{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:CQMM4O3D2377LTIVVNKFX5UZ5T","short_pith_number":"pith:CQMM4O3D","schema_version":"1.0","canonical_sha256":"1418ce3b63d6fff5cd15ab545bf699ece53d01b0d490fa5dea1652df1c0113c9","source":{"kind":"arxiv","id":"1504.00971","version":1},"attestation_state":"computed","paper":{"title":"On the free boundary min-max geodesics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Xin Zhou","submitted_at":"2015-04-04T02:25:53Z","abstract_excerpt":"Given a Riemannian manifold and a closed submanifold, we find a geodesic segment with free boundary on the given submanifold. This is a corollary of the min-max theory which we develop in this article for the free boundary variational problem. In particular, we develop a modified Birkhoff curve shortening process to achieve a strong \"Colding-Minicozzi\" type min-max approximation result."},"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":"1504.00971","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-04T02:25:53Z","cross_cats_sorted":[],"title_canon_sha256":"6c26be73a3e1195cb2c40563ad6dad2ff74417670a501c5f6630684cd2679f98","abstract_canon_sha256":"bcb669d17c4e3aa7c36d036160114ece658e7b142e905d2407c0ebc9101fcef3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:35.452727Z","signature_b64":"m1wJSh3wWhdaTeV2xAXO4Y7/gwxry8ey43b4v2fUd9Xou8ZMB+aXiA74Q3ZSD/fy9KHb1w9KaH8uMGkf2rtGDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1418ce3b63d6fff5cd15ab545bf699ece53d01b0d490fa5dea1652df1c0113c9","last_reissued_at":"2026-05-18T02:19:35.452173Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:35.452173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the free boundary min-max geodesics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Xin Zhou","submitted_at":"2015-04-04T02:25:53Z","abstract_excerpt":"Given a Riemannian manifold and a closed submanifold, we find a geodesic segment with free boundary on the given submanifold. This is a corollary of the min-max theory which we develop in this article for the free boundary variational problem. In particular, we develop a modified Birkhoff curve shortening process to achieve a strong \"Colding-Minicozzi\" type min-max approximation result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00971","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":"1504.00971","created_at":"2026-05-18T02:19:35.452261+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.00971v1","created_at":"2026-05-18T02:19:35.452261+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00971","created_at":"2026-05-18T02:19:35.452261+00:00"},{"alias_kind":"pith_short_12","alias_value":"CQMM4O3D2377","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"CQMM4O3D2377LTIV","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"CQMM4O3D","created_at":"2026-05-18T12:29:17.054201+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/CQMM4O3D2377LTIVVNKFX5UZ5T","json":"https://pith.science/pith/CQMM4O3D2377LTIVVNKFX5UZ5T.json","graph_json":"https://pith.science/api/pith-number/CQMM4O3D2377LTIVVNKFX5UZ5T/graph.json","events_json":"https://pith.science/api/pith-number/CQMM4O3D2377LTIVVNKFX5UZ5T/events.json","paper":"https://pith.science/paper/CQMM4O3D"},"agent_actions":{"view_html":"https://pith.science/pith/CQMM4O3D2377LTIVVNKFX5UZ5T","download_json":"https://pith.science/pith/CQMM4O3D2377LTIVVNKFX5UZ5T.json","view_paper":"https://pith.science/paper/CQMM4O3D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.00971&json=true","fetch_graph":"https://pith.science/api/pith-number/CQMM4O3D2377LTIVVNKFX5UZ5T/graph.json","fetch_events":"https://pith.science/api/pith-number/CQMM4O3D2377LTIVVNKFX5UZ5T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CQMM4O3D2377LTIVVNKFX5UZ5T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CQMM4O3D2377LTIVVNKFX5UZ5T/action/storage_attestation","attest_author":"https://pith.science/pith/CQMM4O3D2377LTIVVNKFX5UZ5T/action/author_attestation","sign_citation":"https://pith.science/pith/CQMM4O3D2377LTIVVNKFX5UZ5T/action/citation_signature","submit_replication":"https://pith.science/pith/CQMM4O3D2377LTIVVNKFX5UZ5T/action/replication_record"}},"created_at":"2026-05-18T02:19:35.452261+00:00","updated_at":"2026-05-18T02:19:35.452261+00:00"}