{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:JRJXZYDZXSGUKMXYTV5N7DM75D","short_pith_number":"pith:JRJXZYDZ","schema_version":"1.0","canonical_sha256":"4c537ce079bc8d4532f89d7adf8d9fe8cc164369363a6ec024f180daae695455","source":{"kind":"arxiv","id":"0808.3665","version":3},"attestation_state":"computed","paper":{"title":"Second order rectifiability of integral varifolds of locally bounded first variation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Ulrich Menne","submitted_at":"2008-08-27T11:25:10Z","abstract_excerpt":"In this work it is shown that every integral varifold in an open subset of Euclidian space of locally bounded first variation can be covered by a countable collection of submanifolds of class C^2. Moreover, the mean curvature of each member of the collection agrees with the mean curvature of the varifold almost everywhere with respect to the varifold."},"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":"0808.3665","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-08-27T11:25:10Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"0eaa2ad6efb7f6eb9dac7ee86a716dfc86f004bcb7a5446078268ab45e620e51","abstract_canon_sha256":"6336d72b7f789df3f874830c7a6beb38a7c0e1cffe39af2e1de363dc6c5b9c63"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:08.357171Z","signature_b64":"kBME/ijWWlJzR70CQ/G4wrx71h8304c9Q1v/6McqNaiPpxygFPZY1TRsOXb44LA2cUIE3Knb4uB8MvuIpCtnAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c537ce079bc8d4532f89d7adf8d9fe8cc164369363a6ec024f180daae695455","last_reissued_at":"2026-05-18T03:32:08.356395Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:08.356395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Second order rectifiability of integral varifolds of locally bounded first variation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Ulrich Menne","submitted_at":"2008-08-27T11:25:10Z","abstract_excerpt":"In this work it is shown that every integral varifold in an open subset of Euclidian space of locally bounded first variation can be covered by a countable collection of submanifolds of class C^2. Moreover, the mean curvature of each member of the collection agrees with the mean curvature of the varifold almost everywhere with respect to the varifold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.3665","kind":"arxiv","version":3},"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":"0808.3665","created_at":"2026-05-18T03:32:08.356519+00:00"},{"alias_kind":"arxiv_version","alias_value":"0808.3665v3","created_at":"2026-05-18T03:32:08.356519+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.3665","created_at":"2026-05-18T03:32:08.356519+00:00"},{"alias_kind":"pith_short_12","alias_value":"JRJXZYDZXSGU","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"JRJXZYDZXSGUKMXY","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"JRJXZYDZ","created_at":"2026-05-18T12:25:57.157939+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/JRJXZYDZXSGUKMXYTV5N7DM75D","json":"https://pith.science/pith/JRJXZYDZXSGUKMXYTV5N7DM75D.json","graph_json":"https://pith.science/api/pith-number/JRJXZYDZXSGUKMXYTV5N7DM75D/graph.json","events_json":"https://pith.science/api/pith-number/JRJXZYDZXSGUKMXYTV5N7DM75D/events.json","paper":"https://pith.science/paper/JRJXZYDZ"},"agent_actions":{"view_html":"https://pith.science/pith/JRJXZYDZXSGUKMXYTV5N7DM75D","download_json":"https://pith.science/pith/JRJXZYDZXSGUKMXYTV5N7DM75D.json","view_paper":"https://pith.science/paper/JRJXZYDZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0808.3665&json=true","fetch_graph":"https://pith.science/api/pith-number/JRJXZYDZXSGUKMXYTV5N7DM75D/graph.json","fetch_events":"https://pith.science/api/pith-number/JRJXZYDZXSGUKMXYTV5N7DM75D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JRJXZYDZXSGUKMXYTV5N7DM75D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JRJXZYDZXSGUKMXYTV5N7DM75D/action/storage_attestation","attest_author":"https://pith.science/pith/JRJXZYDZXSGUKMXYTV5N7DM75D/action/author_attestation","sign_citation":"https://pith.science/pith/JRJXZYDZXSGUKMXYTV5N7DM75D/action/citation_signature","submit_replication":"https://pith.science/pith/JRJXZYDZXSGUKMXYTV5N7DM75D/action/replication_record"}},"created_at":"2026-05-18T03:32:08.356519+00:00","updated_at":"2026-05-18T03:32:08.356519+00:00"}