{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:QVSW5YY4ADVEXQYVHXNIIL7JDM","short_pith_number":"pith:QVSW5YY4","schema_version":"1.0","canonical_sha256":"85656ee31c00ea4bc3153dda842fe91b20df9eb86ae21b0b884b063c8658b0c2","source":{"kind":"arxiv","id":"1011.6026","version":1},"attestation_state":"computed","paper":{"title":"Higher Order Intersections in Low-Dimensional Topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Jim Conant, Peter Teichner, Rob Schneiderman","submitted_at":"2010-11-28T10:27:39Z","abstract_excerpt":"We show how to measure the failure of the Whitney trick in dimension 4 by constructing higher- order intersection invariants of Whitney towers built from iterated Whitney disks on immersed surfaces in 4-manifolds. For Whitney towers on immersed disks in the 4-ball, we identify some of these new invariants with previously known link invariants like Milnor, Sato-Levine and Arf invariants. We also define higher- order Sato-Levine and Arf invariants and show that these invariants detect the obstructions to framing a twisted Whitney tower. Together with Milnor invariants, these higher-order invaria"},"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":"1011.6026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-11-28T10:27:39Z","cross_cats_sorted":[],"title_canon_sha256":"6b1e7ac27a79b3e1489f6f3616c2d6ed49debe9530acdd6d0b77f6a6fdb19191","abstract_canon_sha256":"629e589b8a88389acbdc23ce487c6cf5afec95273a4d8907ba9982cb4abf4ce5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:13.966718Z","signature_b64":"JjkjxqsWwtG3aMIBpZDr+ucxajRA81IJTrxYciLbtux8OKoId70g9xxFgEaA721e2XRBN0Scfp8OHMb0arCuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85656ee31c00ea4bc3153dda842fe91b20df9eb86ae21b0b884b063c8658b0c2","last_reissued_at":"2026-05-18T01:11:13.966097Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:13.966097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher Order Intersections in Low-Dimensional Topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Jim Conant, Peter Teichner, Rob Schneiderman","submitted_at":"2010-11-28T10:27:39Z","abstract_excerpt":"We show how to measure the failure of the Whitney trick in dimension 4 by constructing higher- order intersection invariants of Whitney towers built from iterated Whitney disks on immersed surfaces in 4-manifolds. For Whitney towers on immersed disks in the 4-ball, we identify some of these new invariants with previously known link invariants like Milnor, Sato-Levine and Arf invariants. We also define higher- order Sato-Levine and Arf invariants and show that these invariants detect the obstructions to framing a twisted Whitney tower. Together with Milnor invariants, these higher-order invaria"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6026","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":"1011.6026","created_at":"2026-05-18T01:11:13.966192+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.6026v1","created_at":"2026-05-18T01:11:13.966192+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.6026","created_at":"2026-05-18T01:11:13.966192+00:00"},{"alias_kind":"pith_short_12","alias_value":"QVSW5YY4ADVE","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_16","alias_value":"QVSW5YY4ADVEXQYV","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_8","alias_value":"QVSW5YY4","created_at":"2026-05-18T12:26:13.927090+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/QVSW5YY4ADVEXQYVHXNIIL7JDM","json":"https://pith.science/pith/QVSW5YY4ADVEXQYVHXNIIL7JDM.json","graph_json":"https://pith.science/api/pith-number/QVSW5YY4ADVEXQYVHXNIIL7JDM/graph.json","events_json":"https://pith.science/api/pith-number/QVSW5YY4ADVEXQYVHXNIIL7JDM/events.json","paper":"https://pith.science/paper/QVSW5YY4"},"agent_actions":{"view_html":"https://pith.science/pith/QVSW5YY4ADVEXQYVHXNIIL7JDM","download_json":"https://pith.science/pith/QVSW5YY4ADVEXQYVHXNIIL7JDM.json","view_paper":"https://pith.science/paper/QVSW5YY4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.6026&json=true","fetch_graph":"https://pith.science/api/pith-number/QVSW5YY4ADVEXQYVHXNIIL7JDM/graph.json","fetch_events":"https://pith.science/api/pith-number/QVSW5YY4ADVEXQYVHXNIIL7JDM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QVSW5YY4ADVEXQYVHXNIIL7JDM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QVSW5YY4ADVEXQYVHXNIIL7JDM/action/storage_attestation","attest_author":"https://pith.science/pith/QVSW5YY4ADVEXQYVHXNIIL7JDM/action/author_attestation","sign_citation":"https://pith.science/pith/QVSW5YY4ADVEXQYVHXNIIL7JDM/action/citation_signature","submit_replication":"https://pith.science/pith/QVSW5YY4ADVEXQYVHXNIIL7JDM/action/replication_record"}},"created_at":"2026-05-18T01:11:13.966192+00:00","updated_at":"2026-05-18T01:11:13.966192+00:00"}