{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:T3KAOG4C7TCPF42DWNKPGKKDJO","short_pith_number":"pith:T3KAOG4C","schema_version":"1.0","canonical_sha256":"9ed4071b82fcc4f2f343b354f329434ba3a9423dd6d873a91f43b9e67e88c3e8","source":{"kind":"arxiv","id":"1508.03234","version":1},"attestation_state":"computed","paper":{"title":"Mean Curvature Flow of Arbitrary Co-Dimensional Reifenberg Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Or Hershkovits","submitted_at":"2015-08-13T14:45:52Z","abstract_excerpt":"We study the existence and uniqueness of smooth mean curvature flow, in arbitrary dimension and co-dimension, emanating from so called $k$-dimensional $(\\varepsilon,R)$ Reifenberg flat sets in $\\mathbb{R}^n$. Our results generalize the ones from a previous paper by the author, in which the co-dimension one case (i.e. $k=n-1$) was studied. For $\\varepsilon$ fixed, this class is general enough to include (i) all $C^2$ sub-manifolds (ii) all Lipschitz sub-manifolds with Lipschitz constant less than $\\varepsilon$ (iii) some sets with Hausdorff dimension larger than $k$. The Reifenberg condition, r"},"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":"1508.03234","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-13T14:45:52Z","cross_cats_sorted":[],"title_canon_sha256":"bd65cec357cd58f8bf6d21fb199ac2240907233c18ef3595b4b37e46e9a91f62","abstract_canon_sha256":"01603e0651401ba172e310df7e79075ce4107f1b7837394d0f4d896f9b3e443a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:21.365986Z","signature_b64":"kTVBFPcZ9CzXMSXe5sXX3QbJmHDaDsLVqwwG1iJhT7yvATmUPDmj1iuUYbtaFNaXAOvt57prOIbI4N9dHl6bCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ed4071b82fcc4f2f343b354f329434ba3a9423dd6d873a91f43b9e67e88c3e8","last_reissued_at":"2026-05-18T01:35:21.365306Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:21.365306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mean Curvature Flow of Arbitrary Co-Dimensional Reifenberg Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Or Hershkovits","submitted_at":"2015-08-13T14:45:52Z","abstract_excerpt":"We study the existence and uniqueness of smooth mean curvature flow, in arbitrary dimension and co-dimension, emanating from so called $k$-dimensional $(\\varepsilon,R)$ Reifenberg flat sets in $\\mathbb{R}^n$. Our results generalize the ones from a previous paper by the author, in which the co-dimension one case (i.e. $k=n-1$) was studied. For $\\varepsilon$ fixed, this class is general enough to include (i) all $C^2$ sub-manifolds (ii) all Lipschitz sub-manifolds with Lipschitz constant less than $\\varepsilon$ (iii) some sets with Hausdorff dimension larger than $k$. The Reifenberg condition, r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03234","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":"1508.03234","created_at":"2026-05-18T01:35:21.365429+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.03234v1","created_at":"2026-05-18T01:35:21.365429+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03234","created_at":"2026-05-18T01:35:21.365429+00:00"},{"alias_kind":"pith_short_12","alias_value":"T3KAOG4C7TCP","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"T3KAOG4C7TCPF42D","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"T3KAOG4C","created_at":"2026-05-18T12:29:42.218222+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/T3KAOG4C7TCPF42DWNKPGKKDJO","json":"https://pith.science/pith/T3KAOG4C7TCPF42DWNKPGKKDJO.json","graph_json":"https://pith.science/api/pith-number/T3KAOG4C7TCPF42DWNKPGKKDJO/graph.json","events_json":"https://pith.science/api/pith-number/T3KAOG4C7TCPF42DWNKPGKKDJO/events.json","paper":"https://pith.science/paper/T3KAOG4C"},"agent_actions":{"view_html":"https://pith.science/pith/T3KAOG4C7TCPF42DWNKPGKKDJO","download_json":"https://pith.science/pith/T3KAOG4C7TCPF42DWNKPGKKDJO.json","view_paper":"https://pith.science/paper/T3KAOG4C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.03234&json=true","fetch_graph":"https://pith.science/api/pith-number/T3KAOG4C7TCPF42DWNKPGKKDJO/graph.json","fetch_events":"https://pith.science/api/pith-number/T3KAOG4C7TCPF42DWNKPGKKDJO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T3KAOG4C7TCPF42DWNKPGKKDJO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T3KAOG4C7TCPF42DWNKPGKKDJO/action/storage_attestation","attest_author":"https://pith.science/pith/T3KAOG4C7TCPF42DWNKPGKKDJO/action/author_attestation","sign_citation":"https://pith.science/pith/T3KAOG4C7TCPF42DWNKPGKKDJO/action/citation_signature","submit_replication":"https://pith.science/pith/T3KAOG4C7TCPF42DWNKPGKKDJO/action/replication_record"}},"created_at":"2026-05-18T01:35:21.365429+00:00","updated_at":"2026-05-18T01:35:21.365429+00:00"}