{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:EU3OT53RIIYOMQ5LICJVUU5HIT","short_pith_number":"pith:EU3OT53R","schema_version":"1.0","canonical_sha256":"2536e9f7714230e643ab40935a53a744e1891ed0bffb05fe27dc146994f3bcf1","source":{"kind":"arxiv","id":"2507.07655","version":2},"attestation_state":"computed","paper":{"title":"Fenchel-Willmore inequality for submanifolds in manifolds with non-negative $k$-Ricci curvature","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Kwok-Kun Kwong, Meng Ji","submitted_at":"2025-07-10T11:30:22Z","abstract_excerpt":"We establish a sharp Fenchel-Willmore inequality for closed submanifolds of arbitrary dimension and codimension immersed in a complete Riemannian manifold with non-negative intermediate Ricci curvature and Euclidean volume growth. In the hypersurface case, this reduces to non-negative Ricci curvature. We also characterize the equality case. This generalizes the recent work of Agostiniani, Fogagnolo, and Mazzieri \\cite{Agostiniani-Fogagnolo-Mazzieri}, as well as classical results by Chen, Fenchel, Willmore, and others."},"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":"2507.07655","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-07-10T11:30:22Z","cross_cats_sorted":[],"title_canon_sha256":"a9d42eddd8baff2914ea80dbb9824e6dee12973102af9518b8d1023101e3b169","abstract_canon_sha256":"d32e6a263aeffd3fbbd775227344e1dfe25aa8e9d353328dd2a41a6ae4e48e68"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:39:56.355084Z","signature_b64":"n73KYsn4VITmFdCrsQoQtrxUd9We9GKevBpAMVzz3p9LP2qveSlI4hBNApe/+m0FEumHNDjqRIlzvzXEHbXYDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2536e9f7714230e643ab40935a53a744e1891ed0bffb05fe27dc146994f3bcf1","last_reissued_at":"2026-07-05T11:39:56.354508Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:39:56.354508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fenchel-Willmore inequality for submanifolds in manifolds with non-negative $k$-Ricci curvature","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Kwok-Kun Kwong, Meng Ji","submitted_at":"2025-07-10T11:30:22Z","abstract_excerpt":"We establish a sharp Fenchel-Willmore inequality for closed submanifolds of arbitrary dimension and codimension immersed in a complete Riemannian manifold with non-negative intermediate Ricci curvature and Euclidean volume growth. In the hypersurface case, this reduces to non-negative Ricci curvature. We also characterize the equality case. This generalizes the recent work of Agostiniani, Fogagnolo, and Mazzieri \\cite{Agostiniani-Fogagnolo-Mazzieri}, as well as classical results by Chen, Fenchel, Willmore, and others."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.07655","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.07655/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2507.07655","created_at":"2026-07-05T11:39:56.354569+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.07655v2","created_at":"2026-07-05T11:39:56.354569+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.07655","created_at":"2026-07-05T11:39:56.354569+00:00"},{"alias_kind":"pith_short_12","alias_value":"EU3OT53RIIYO","created_at":"2026-07-05T11:39:56.354569+00:00"},{"alias_kind":"pith_short_16","alias_value":"EU3OT53RIIYOMQ5L","created_at":"2026-07-05T11:39:56.354569+00:00"},{"alias_kind":"pith_short_8","alias_value":"EU3OT53R","created_at":"2026-07-05T11:39:56.354569+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.01171","citing_title":"Fenchel-Willmore-Chen inequality under lower bounds on weighted intermediate Ricci curvature","ref_index":11,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EU3OT53RIIYOMQ5LICJVUU5HIT","json":"https://pith.science/pith/EU3OT53RIIYOMQ5LICJVUU5HIT.json","graph_json":"https://pith.science/api/pith-number/EU3OT53RIIYOMQ5LICJVUU5HIT/graph.json","events_json":"https://pith.science/api/pith-number/EU3OT53RIIYOMQ5LICJVUU5HIT/events.json","paper":"https://pith.science/paper/EU3OT53R"},"agent_actions":{"view_html":"https://pith.science/pith/EU3OT53RIIYOMQ5LICJVUU5HIT","download_json":"https://pith.science/pith/EU3OT53RIIYOMQ5LICJVUU5HIT.json","view_paper":"https://pith.science/paper/EU3OT53R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.07655&json=true","fetch_graph":"https://pith.science/api/pith-number/EU3OT53RIIYOMQ5LICJVUU5HIT/graph.json","fetch_events":"https://pith.science/api/pith-number/EU3OT53RIIYOMQ5LICJVUU5HIT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EU3OT53RIIYOMQ5LICJVUU5HIT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EU3OT53RIIYOMQ5LICJVUU5HIT/action/storage_attestation","attest_author":"https://pith.science/pith/EU3OT53RIIYOMQ5LICJVUU5HIT/action/author_attestation","sign_citation":"https://pith.science/pith/EU3OT53RIIYOMQ5LICJVUU5HIT/action/citation_signature","submit_replication":"https://pith.science/pith/EU3OT53RIIYOMQ5LICJVUU5HIT/action/replication_record"}},"created_at":"2026-07-05T11:39:56.354569+00:00","updated_at":"2026-07-05T11:39:56.354569+00:00"}