{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:OSELPLILIWNTY54ARV4RXEMKCX","short_pith_number":"pith:OSELPLIL","schema_version":"1.0","canonical_sha256":"7488b7ad0b459b3c77808d791b918a15d9468f24a6b1c8f03f0b4b3bd25d7cf7","source":{"kind":"arxiv","id":"1411.1621","version":3},"attestation_state":"computed","paper":{"title":"Casson towers and slice links","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Jae Choon Cha, Mark Powell","submitted_at":"2014-11-06T14:09:17Z","abstract_excerpt":"We prove that a Casson tower of height 4 contains a flat embedded disc bounded by the attaching circle, and we prove disc embedding results for height 2 and 3 Casson towers which are embedded into a 4-manifold, with some additional fundamental group assumptions. In the proofs we create a capped grope from a Casson tower and use a refined height raising argument to establish the existence of a symmetric grope which has two layers of caps, data which is sufficient for a topological disc to exist, with the desired boundary. As applications, we present new slice knots and links by giving direct ge"},"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":"1411.1621","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-11-06T14:09:17Z","cross_cats_sorted":[],"title_canon_sha256":"02e7c76ebe8c41035c0b49308de22e78b4715ce43711afec0a272caf31ead33b","abstract_canon_sha256":"2c9532238a3602ff3f358175c0c91f47273f50993b6bec8038743d7994d0057f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:30.806865Z","signature_b64":"8tyKcY4Tk8nuDnd95uNAdgAuNrUNTUOtqZR9PwquujRikgirrWkgXjx7DtUGV295USmnBnKVcPBI2nrAc41IAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7488b7ad0b459b3c77808d791b918a15d9468f24a6b1c8f03f0b4b3bd25d7cf7","last_reissued_at":"2026-05-18T01:25:30.806231Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:30.806231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Casson towers and slice links","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Jae Choon Cha, Mark Powell","submitted_at":"2014-11-06T14:09:17Z","abstract_excerpt":"We prove that a Casson tower of height 4 contains a flat embedded disc bounded by the attaching circle, and we prove disc embedding results for height 2 and 3 Casson towers which are embedded into a 4-manifold, with some additional fundamental group assumptions. In the proofs we create a capped grope from a Casson tower and use a refined height raising argument to establish the existence of a symmetric grope which has two layers of caps, data which is sufficient for a topological disc to exist, with the desired boundary. As applications, we present new slice knots and links by giving direct ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1621","kind":"arxiv","version":3},"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":"1411.1621","created_at":"2026-05-18T01:25:30.806329+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.1621v3","created_at":"2026-05-18T01:25:30.806329+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1621","created_at":"2026-05-18T01:25:30.806329+00:00"},{"alias_kind":"pith_short_12","alias_value":"OSELPLILIWNT","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OSELPLILIWNTY54A","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OSELPLIL","created_at":"2026-05-18T12:28:43.426989+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/OSELPLILIWNTY54ARV4RXEMKCX","json":"https://pith.science/pith/OSELPLILIWNTY54ARV4RXEMKCX.json","graph_json":"https://pith.science/api/pith-number/OSELPLILIWNTY54ARV4RXEMKCX/graph.json","events_json":"https://pith.science/api/pith-number/OSELPLILIWNTY54ARV4RXEMKCX/events.json","paper":"https://pith.science/paper/OSELPLIL"},"agent_actions":{"view_html":"https://pith.science/pith/OSELPLILIWNTY54ARV4RXEMKCX","download_json":"https://pith.science/pith/OSELPLILIWNTY54ARV4RXEMKCX.json","view_paper":"https://pith.science/paper/OSELPLIL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.1621&json=true","fetch_graph":"https://pith.science/api/pith-number/OSELPLILIWNTY54ARV4RXEMKCX/graph.json","fetch_events":"https://pith.science/api/pith-number/OSELPLILIWNTY54ARV4RXEMKCX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OSELPLILIWNTY54ARV4RXEMKCX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OSELPLILIWNTY54ARV4RXEMKCX/action/storage_attestation","attest_author":"https://pith.science/pith/OSELPLILIWNTY54ARV4RXEMKCX/action/author_attestation","sign_citation":"https://pith.science/pith/OSELPLILIWNTY54ARV4RXEMKCX/action/citation_signature","submit_replication":"https://pith.science/pith/OSELPLILIWNTY54ARV4RXEMKCX/action/replication_record"}},"created_at":"2026-05-18T01:25:30.806329+00:00","updated_at":"2026-05-18T01:25:30.806329+00:00"}