{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:JRJXZYDZXSGUKMXYTV5N7DM75D","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":"6336d72b7f789df3f874830c7a6beb38a7c0e1cffe39af2e1de363dc6c5b9c63","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-08-27T11:25:10Z","title_canon_sha256":"0eaa2ad6efb7f6eb9dac7ee86a716dfc86f004bcb7a5446078268ab45e620e51"},"schema_version":"1.0","source":{"id":"0808.3665","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.3665","created_at":"2026-05-18T03:32:08Z"},{"alias_kind":"arxiv_version","alias_value":"0808.3665v3","created_at":"2026-05-18T03:32:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.3665","created_at":"2026-05-18T03:32:08Z"},{"alias_kind":"pith_short_12","alias_value":"JRJXZYDZXSGU","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"JRJXZYDZXSGUKMXY","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"JRJXZYDZ","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:20b61dfaf3c971558b536f2d061c5d0283105bb014bc509c8dbca737ba8c12f5","target":"graph","created_at":"2026-05-18T03:32:08Z","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":"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.","authors_text":"Ulrich Menne","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-08-27T11:25:10Z","title":"Second order rectifiability of integral varifolds of locally bounded first variation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.3665","kind":"arxiv","version":3},"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":"sha256:6a586abd637bc34669b9608f99b1adea623056724d7bd9b6a6d7c2d5fa832c5d","target":"record","created_at":"2026-05-18T03:32:08Z","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":"6336d72b7f789df3f874830c7a6beb38a7c0e1cffe39af2e1de363dc6c5b9c63","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-08-27T11:25:10Z","title_canon_sha256":"0eaa2ad6efb7f6eb9dac7ee86a716dfc86f004bcb7a5446078268ab45e620e51"},"schema_version":"1.0","source":{"id":"0808.3665","kind":"arxiv","version":3}},"canonical_sha256":"4c537ce079bc8d4532f89d7adf8d9fe8cc164369363a6ec024f180daae695455","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c537ce079bc8d4532f89d7adf8d9fe8cc164369363a6ec024f180daae695455","first_computed_at":"2026-05-18T03:32:08.356395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:08.356395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kBME/ijWWlJzR70CQ/G4wrx71h8304c9Q1v/6McqNaiPpxygFPZY1TRsOXb44LA2cUIE3Knb4uB8MvuIpCtnAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:08.357171Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.3665","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a586abd637bc34669b9608f99b1adea623056724d7bd9b6a6d7c2d5fa832c5d","sha256:20b61dfaf3c971558b536f2d061c5d0283105bb014bc509c8dbca737ba8c12f5"],"state_sha256":"123be6e37a2d51c3060daa7215c53f2a8f32a39453594ba1ebe89e87f062ccdc"}