{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:I5I2DNVRFAU2I2JXUWWPRY7RPR","short_pith_number":"pith:I5I2DNVR","canonical_record":{"source":{"id":"1111.1320","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-11-05T15:25:57Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"81751b5e87e0efb568e6a260f7ab2cf18fad4c684eeb3acf1982e3b322380021","abstract_canon_sha256":"c4810ccc11b9b8b1a26ed077f96b3de906cae8e2fef7b9916b196b9364422f20"},"schema_version":"1.0"},"canonical_sha256":"4751a1b6b12829a46937a5acf8e3f17c5ed8ad9d5682e278e72d582f3156175a","source":{"kind":"arxiv","id":"1111.1320","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1320","created_at":"2026-05-18T02:56:19Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1320v1","created_at":"2026-05-18T02:56:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1320","created_at":"2026-05-18T02:56:19Z"},{"alias_kind":"pith_short_12","alias_value":"I5I2DNVRFAU2","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"I5I2DNVRFAU2I2JX","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"I5I2DNVR","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:I5I2DNVRFAU2I2JXUWWPRY7RPR","target":"record","payload":{"canonical_record":{"source":{"id":"1111.1320","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-11-05T15:25:57Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"81751b5e87e0efb568e6a260f7ab2cf18fad4c684eeb3acf1982e3b322380021","abstract_canon_sha256":"c4810ccc11b9b8b1a26ed077f96b3de906cae8e2fef7b9916b196b9364422f20"},"schema_version":"1.0"},"canonical_sha256":"4751a1b6b12829a46937a5acf8e3f17c5ed8ad9d5682e278e72d582f3156175a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:19.521770Z","signature_b64":"QraamgNBHTQ+O28AG8lNJL24s85L+OgARV0IlHXson32DaS7p/Rxu1k/YCIDOsrFE0x7/P1tWJ6AN2ZtO7snCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4751a1b6b12829a46937a5acf8e3f17c5ed8ad9d5682e278e72d582f3156175a","last_reissued_at":"2026-05-18T02:56:19.521131Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:19.521131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.1320","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:56:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pgJ7keCna2wXjNFM+HJgJKnassCGplSLQpS4xipx/ogw7qptR50azrf2k6txmAZvJuFL3VnOUT3NTRzj0kGOAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:19:21.367841Z"},"content_sha256":"2b4d261801b82912e3384e757d58b8a5a500d4a2ccef036813cddb3e7acb49e6","schema_version":"1.0","event_id":"sha256:2b4d261801b82912e3384e757d58b8a5a500d4a2ccef036813cddb3e7acb49e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:I5I2DNVRFAU2I2JXUWWPRY7RPR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The odd nilHecke algebra and its diagrammatics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Aaron D. Lauda, Alexander P. Ellis, Mikhail Khovanov","submitted_at":"2011-11-05T15:25:57Z","abstract_excerpt":"We introduce an odd version of the nilHecke algebra and develop an odd analogue of the thick diagrammatic calculus for nilHecke algebras. We graphically describe idempotents which give a Morita equivalence between odd nilHecke algebras and the rings of odd symmetric functions in finitely many variables. Cyclotomic quotients of odd nilHecke algebras are Morita equivalent to rings which are odd analogues of the cohomology rings of Grassmannians. Like their even counterparts, odd nilHecke algebras categorify the positive half of quantum sl(2)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1320","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:56:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CviSyfFty5pxFj8KApGaI3Gb+Fl3BJI4rBU1wCouxnjAzkDo+wAhF8x29mqpe1V8xxo1KEBKuyltZxxa3GadCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:19:21.368197Z"},"content_sha256":"6c47c36ea0bc6661d5cb4c23030e3d8f8ca9dd4cf831c95ecb6ae76bd6d1e395","schema_version":"1.0","event_id":"sha256:6c47c36ea0bc6661d5cb4c23030e3d8f8ca9dd4cf831c95ecb6ae76bd6d1e395"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I5I2DNVRFAU2I2JXUWWPRY7RPR/bundle.json","state_url":"https://pith.science/pith/I5I2DNVRFAU2I2JXUWWPRY7RPR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I5I2DNVRFAU2I2JXUWWPRY7RPR/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":"2026-05-28T02:19:21Z","links":{"resolver":"https://pith.science/pith/I5I2DNVRFAU2I2JXUWWPRY7RPR","bundle":"https://pith.science/pith/I5I2DNVRFAU2I2JXUWWPRY7RPR/bundle.json","state":"https://pith.science/pith/I5I2DNVRFAU2I2JXUWWPRY7RPR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I5I2DNVRFAU2I2JXUWWPRY7RPR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:I5I2DNVRFAU2I2JXUWWPRY7RPR","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":"c4810ccc11b9b8b1a26ed077f96b3de906cae8e2fef7b9916b196b9364422f20","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-11-05T15:25:57Z","title_canon_sha256":"81751b5e87e0efb568e6a260f7ab2cf18fad4c684eeb3acf1982e3b322380021"},"schema_version":"1.0","source":{"id":"1111.1320","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1320","created_at":"2026-05-18T02:56:19Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1320v1","created_at":"2026-05-18T02:56:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1320","created_at":"2026-05-18T02:56:19Z"},{"alias_kind":"pith_short_12","alias_value":"I5I2DNVRFAU2","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"I5I2DNVRFAU2I2JX","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"I5I2DNVR","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:6c47c36ea0bc6661d5cb4c23030e3d8f8ca9dd4cf831c95ecb6ae76bd6d1e395","target":"graph","created_at":"2026-05-18T02:56:19Z","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 introduce an odd version of the nilHecke algebra and develop an odd analogue of the thick diagrammatic calculus for nilHecke algebras. We graphically describe idempotents which give a Morita equivalence between odd nilHecke algebras and the rings of odd symmetric functions in finitely many variables. Cyclotomic quotients of odd nilHecke algebras are Morita equivalent to rings which are odd analogues of the cohomology rings of Grassmannians. Like their even counterparts, odd nilHecke algebras categorify the positive half of quantum sl(2).","authors_text":"Aaron D. Lauda, Alexander P. Ellis, Mikhail Khovanov","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-11-05T15:25:57Z","title":"The odd nilHecke algebra and its diagrammatics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1320","kind":"arxiv","version":1},"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":"sha256:2b4d261801b82912e3384e757d58b8a5a500d4a2ccef036813cddb3e7acb49e6","target":"record","created_at":"2026-05-18T02:56:19Z","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":"c4810ccc11b9b8b1a26ed077f96b3de906cae8e2fef7b9916b196b9364422f20","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-11-05T15:25:57Z","title_canon_sha256":"81751b5e87e0efb568e6a260f7ab2cf18fad4c684eeb3acf1982e3b322380021"},"schema_version":"1.0","source":{"id":"1111.1320","kind":"arxiv","version":1}},"canonical_sha256":"4751a1b6b12829a46937a5acf8e3f17c5ed8ad9d5682e278e72d582f3156175a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4751a1b6b12829a46937a5acf8e3f17c5ed8ad9d5682e278e72d582f3156175a","first_computed_at":"2026-05-18T02:56:19.521131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:19.521131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QraamgNBHTQ+O28AG8lNJL24s85L+OgARV0IlHXson32DaS7p/Rxu1k/YCIDOsrFE0x7/P1tWJ6AN2ZtO7snCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:19.521770Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.1320","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b4d261801b82912e3384e757d58b8a5a500d4a2ccef036813cddb3e7acb49e6","sha256:6c47c36ea0bc6661d5cb4c23030e3d8f8ca9dd4cf831c95ecb6ae76bd6d1e395"],"state_sha256":"29e3afd81983d8f0b32f9c8dd254b069f38db39bf54f0b3394817c2e90f125d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"poxaVatl3Augu7ztzL+NgH0FIxdKp/EpuQClekYCMSEAYjzb7dk/R1tarh58YffgTSCMh8C4IubBogQ6/lWzBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:19:21.370379Z","bundle_sha256":"e3f53ac79a3db5b7f0bc1fd05c39b1a247f56247f700d54a3c56728d6a64c690"}}