{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:TY7L5563LPDDVNAFYGBWOLNCAH","short_pith_number":"pith:TY7L5563","schema_version":"1.0","canonical_sha256":"9e3ebef7db5bc63ab405c183672da201c025b8c893d005b25c9bf0a467e6fd90","source":{"kind":"arxiv","id":"1509.06021","version":1},"attestation_state":"computed","paper":{"title":"Minimal surfaces with two ends which have the least total absolute curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Shoichi Fujimori, Toshihiro Shoda","submitted_at":"2015-09-20T14:50:08Z","abstract_excerpt":"In this paper, we consider complete non-catenoidal minimal surfaces of finite total curvature with two ends. A family of such minimal surfaces with least total absolute curvature is given. Moreover, we obtain a uniqueness theorem for this family from its symmetries."},"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":"1509.06021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-20T14:50:08Z","cross_cats_sorted":[],"title_canon_sha256":"ba552795d3e52865b4712034fd782773158e5674696c24719e9d187e45686e7e","abstract_canon_sha256":"8ef5bf620a1b3307c75080195e6ecdd5b4e52565a35a65c76761878b084b0a7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:29.527643Z","signature_b64":"Rqc5TK15pR0+WqvcV+n1aDSPgbWSVZpjbpdN7b56a00UD0OkvFRQzKtN6pw4YAYgWCVgHq62kkMfvypxYqoQAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e3ebef7db5bc63ab405c183672da201c025b8c893d005b25c9bf0a467e6fd90","last_reissued_at":"2026-05-18T01:19:29.526906Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:29.526906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimal surfaces with two ends which have the least total absolute curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Shoichi Fujimori, Toshihiro Shoda","submitted_at":"2015-09-20T14:50:08Z","abstract_excerpt":"In this paper, we consider complete non-catenoidal minimal surfaces of finite total curvature with two ends. A family of such minimal surfaces with least total absolute curvature is given. Moreover, we obtain a uniqueness theorem for this family from its symmetries."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06021","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":"1509.06021","created_at":"2026-05-18T01:19:29.527030+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.06021v1","created_at":"2026-05-18T01:19:29.527030+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06021","created_at":"2026-05-18T01:19:29.527030+00:00"},{"alias_kind":"pith_short_12","alias_value":"TY7L5563LPDD","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"TY7L5563LPDDVNAF","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"TY7L5563","created_at":"2026-05-18T12:29:44.643036+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/TY7L5563LPDDVNAFYGBWOLNCAH","json":"https://pith.science/pith/TY7L5563LPDDVNAFYGBWOLNCAH.json","graph_json":"https://pith.science/api/pith-number/TY7L5563LPDDVNAFYGBWOLNCAH/graph.json","events_json":"https://pith.science/api/pith-number/TY7L5563LPDDVNAFYGBWOLNCAH/events.json","paper":"https://pith.science/paper/TY7L5563"},"agent_actions":{"view_html":"https://pith.science/pith/TY7L5563LPDDVNAFYGBWOLNCAH","download_json":"https://pith.science/pith/TY7L5563LPDDVNAFYGBWOLNCAH.json","view_paper":"https://pith.science/paper/TY7L5563","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.06021&json=true","fetch_graph":"https://pith.science/api/pith-number/TY7L5563LPDDVNAFYGBWOLNCAH/graph.json","fetch_events":"https://pith.science/api/pith-number/TY7L5563LPDDVNAFYGBWOLNCAH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TY7L5563LPDDVNAFYGBWOLNCAH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TY7L5563LPDDVNAFYGBWOLNCAH/action/storage_attestation","attest_author":"https://pith.science/pith/TY7L5563LPDDVNAFYGBWOLNCAH/action/author_attestation","sign_citation":"https://pith.science/pith/TY7L5563LPDDVNAFYGBWOLNCAH/action/citation_signature","submit_replication":"https://pith.science/pith/TY7L5563LPDDVNAFYGBWOLNCAH/action/replication_record"}},"created_at":"2026-05-18T01:19:29.527030+00:00","updated_at":"2026-05-18T01:19:29.527030+00:00"}