{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:LNQDYZQNLODH5OF2GHZN352UAW","short_pith_number":"pith:LNQDYZQN","schema_version":"1.0","canonical_sha256":"5b603c660d5b867eb8ba31f2ddf75405bbd17d5748fe56a9ca1306a1b3c126c7","source":{"kind":"arxiv","id":"1312.1581","version":2},"attestation_state":"computed","paper":{"title":"Large isoperimetric regions in the product of a compact manifold with Euclidean space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Efstratios Vernadakis, Manuel Ritor\\'e","submitted_at":"2013-12-05T15:34:41Z","abstract_excerpt":"Given a compact Riemannian manifold $M$ without boundary, we show that large isoperimetric regions in $M\\times\\mathbb{R}^k$ are tubular neighborhoods of $M\\times\\{x\\}$, with $x\\in\\mathbb{R}^k$."},"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":"1312.1581","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-05T15:34:41Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"58b554e059cce8380264bf0ae6fee53744cf7b1b3168926daa84ffc64140742c","abstract_canon_sha256":"ee745f0f0ff771daa9331ca6e946e302094f7a80792390aada074f664777ea1c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:10.554196Z","signature_b64":"sGzRdqXTe6/7s5l2pzIbqQWEZ+RaAPpCN6eGFYRybHN22Pxe3vGZdZNHGo02RjbMWyf/UxSJ3xW777tDCekNBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b603c660d5b867eb8ba31f2ddf75405bbd17d5748fe56a9ca1306a1b3c126c7","last_reissued_at":"2026-05-18T01:00:10.553546Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:10.553546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large isoperimetric regions in the product of a compact manifold with Euclidean space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Efstratios Vernadakis, Manuel Ritor\\'e","submitted_at":"2013-12-05T15:34:41Z","abstract_excerpt":"Given a compact Riemannian manifold $M$ without boundary, we show that large isoperimetric regions in $M\\times\\mathbb{R}^k$ are tubular neighborhoods of $M\\times\\{x\\}$, with $x\\in\\mathbb{R}^k$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1581","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":""},"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":"1312.1581","created_at":"2026-05-18T01:00:10.553638+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.1581v2","created_at":"2026-05-18T01:00:10.553638+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1581","created_at":"2026-05-18T01:00:10.553638+00:00"},{"alias_kind":"pith_short_12","alias_value":"LNQDYZQNLODH","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"LNQDYZQNLODH5OF2","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"LNQDYZQN","created_at":"2026-05-18T12:27:51.066281+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/LNQDYZQNLODH5OF2GHZN352UAW","json":"https://pith.science/pith/LNQDYZQNLODH5OF2GHZN352UAW.json","graph_json":"https://pith.science/api/pith-number/LNQDYZQNLODH5OF2GHZN352UAW/graph.json","events_json":"https://pith.science/api/pith-number/LNQDYZQNLODH5OF2GHZN352UAW/events.json","paper":"https://pith.science/paper/LNQDYZQN"},"agent_actions":{"view_html":"https://pith.science/pith/LNQDYZQNLODH5OF2GHZN352UAW","download_json":"https://pith.science/pith/LNQDYZQNLODH5OF2GHZN352UAW.json","view_paper":"https://pith.science/paper/LNQDYZQN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.1581&json=true","fetch_graph":"https://pith.science/api/pith-number/LNQDYZQNLODH5OF2GHZN352UAW/graph.json","fetch_events":"https://pith.science/api/pith-number/LNQDYZQNLODH5OF2GHZN352UAW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LNQDYZQNLODH5OF2GHZN352UAW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LNQDYZQNLODH5OF2GHZN352UAW/action/storage_attestation","attest_author":"https://pith.science/pith/LNQDYZQNLODH5OF2GHZN352UAW/action/author_attestation","sign_citation":"https://pith.science/pith/LNQDYZQNLODH5OF2GHZN352UAW/action/citation_signature","submit_replication":"https://pith.science/pith/LNQDYZQNLODH5OF2GHZN352UAW/action/replication_record"}},"created_at":"2026-05-18T01:00:10.553638+00:00","updated_at":"2026-05-18T01:00:10.553638+00:00"}