{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:LXOCK5GDCUWUZEPTKYR6JNWJWI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"826b138404a48a088a5c740717401a8a3f78e7d09a4a476d2597a82248c3aa60","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2000-08-14T13:53:55Z","title_canon_sha256":"3dfd3d065544a44c19fac9844fe0bc107b8e2ed0968dc4bfdd62cde84a8c039e"},"schema_version":"1.0","source":{"id":"math/0008099","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0008099","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"arxiv_version","alias_value":"math/0008099v2","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0008099","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"pith_short_12","alias_value":"LXOCK5GDCUWU","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"LXOCK5GDCUWUZEPT","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"LXOCK5GD","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:3b41991caa119cecc22a37798992d5e20d08ddcc3b511d1ec72997854e982233","target":"graph","created_at":"2026-05-18T02:41:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"J. Scott Carter, Masahico Saito, Seiichi Kamada, Shin Satoh","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2000-08-14T13:53:55Z","title":"A Theorem of Sanderson on Link Bordisms in Dimension 4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0008099","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:db9c146a7da7eed76a50da0759a30c34946442826f149bca0acc8e955082c28b","target":"record","created_at":"2026-05-18T02:41:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"826b138404a48a088a5c740717401a8a3f78e7d09a4a476d2597a82248c3aa60","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2000-08-14T13:53:55Z","title_canon_sha256":"3dfd3d065544a44c19fac9844fe0bc107b8e2ed0968dc4bfdd62cde84a8c039e"},"schema_version":"1.0","source":{"id":"math/0008099","kind":"arxiv","version":2}},"canonical_sha256":"5ddc2574c3152d4c91f35623e4b6c9b201a8130bbf1c3b3c8b69ccf73774921b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ddc2574c3152d4c91f35623e4b6c9b201a8130bbf1c3b3c8b69ccf73774921b","first_computed_at":"2026-05-18T02:41:33.414214Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:33.414214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E4ZmhtLOVO+PqDM3dNkUtQI2fGJ5X05HRryEK+ECVbYSkDXFKg+vJpci9aAayuG6qsbVP8KPRMmm4xnGnAfXAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:33.414603Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0008099","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db9c146a7da7eed76a50da0759a30c34946442826f149bca0acc8e955082c28b","sha256:3b41991caa119cecc22a37798992d5e20d08ddcc3b511d1ec72997854e982233"],"state_sha256":"fb01d6afe330ef41f55fcb43b396f6a5ac4472d6e747ce8d161fe7df7098353c"}