{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ORE6JAYZA332FWZRHSUOUAN7R4","short_pith_number":"pith:ORE6JAYZ","schema_version":"1.0","canonical_sha256":"7449e4831906f7a2db313ca8ea01bf8f11c621f04f2f45b0357314fc5058e32e","source":{"kind":"arxiv","id":"1309.4278","version":2},"attestation_state":"computed","paper":{"title":"Mean-convex Alexandrov embedded constant mean curvature tori in the 3-sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"L. Hauswirth, M. Kilian, M.U. Schmidt","submitted_at":"2013-09-17T12:17:33Z","abstract_excerpt":"We introduce the moduli space of spectral curves of constant mean curvature (\\cmc\\hspace{-5pt}) cylinders of finite type in the round unit 3-sphere. The subset of spectral curves of mean-convex Alexandrov embedded cylinders is explicitly determined using a combination of integrable systems and geometric analysis techniques. We prove that these cylinders are surfaces of revolution. As a consequence all mean-convex Alexandrov embedded {\\sc{cmc}} tori in the 3-sphere are surfaces of revolution."},"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":"1309.4278","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-09-17T12:17:33Z","cross_cats_sorted":[],"title_canon_sha256":"6ea21260b474194033bed9c1612561344d1046c0fc9ee87adafc72a705217c12","abstract_canon_sha256":"05529a2caac71812b6d176a8e1649129cf5e0a2140f1382573126bcf3e31098e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:18.878886Z","signature_b64":"IAsV2LjGK9ukAGnsBv2RdTcRTeoxVEbyIZosCK3KGYC2sfyfmh6LjXud7utTDlM5eObXGDl1QF5l2AiMs+7xCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7449e4831906f7a2db313ca8ea01bf8f11c621f04f2f45b0357314fc5058e32e","last_reissued_at":"2026-05-18T01:19:18.878312Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:18.878312Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mean-convex Alexandrov embedded constant mean curvature tori in the 3-sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"L. Hauswirth, M. Kilian, M.U. Schmidt","submitted_at":"2013-09-17T12:17:33Z","abstract_excerpt":"We introduce the moduli space of spectral curves of constant mean curvature (\\cmc\\hspace{-5pt}) cylinders of finite type in the round unit 3-sphere. The subset of spectral curves of mean-convex Alexandrov embedded cylinders is explicitly determined using a combination of integrable systems and geometric analysis techniques. We prove that these cylinders are surfaces of revolution. As a consequence all mean-convex Alexandrov embedded {\\sc{cmc}} tori in the 3-sphere are surfaces of revolution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4278","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":"1309.4278","created_at":"2026-05-18T01:19:18.878415+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.4278v2","created_at":"2026-05-18T01:19:18.878415+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4278","created_at":"2026-05-18T01:19:18.878415+00:00"},{"alias_kind":"pith_short_12","alias_value":"ORE6JAYZA332","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"ORE6JAYZA332FWZR","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"ORE6JAYZ","created_at":"2026-05-18T12:27:54.935989+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/ORE6JAYZA332FWZRHSUOUAN7R4","json":"https://pith.science/pith/ORE6JAYZA332FWZRHSUOUAN7R4.json","graph_json":"https://pith.science/api/pith-number/ORE6JAYZA332FWZRHSUOUAN7R4/graph.json","events_json":"https://pith.science/api/pith-number/ORE6JAYZA332FWZRHSUOUAN7R4/events.json","paper":"https://pith.science/paper/ORE6JAYZ"},"agent_actions":{"view_html":"https://pith.science/pith/ORE6JAYZA332FWZRHSUOUAN7R4","download_json":"https://pith.science/pith/ORE6JAYZA332FWZRHSUOUAN7R4.json","view_paper":"https://pith.science/paper/ORE6JAYZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.4278&json=true","fetch_graph":"https://pith.science/api/pith-number/ORE6JAYZA332FWZRHSUOUAN7R4/graph.json","fetch_events":"https://pith.science/api/pith-number/ORE6JAYZA332FWZRHSUOUAN7R4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ORE6JAYZA332FWZRHSUOUAN7R4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ORE6JAYZA332FWZRHSUOUAN7R4/action/storage_attestation","attest_author":"https://pith.science/pith/ORE6JAYZA332FWZRHSUOUAN7R4/action/author_attestation","sign_citation":"https://pith.science/pith/ORE6JAYZA332FWZRHSUOUAN7R4/action/citation_signature","submit_replication":"https://pith.science/pith/ORE6JAYZA332FWZRHSUOUAN7R4/action/replication_record"}},"created_at":"2026-05-18T01:19:18.878415+00:00","updated_at":"2026-05-18T01:19:18.878415+00:00"}