{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:6UOWCOHDFDYT25XSNGC7QJUWS2","short_pith_number":"pith:6UOWCOHD","schema_version":"1.0","canonical_sha256":"f51d6138e328f13d76f26985f8269696aaad5f5080eafa7f54ec2435c1ab120e","source":{"kind":"arxiv","id":"1309.6245","version":1},"attestation_state":"computed","paper":{"title":"Regularity of minimal hypersurfaces with a common free boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Brian Krummel","submitted_at":"2013-09-24T16:37:10Z","abstract_excerpt":"Let $N$ be a Riemannian manifold and consider a stationary union of three or more $C^{1,\\mu}$ hypersurfaces-with-boundary $M_k$ in $N$ with a common boundary $\\Gamma$. We show that if $N$ is smooth, then $\\Gamma$ is smooth and each $M_k$ is smooth up to $\\Gamma$ (real analytic in the case $N$ is real analytic). Consequently we strengthen a result of Wickramasekera to conclude that under the stronger hypothesis that $V$ is a stationary, stable, integral $n$-varifold in an $(n+1)$-dimensional, smooth (real analytic) Riemannian manifold such that the support of $\\|V\\|$ is nowhere locally the unio"},"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":"1309.6245","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-09-24T16:37:10Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"7cceaa55c084992a58301557647c3ec74e73652bbcda3185dda917b67280506f","abstract_canon_sha256":"a0c2cc6cefbd4304f01c4d38fc0cceb6fb0d8c5c9db0f63d8b39d30bfd0a87f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:32.181950Z","signature_b64":"95N4pHh4NiOF88+fafYVxZhcxYs7oguN+KbHrYPp2Z34K84Bv5UNwR6QvUkwGgWfLRYwm4BJ/XGTdG11qJhvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f51d6138e328f13d76f26985f8269696aaad5f5080eafa7f54ec2435c1ab120e","last_reissued_at":"2026-05-18T02:39:32.181366Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:32.181366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularity of minimal hypersurfaces with a common free boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Brian Krummel","submitted_at":"2013-09-24T16:37:10Z","abstract_excerpt":"Let $N$ be a Riemannian manifold and consider a stationary union of three or more $C^{1,\\mu}$ hypersurfaces-with-boundary $M_k$ in $N$ with a common boundary $\\Gamma$. We show that if $N$ is smooth, then $\\Gamma$ is smooth and each $M_k$ is smooth up to $\\Gamma$ (real analytic in the case $N$ is real analytic). Consequently we strengthen a result of Wickramasekera to conclude that under the stronger hypothesis that $V$ is a stationary, stable, integral $n$-varifold in an $(n+1)$-dimensional, smooth (real analytic) Riemannian manifold such that the support of $\\|V\\|$ is nowhere locally the unio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6245","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":"1309.6245","created_at":"2026-05-18T02:39:32.181440+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.6245v1","created_at":"2026-05-18T02:39:32.181440+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6245","created_at":"2026-05-18T02:39:32.181440+00:00"},{"alias_kind":"pith_short_12","alias_value":"6UOWCOHDFDYT","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"6UOWCOHDFDYT25XS","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"6UOWCOHD","created_at":"2026-05-18T12:27:36.564083+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/6UOWCOHDFDYT25XSNGC7QJUWS2","json":"https://pith.science/pith/6UOWCOHDFDYT25XSNGC7QJUWS2.json","graph_json":"https://pith.science/api/pith-number/6UOWCOHDFDYT25XSNGC7QJUWS2/graph.json","events_json":"https://pith.science/api/pith-number/6UOWCOHDFDYT25XSNGC7QJUWS2/events.json","paper":"https://pith.science/paper/6UOWCOHD"},"agent_actions":{"view_html":"https://pith.science/pith/6UOWCOHDFDYT25XSNGC7QJUWS2","download_json":"https://pith.science/pith/6UOWCOHDFDYT25XSNGC7QJUWS2.json","view_paper":"https://pith.science/paper/6UOWCOHD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.6245&json=true","fetch_graph":"https://pith.science/api/pith-number/6UOWCOHDFDYT25XSNGC7QJUWS2/graph.json","fetch_events":"https://pith.science/api/pith-number/6UOWCOHDFDYT25XSNGC7QJUWS2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6UOWCOHDFDYT25XSNGC7QJUWS2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6UOWCOHDFDYT25XSNGC7QJUWS2/action/storage_attestation","attest_author":"https://pith.science/pith/6UOWCOHDFDYT25XSNGC7QJUWS2/action/author_attestation","sign_citation":"https://pith.science/pith/6UOWCOHDFDYT25XSNGC7QJUWS2/action/citation_signature","submit_replication":"https://pith.science/pith/6UOWCOHDFDYT25XSNGC7QJUWS2/action/replication_record"}},"created_at":"2026-05-18T02:39:32.181440+00:00","updated_at":"2026-05-18T02:39:32.181440+00:00"}