{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5I4F2OHMTCGXETBCYAMWILMQL2","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":"1592249fa93cc287a8167dc22f1bb1bba74d0efa57ebc04b1f5c70befe70918a","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-07-09T15:18:06Z","title_canon_sha256":"db5015ea541bc35714c97d74be088bd4782831490acb77e174b4ea39f78bf5d7"},"schema_version":"1.0","source":{"id":"1207.2074","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2074","created_at":"2026-05-18T02:43:45Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2074v3","created_at":"2026-05-18T02:43:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2074","created_at":"2026-05-18T02:43:45Z"},{"alias_kind":"pith_short_12","alias_value":"5I4F2OHMTCGX","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5I4F2OHMTCGXETBC","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5I4F2OHM","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:aca95ef966e199247a9e4716279f175b593d380511f8d81e25d84410f8eee5de","target":"graph","created_at":"2026-05-18T02:43:45Z","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":"We categorify all the Reshetikhin-Turaev tangle invariants of type A. Our main tool is a categorification of the generalized Jones-Wenzl projectors (a.k.a. clasps) as infinite twists. Applying this to certain convolution product varieties on the affine Grassmannian we extend our earlier work with Kamnitzer from standard to arbitrary representations.","authors_text":"Sabin Cautis","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-07-09T15:18:06Z","title":"Clasp technology to knot homology via the affine Grassmannian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2074","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":"sha256:4bd5c65f828c09b4b6efd8d0a979b76f1fdd1d8db15040abc94f3b1e2af1ddc6","target":"record","created_at":"2026-05-18T02:43:45Z","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":"1592249fa93cc287a8167dc22f1bb1bba74d0efa57ebc04b1f5c70befe70918a","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-07-09T15:18:06Z","title_canon_sha256":"db5015ea541bc35714c97d74be088bd4782831490acb77e174b4ea39f78bf5d7"},"schema_version":"1.0","source":{"id":"1207.2074","kind":"arxiv","version":3}},"canonical_sha256":"ea385d38ec988d724c22c019642d905eab10a83c5183d477d7cb7003f8fa7069","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea385d38ec988d724c22c019642d905eab10a83c5183d477d7cb7003f8fa7069","first_computed_at":"2026-05-18T02:43:45.735163Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:45.735163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IPIOKSS1+/jiD2YaNjguCCLlPcpeijjsOtLBcgaJng9nP1nlXPdKv70rQ1ReZ8DgUVcnasmzXNP6kz3V68mWBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:45.735661Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.2074","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4bd5c65f828c09b4b6efd8d0a979b76f1fdd1d8db15040abc94f3b1e2af1ddc6","sha256:aca95ef966e199247a9e4716279f175b593d380511f8d81e25d84410f8eee5de"],"state_sha256":"396bbaa085b3027388d9ce12024e7b37e1fcec703942cb80147e6871d6e851dc"}