{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:GXJGAVMORPHWZOZNLS2HOKPPJB","short_pith_number":"pith:GXJGAVMO","canonical_record":{"source":{"id":"1003.3416","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-03-17T17:32:06Z","cross_cats_sorted":[],"title_canon_sha256":"9fb900ee63c857b8d652f21b8cf690edea8c941cd18f9609e4682d3244124530","abstract_canon_sha256":"9631d98e6604c93c1c3d2b2c35cd1bde3cd59dbe53cf0fcaf35353fa64c63119"},"schema_version":"1.0"},"canonical_sha256":"35d260558e8bcf6cbb2d5cb47729ef4876f27e3dae3b9f076e6bfaea913eb7d4","source":{"kind":"arxiv","id":"1003.3416","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.3416","created_at":"2026-05-18T01:19:35Z"},{"alias_kind":"arxiv_version","alias_value":"1003.3416v2","created_at":"2026-05-18T01:19:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.3416","created_at":"2026-05-18T01:19:35Z"},{"alias_kind":"pith_short_12","alias_value":"GXJGAVMORPHW","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GXJGAVMORPHWZOZN","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GXJGAVMO","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:GXJGAVMORPHWZOZNLS2HOKPPJB","target":"record","payload":{"canonical_record":{"source":{"id":"1003.3416","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-03-17T17:32:06Z","cross_cats_sorted":[],"title_canon_sha256":"9fb900ee63c857b8d652f21b8cf690edea8c941cd18f9609e4682d3244124530","abstract_canon_sha256":"9631d98e6604c93c1c3d2b2c35cd1bde3cd59dbe53cf0fcaf35353fa64c63119"},"schema_version":"1.0"},"canonical_sha256":"35d260558e8bcf6cbb2d5cb47729ef4876f27e3dae3b9f076e6bfaea913eb7d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:35.570211Z","signature_b64":"Qr3ZQY6iu86kHxb1N9LGxS1coLIjCVF2GxoHiPaTNHl+RIBpMYLpncEM39Q72U63QIQZUcAbfaRL0/sl/VonDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35d260558e8bcf6cbb2d5cb47729ef4876f27e3dae3b9f076e6bfaea913eb7d4","last_reissued_at":"2026-05-18T01:19:35.569718Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:35.569718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.3416","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dxvkd/nNqILT2jCu4khd2h0JDagk0Xf0klOULu18EQpufwWviH/k33ZlHsGjmWu1DeJP+2W8WHEO8rYWNJEvBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T13:52:07.503859Z"},"content_sha256":"67f14399d5083d8d9ba7d1fef4ac46b86e394c1bbd64b59a9243bb3bbabea932","schema_version":"1.0","event_id":"sha256:67f14399d5083d8d9ba7d1fef4ac46b86e394c1bbd64b59a9243bb3bbabea932"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:GXJGAVMORPHWZOZNLS2HOKPPJB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Diagrammatic Temperley-Lieb Categorification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ben Elias","submitted_at":"2010-03-17T17:32:06Z","abstract_excerpt":"The monoidal category of Soergel bimodules categorifies the Hecke algebra of a finite Weyl group. In the case of the symmetric group, morphisms in this category can be drawn as graphs in the plane. We define a quotient category, also given in terms of planar graphs, which categorifies the Temperley-Lieb algebra. Certain ideals appearing in this quotient are related both to the 1-skeleton of the Coxeter complex and to the topology of 2D cobordisms. We demonstrate how further subquotients of this category will categorify the cell modules of the Temperley-Lieb algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3416","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7N3hMlbOzEYHzGvoOQrG/pxQQgrymvl3nrr6cRrAANuxZFya+Le5EdaM6Sa6cIKQoS7ShSlbNz6c2yBEYb+hDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T13:52:07.504428Z"},"content_sha256":"3754a8243554661d8e685ca1bbd2851a691970557030505a3605171931a307f8","schema_version":"1.0","event_id":"sha256:3754a8243554661d8e685ca1bbd2851a691970557030505a3605171931a307f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GXJGAVMORPHWZOZNLS2HOKPPJB/bundle.json","state_url":"https://pith.science/pith/GXJGAVMORPHWZOZNLS2HOKPPJB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GXJGAVMORPHWZOZNLS2HOKPPJB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T13:52:07Z","links":{"resolver":"https://pith.science/pith/GXJGAVMORPHWZOZNLS2HOKPPJB","bundle":"https://pith.science/pith/GXJGAVMORPHWZOZNLS2HOKPPJB/bundle.json","state":"https://pith.science/pith/GXJGAVMORPHWZOZNLS2HOKPPJB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GXJGAVMORPHWZOZNLS2HOKPPJB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GXJGAVMORPHWZOZNLS2HOKPPJB","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":"9631d98e6604c93c1c3d2b2c35cd1bde3cd59dbe53cf0fcaf35353fa64c63119","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-03-17T17:32:06Z","title_canon_sha256":"9fb900ee63c857b8d652f21b8cf690edea8c941cd18f9609e4682d3244124530"},"schema_version":"1.0","source":{"id":"1003.3416","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.3416","created_at":"2026-05-18T01:19:35Z"},{"alias_kind":"arxiv_version","alias_value":"1003.3416v2","created_at":"2026-05-18T01:19:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.3416","created_at":"2026-05-18T01:19:35Z"},{"alias_kind":"pith_short_12","alias_value":"GXJGAVMORPHW","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GXJGAVMORPHWZOZN","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GXJGAVMO","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:3754a8243554661d8e685ca1bbd2851a691970557030505a3605171931a307f8","target":"graph","created_at":"2026-05-18T01:19:35Z","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 monoidal category of Soergel bimodules categorifies the Hecke algebra of a finite Weyl group. In the case of the symmetric group, morphisms in this category can be drawn as graphs in the plane. We define a quotient category, also given in terms of planar graphs, which categorifies the Temperley-Lieb algebra. Certain ideals appearing in this quotient are related both to the 1-skeleton of the Coxeter complex and to the topology of 2D cobordisms. We demonstrate how further subquotients of this category will categorify the cell modules of the Temperley-Lieb algebra.","authors_text":"Ben Elias","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-03-17T17:32:06Z","title":"A Diagrammatic Temperley-Lieb Categorification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3416","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":"sha256:67f14399d5083d8d9ba7d1fef4ac46b86e394c1bbd64b59a9243bb3bbabea932","target":"record","created_at":"2026-05-18T01:19:35Z","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":"9631d98e6604c93c1c3d2b2c35cd1bde3cd59dbe53cf0fcaf35353fa64c63119","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-03-17T17:32:06Z","title_canon_sha256":"9fb900ee63c857b8d652f21b8cf690edea8c941cd18f9609e4682d3244124530"},"schema_version":"1.0","source":{"id":"1003.3416","kind":"arxiv","version":2}},"canonical_sha256":"35d260558e8bcf6cbb2d5cb47729ef4876f27e3dae3b9f076e6bfaea913eb7d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35d260558e8bcf6cbb2d5cb47729ef4876f27e3dae3b9f076e6bfaea913eb7d4","first_computed_at":"2026-05-18T01:19:35.569718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:35.569718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qr3ZQY6iu86kHxb1N9LGxS1coLIjCVF2GxoHiPaTNHl+RIBpMYLpncEM39Q72U63QIQZUcAbfaRL0/sl/VonDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:35.570211Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.3416","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67f14399d5083d8d9ba7d1fef4ac46b86e394c1bbd64b59a9243bb3bbabea932","sha256:3754a8243554661d8e685ca1bbd2851a691970557030505a3605171931a307f8"],"state_sha256":"7e53b2e3fabd871d8b16d1e0487dc828cf43fb32525bbb3cde0f03df76b3c8f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ovLc7zymVD3MxBVgDErhs2J1dGBHZtVWXobSj3reCRDBRNfHI4QgFHcTF0VaayD9IGeUsvlFSS15cMOsEtfBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T13:52:07.509924Z","bundle_sha256":"89ffccc682dd3758dbf2a37b4685b87fec4c45bfee981d115e9b30a4b8be0f2c"}}