estimates for fully nonlinear curvature flows and applications to ancient solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mat Langford, Stephen Lynch","submitted_at":"2017-04-12T15:41:45Z","abstract_excerpt":"We prove several sharp one-sided pinching estimates for immersed and embedded hypersurfaces evolving by various fully nonlinear, one-homogeneous curvature flows by the method of Stampacchia iteration. These include sharp estimates for the largest principal curvature and the inscribed curvature ('cylindrical estimates') for flows by concave speeds and a sharp estimate for the exscribed curvature for flows by convex speeds. Making use of a recent idea of Huisken and Sinestrari, we then obtain corresponding estimates for ancient solutions. In particular, this leads to various characterisations of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03802","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":"1704.03802","created_at":"2026-05-18T00:46:26.839102+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.03802v1","created_at":"2026-05-18T00:46:26.839102+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03802","created_at":"2026-05-18T00:46:26.839102+00:00"},{"alias_kind":"pith_short_12","alias_value":"EBODRZFIUJBK","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"EBODRZFIUJBKNOMC","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"EBODRZFI","created_at":"2026-05-18T12:31:12.930513+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/EBODRZFIUJBKNOMC65MI3JQUOM","json":"https://pith.science/pith/EBODRZFIUJBKNOMC65MI3JQUOM.json","graph_json":"https://pith.science/api/pith-number/EBODRZFIUJBKNOMC65MI3JQUOM/graph.json","events_json":"https://pith.science/api/pith-number/EBODRZFIUJBKNOMC65MI3JQUOM/events.json","paper":"https://pith.science/paper/EBODRZFI"},"agent_actions":{"view_html":"https://pith.science/pith/EBODRZFIUJBKNOMC65MI3JQUOM","download_json":"https://pith.science/pith/EBODRZFIUJBKNOMC65MI3JQUOM.json","view_paper":"https://pith.science/paper/EBODRZFI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.03802&json=true","fetch_graph":"https://pith.science/api/pith-number/EBODRZFIUJBKNOMC65MI3JQUOM/graph.json","fetch_events":"https://pith.science/api/pith-number/EBODRZFIUJBKNOMC65MI3JQUOM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EBODRZFIUJBKNOMC65MI3JQUOM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EBODRZFIUJBKNOMC65MI3JQUOM/action/storage_attestation","attest_author":"https://pith.science/pith/EBODRZFIUJBKNOMC65MI3JQUOM/action/author_attestation","sign_citation":"https://pith.science/pith/EBODRZFIUJBKNOMC65MI3JQUOM/action/citation_signature","submit_replication":"https://pith.science/pith/EBODRZFIUJBKNOMC65MI3JQUOM/action/replication_record"}},"created_at":"2026-05-18T00:46:26.839102+00:00","updated_at":"2026-05-18T00:46:26.839102+00:00"}