{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HKWS7CB2G7KM7N2DRV3YJUJRHC","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":"aec8c26668d123750ed6b529a066f3dcf03b744474009516ca6ddf099e92bb70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-01-18T15:31:34Z","title_canon_sha256":"115505bbf4e4b64f38f7a1d4869fbc236756f58654aee19c1534c3c39042afe1"},"schema_version":"1.0","source":{"id":"1101.3477","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3477","created_at":"2026-05-18T02:22:51Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3477v3","created_at":"2026-05-18T02:22:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3477","created_at":"2026-05-18T02:22:51Z"},{"alias_kind":"pith_short_12","alias_value":"HKWS7CB2G7KM","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HKWS7CB2G7KM7N2D","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HKWS7CB2","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:2e2d138afd41672c51fb2830c807e0a333304ec48fe9d0ca40afa11f2e9889a6","target":"graph","created_at":"2026-05-18T02:22:51Z","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":"This paper describes grope and Whitney tower filtrations on the set of concordance classes of classical links in terms of class and order respectively. Using the tree-valued intersection theory of Whitney towers, the associated graded quotients are shown to be finitely generated abelian groups under a (surprisingly) well-defined connected sum operation. Twisted Whitney towers are also introduced, along with a corresponding quadratic enhancement of the intersection theory for framed Whitney towers that measures Whitney-disk framing obstructions. The obstruction theory in the framed setting is s","authors_text":"James Conant, Peter Teichner, Rob Schneiderman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-01-18T15:31:34Z","title":"Geometric Filtrations of Classical Link Concordance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3477","kind":"arxiv","version":3},"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":"sha256:96a548a1a43c9685a8fef9e8221b188397b7313485b5abc976df713ef9bbf997","target":"record","created_at":"2026-05-18T02:22:51Z","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":"aec8c26668d123750ed6b529a066f3dcf03b744474009516ca6ddf099e92bb70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-01-18T15:31:34Z","title_canon_sha256":"115505bbf4e4b64f38f7a1d4869fbc236756f58654aee19c1534c3c39042afe1"},"schema_version":"1.0","source":{"id":"1101.3477","kind":"arxiv","version":3}},"canonical_sha256":"3aad2f883a37d4cfb7438d7784d13138a565643ca722991c6b4b8ec42067ccfe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3aad2f883a37d4cfb7438d7784d13138a565643ca722991c6b4b8ec42067ccfe","first_computed_at":"2026-05-18T02:22:51.694297Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:51.694297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jXhQjJJrp9GPpFUqXpwvKA2rspXgcjR57MoG/XqgQkGklFuqasuCK4uWJJgDBYKI94TENM4z1Seg65sBNFRCDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:51.694782Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.3477","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96a548a1a43c9685a8fef9e8221b188397b7313485b5abc976df713ef9bbf997","sha256:2e2d138afd41672c51fb2830c807e0a333304ec48fe9d0ca40afa11f2e9889a6"],"state_sha256":"74d0e4dc67fc2f892175e86f5372b1b089c006b4f160d68ca074e75ef3aed1d4"}