{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:V4UQV42SYI456CCQRDHMBVI4CR","short_pith_number":"pith:V4UQV42S","schema_version":"1.0","canonical_sha256":"af290af352c239df085088cec0d51c1465488fb842bb71c06a03c81f72854f77","source":{"kind":"arxiv","id":"1507.00681","version":1},"attestation_state":"computed","paper":{"title":"Closed Mean Curvature Self-Shrinking Surfaces of Generalized Rotational Type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Peter McGrath","submitted_at":"2015-07-02T18:13:34Z","abstract_excerpt":"For each $n\\geq 2$ we construct a new closed embedded mean curvature self-shrinking hypersurface in $\\mathbb{R}^{2n}$. These self-shrinkers are diffeomorphic to $S^{n-1}\\times S^{n-1}\\times S^1$ and are $SO(n)\\times SO(n)$ invariant. The method is inspired by constructions of Hsiang and these surfaces generalize self-shrinking \"tori\" diffeomorphic to $S^{n-1}\\times S^1$ constructed by Angenent."},"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":"1507.00681","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-07-02T18:13:34Z","cross_cats_sorted":[],"title_canon_sha256":"0e703bbadc982a1e0bcd2bf53190bcaf9bd6941b0ad25703027628e0c27a23b0","abstract_canon_sha256":"d3444a7ceb8ce7b0b42ab815efe9c40cb305e26a0cb12fb919aae832dde88296"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:23.902701Z","signature_b64":"u/jr3iBGRdCqkFsjnKzrMi8p2MF3WwoSRwPeb+wlpfCBbhtEkRdgwTg0zGOtr8d4zOpIXbzGxrwPTMyEwK8WDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af290af352c239df085088cec0d51c1465488fb842bb71c06a03c81f72854f77","last_reissued_at":"2026-05-18T01:37:23.901852Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:23.901852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Closed Mean Curvature Self-Shrinking Surfaces of Generalized Rotational Type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Peter McGrath","submitted_at":"2015-07-02T18:13:34Z","abstract_excerpt":"For each $n\\geq 2$ we construct a new closed embedded mean curvature self-shrinking hypersurface in $\\mathbb{R}^{2n}$. These self-shrinkers are diffeomorphic to $S^{n-1}\\times S^{n-1}\\times S^1$ and are $SO(n)\\times SO(n)$ invariant. The method is inspired by constructions of Hsiang and these surfaces generalize self-shrinking \"tori\" diffeomorphic to $S^{n-1}\\times S^1$ constructed by Angenent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00681","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":"1507.00681","created_at":"2026-05-18T01:37:23.901987+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.00681v1","created_at":"2026-05-18T01:37:23.901987+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00681","created_at":"2026-05-18T01:37:23.901987+00:00"},{"alias_kind":"pith_short_12","alias_value":"V4UQV42SYI45","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"V4UQV42SYI456CCQ","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"V4UQV42S","created_at":"2026-05-18T12:29:44.643036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.05022","citing_title":"Existence of rotationally symmetric embedded f-minimal tori","ref_index":8,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V4UQV42SYI456CCQRDHMBVI4CR","json":"https://pith.science/pith/V4UQV42SYI456CCQRDHMBVI4CR.json","graph_json":"https://pith.science/api/pith-number/V4UQV42SYI456CCQRDHMBVI4CR/graph.json","events_json":"https://pith.science/api/pith-number/V4UQV42SYI456CCQRDHMBVI4CR/events.json","paper":"https://pith.science/paper/V4UQV42S"},"agent_actions":{"view_html":"https://pith.science/pith/V4UQV42SYI456CCQRDHMBVI4CR","download_json":"https://pith.science/pith/V4UQV42SYI456CCQRDHMBVI4CR.json","view_paper":"https://pith.science/paper/V4UQV42S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.00681&json=true","fetch_graph":"https://pith.science/api/pith-number/V4UQV42SYI456CCQRDHMBVI4CR/graph.json","fetch_events":"https://pith.science/api/pith-number/V4UQV42SYI456CCQRDHMBVI4CR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V4UQV42SYI456CCQRDHMBVI4CR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V4UQV42SYI456CCQRDHMBVI4CR/action/storage_attestation","attest_author":"https://pith.science/pith/V4UQV42SYI456CCQRDHMBVI4CR/action/author_attestation","sign_citation":"https://pith.science/pith/V4UQV42SYI456CCQRDHMBVI4CR/action/citation_signature","submit_replication":"https://pith.science/pith/V4UQV42SYI456CCQRDHMBVI4CR/action/replication_record"}},"created_at":"2026-05-18T01:37:23.901987+00:00","updated_at":"2026-05-18T01:37:23.901987+00:00"}