{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2000:LXOCK5GDCUWUZEPTKYR6JNWJWI","short_pith_number":"pith:LXOCK5GD","schema_version":"1.0","canonical_sha256":"5ddc2574c3152d4c91f35623e4b6c9b201a8130bbf1c3b3c8b69ccf73774921b","source":{"kind":"arxiv","id":"math/0008099","version":2},"attestation_state":"computed","paper":{"title":"A Theorem of Sanderson on Link Bordisms in Dimension 4","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"J. Scott Carter, Masahico Saito, Seiichi Kamada, Shin Satoh","submitted_at":"2000-08-14T13:53:55Z","abstract_excerpt":"The groups of link bordism can be identified with homotopy groups via the Pontryagin-Thom construction. B.J. Sanderson computed the bordism group of 3 component surface-links using the Hilton-Milnor Theorem, and later gave a geometric interpretation of the groups in terms of intersections of Seifert hypersurfaces and their framings. In this paper, we geometrically represent every element of the bordism group uniquely by a certain standard form of a surface-link, a generalization of a Hopf link. The standard forms give rise to an inverse of Sanderson's geometrically defined invariant."},"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":"math/0008099","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2000-08-14T13:53:55Z","cross_cats_sorted":[],"title_canon_sha256":"3dfd3d065544a44c19fac9844fe0bc107b8e2ed0968dc4bfdd62cde84a8c039e","abstract_canon_sha256":"826b138404a48a088a5c740717401a8a3f78e7d09a4a476d2597a82248c3aa60"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:33.414603Z","signature_b64":"E4ZmhtLOVO+PqDM3dNkUtQI2fGJ5X05HRryEK+ECVbYSkDXFKg+vJpci9aAayuG6qsbVP8KPRMmm4xnGnAfXAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ddc2574c3152d4c91f35623e4b6c9b201a8130bbf1c3b3c8b69ccf73774921b","last_reissued_at":"2026-05-18T02:41:33.414214Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:33.414214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Theorem of Sanderson on Link Bordisms in Dimension 4","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"J. Scott Carter, Masahico Saito, Seiichi Kamada, Shin Satoh","submitted_at":"2000-08-14T13:53:55Z","abstract_excerpt":"The groups of link bordism can be identified with homotopy groups via the Pontryagin-Thom construction. B.J. Sanderson computed the bordism group of 3 component surface-links using the Hilton-Milnor Theorem, and later gave a geometric interpretation of the groups in terms of intersections of Seifert hypersurfaces and their framings. In this paper, we geometrically represent every element of the bordism group uniquely by a certain standard form of a surface-link, a generalization of a Hopf link. The standard forms give rise to an inverse of Sanderson's geometrically defined invariant."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0008099","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":"math/0008099","created_at":"2026-05-18T02:41:33.414275+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0008099v2","created_at":"2026-05-18T02:41:33.414275+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0008099","created_at":"2026-05-18T02:41:33.414275+00:00"},{"alias_kind":"pith_short_12","alias_value":"LXOCK5GDCUWU","created_at":"2026-05-18T12:25:50.254431+00:00"},{"alias_kind":"pith_short_16","alias_value":"LXOCK5GDCUWUZEPT","created_at":"2026-05-18T12:25:50.254431+00:00"},{"alias_kind":"pith_short_8","alias_value":"LXOCK5GD","created_at":"2026-05-18T12:25:50.254431+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/LXOCK5GDCUWUZEPTKYR6JNWJWI","json":"https://pith.science/pith/LXOCK5GDCUWUZEPTKYR6JNWJWI.json","graph_json":"https://pith.science/api/pith-number/LXOCK5GDCUWUZEPTKYR6JNWJWI/graph.json","events_json":"https://pith.science/api/pith-number/LXOCK5GDCUWUZEPTKYR6JNWJWI/events.json","paper":"https://pith.science/paper/LXOCK5GD"},"agent_actions":{"view_html":"https://pith.science/pith/LXOCK5GDCUWUZEPTKYR6JNWJWI","download_json":"https://pith.science/pith/LXOCK5GDCUWUZEPTKYR6JNWJWI.json","view_paper":"https://pith.science/paper/LXOCK5GD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0008099&json=true","fetch_graph":"https://pith.science/api/pith-number/LXOCK5GDCUWUZEPTKYR6JNWJWI/graph.json","fetch_events":"https://pith.science/api/pith-number/LXOCK5GDCUWUZEPTKYR6JNWJWI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LXOCK5GDCUWUZEPTKYR6JNWJWI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LXOCK5GDCUWUZEPTKYR6JNWJWI/action/storage_attestation","attest_author":"https://pith.science/pith/LXOCK5GDCUWUZEPTKYR6JNWJWI/action/author_attestation","sign_citation":"https://pith.science/pith/LXOCK5GDCUWUZEPTKYR6JNWJWI/action/citation_signature","submit_replication":"https://pith.science/pith/LXOCK5GDCUWUZEPTKYR6JNWJWI/action/replication_record"}},"created_at":"2026-05-18T02:41:33.414275+00:00","updated_at":"2026-05-18T02:41:33.414275+00:00"}