{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:LW3H5SABM7YIGGO65ZWH7RQW6U","short_pith_number":"pith:LW3H5SAB","schema_version":"1.0","canonical_sha256":"5db67ec80167f08319deee6c7fc616f5300d1375a6868183f555c68506aff8ca","source":{"kind":"arxiv","id":"2608.01171","version":1},"attestation_state":"computed","paper":{"title":"Fenchel-Willmore-Chen inequality under lower bounds on weighted intermediate Ricci curvature","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Guofang Wei, Jihye Lee","submitted_at":"2026-08-02T11:45:55Z","abstract_excerpt":"We establish a Fenchel-Willmore-Chen inequality for smooth metric measure spaces with a lower bound on the 1-Bakry-Emery k-Ricci curvature. This extends previous results and yields a unified proof. In addition, a Sobolev and isoperimetric inequality for nonnegative 1-weighted Ricci curvature is proven."},"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":"2608.01171","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-08-02T11:45:55Z","cross_cats_sorted":[],"title_canon_sha256":"9376e76c0a1a4acd197bd0b90559ee956fa8caef3f2b33f6e4ceffe36a8387cd","abstract_canon_sha256":"32a5b11e44d811cd53f640400b267edddc0214332b8c0243796d808f50f141be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T02:01:50.764892Z","signature_b64":"gVaGhUV+rdhZqy9UBVyH6Lojnxolp89zyNU7bIQg68X+B2QBdeJjzTyCfazK2bS1WXp8eMohExXMqjmgq7s+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5db67ec80167f08319deee6c7fc616f5300d1375a6868183f555c68506aff8ca","last_reissued_at":"2026-08-04T02:01:50.763082Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T02:01:50.763082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fenchel-Willmore-Chen inequality under lower bounds on weighted intermediate Ricci curvature","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Guofang Wei, Jihye Lee","submitted_at":"2026-08-02T11:45:55Z","abstract_excerpt":"We establish a Fenchel-Willmore-Chen inequality for smooth metric measure spaces with a lower bound on the 1-Bakry-Emery k-Ricci curvature. This extends previous results and yields a unified proof. In addition, a Sobolev and isoperimetric inequality for nonnegative 1-weighted Ricci curvature is proven."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.01171","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.01171/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":"2608.01171","created_at":"2026-08-04T02:01:50.764605+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.01171v1","created_at":"2026-08-04T02:01:50.764605+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.01171","created_at":"2026-08-04T02:01:50.764605+00:00"},{"alias_kind":"pith_short_12","alias_value":"LW3H5SABM7YI","created_at":"2026-08-04T02:01:50.764605+00:00"},{"alias_kind":"pith_short_16","alias_value":"LW3H5SABM7YIGGO6","created_at":"2026-08-04T02:01:50.764605+00:00"},{"alias_kind":"pith_short_8","alias_value":"LW3H5SAB","created_at":"2026-08-04T02:01:50.764605+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/LW3H5SABM7YIGGO65ZWH7RQW6U","json":"https://pith.science/pith/LW3H5SABM7YIGGO65ZWH7RQW6U.json","graph_json":"https://pith.science/api/pith-number/LW3H5SABM7YIGGO65ZWH7RQW6U/graph.json","events_json":"https://pith.science/api/pith-number/LW3H5SABM7YIGGO65ZWH7RQW6U/events.json","paper":"https://pith.science/paper/LW3H5SAB"},"agent_actions":{"view_html":"https://pith.science/pith/LW3H5SABM7YIGGO65ZWH7RQW6U","download_json":"https://pith.science/pith/LW3H5SABM7YIGGO65ZWH7RQW6U.json","view_paper":"https://pith.science/paper/LW3H5SAB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.01171&json=true","fetch_graph":"https://pith.science/api/pith-number/LW3H5SABM7YIGGO65ZWH7RQW6U/graph.json","fetch_events":"https://pith.science/api/pith-number/LW3H5SABM7YIGGO65ZWH7RQW6U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LW3H5SABM7YIGGO65ZWH7RQW6U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LW3H5SABM7YIGGO65ZWH7RQW6U/action/storage_attestation","attest_author":"https://pith.science/pith/LW3H5SABM7YIGGO65ZWH7RQW6U/action/author_attestation","sign_citation":"https://pith.science/pith/LW3H5SABM7YIGGO65ZWH7RQW6U/action/citation_signature","submit_replication":"https://pith.science/pith/LW3H5SABM7YIGGO65ZWH7RQW6U/action/replication_record"}},"created_at":"2026-08-04T02:01:50.764605+00:00","updated_at":"2026-08-04T02:01:50.764605+00:00"}