{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:6XA6OVYQXVR5AQ4EGONDTDBXL6","short_pith_number":"pith:6XA6OVYQ","canonical_record":{"source":{"id":"1102.3952","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-02-19T02:38:25Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"aef8162bb60ffd0f032dbfdf7d63c088d7328a87e754da4c08028cda9a95ef71","abstract_canon_sha256":"e932cb1a6f36fbc868cad387ba95d21f96afcf8971f19f8f0ba9041434ce2f42"},"schema_version":"1.0"},"canonical_sha256":"f5c1e75710bd63d04384339a398c375fba930052a51bad8e683536ed9978468f","source":{"kind":"arxiv","id":"1102.3952","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3952","created_at":"2026-05-18T03:43:27Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3952v2","created_at":"2026-05-18T03:43:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3952","created_at":"2026-05-18T03:43:27Z"},{"alias_kind":"pith_short_12","alias_value":"6XA6OVYQXVR5","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6XA6OVYQXVR5AQ4E","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6XA6OVYQ","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:6XA6OVYQXVR5AQ4EGONDTDBXL6","target":"record","payload":{"canonical_record":{"source":{"id":"1102.3952","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-02-19T02:38:25Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"aef8162bb60ffd0f032dbfdf7d63c088d7328a87e754da4c08028cda9a95ef71","abstract_canon_sha256":"e932cb1a6f36fbc868cad387ba95d21f96afcf8971f19f8f0ba9041434ce2f42"},"schema_version":"1.0"},"canonical_sha256":"f5c1e75710bd63d04384339a398c375fba930052a51bad8e683536ed9978468f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:27.443001Z","signature_b64":"/xkL0hFaxCdtuh8+KENDHCfiWI92+8jl1WLwY1h3w53FyR2NjyyDfIgycsczbdZazIOnHjgX2xSj02Y/JxhhBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5c1e75710bd63d04384339a398c375fba930052a51bad8e683536ed9978468f","last_reissued_at":"2026-05-18T03:43:27.442424Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:27.442424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.3952","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":"2026-05-18T03:43:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7e8JNS3F6YBI7qrzVuoC+/fiJJCUnDaIwKsnQtPpcg7Mm8rgdJOOyzswBwv95L0TIeRS4Q+23n3Q2EZcxlQ8Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T07:13:50.999780Z"},"content_sha256":"11602e19abfa301ea1e5af848fa080e661c367a79469da607e79f43733364a81","schema_version":"1.0","event_id":"sha256:11602e19abfa301ea1e5af848fa080e661c367a79469da607e79f43733364a81"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:6XA6OVYQXVR5AQ4EGONDTDBXL6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Categorification of the Spin Representation of $U(\\mf{so}(7,\\C))$ via Projective Functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Shilin Yang, Yongjun Xu","submitted_at":"2011-02-19T02:38:25Z","abstract_excerpt":"The purpose of this paper is to study a categorification of the $n$-th tensor power of the spin representation of $U(\\mf{so}(7,\\C))$ by using certain singular blocks and projective functors of the BGG category of the complex Lie algebra $\\mf{gl}_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3952","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":"2026-05-18T03:43:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ItusQq62/zf7RD8O81T59uv0sIv43pttPtJ8H0lZGNSQO7Ola49WPjg7yhifIIZ8fcFdIvlkZY6iVsekSup9Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T07:13:51.000125Z"},"content_sha256":"80b037b855b8cff6b23faaa84517c46b3a8ce1f7e737eddbbf0701458e5e90ce","schema_version":"1.0","event_id":"sha256:80b037b855b8cff6b23faaa84517c46b3a8ce1f7e737eddbbf0701458e5e90ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6XA6OVYQXVR5AQ4EGONDTDBXL6/bundle.json","state_url":"https://pith.science/pith/6XA6OVYQXVR5AQ4EGONDTDBXL6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6XA6OVYQXVR5AQ4EGONDTDBXL6/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":"2026-06-22T07:13:51Z","links":{"resolver":"https://pith.science/pith/6XA6OVYQXVR5AQ4EGONDTDBXL6","bundle":"https://pith.science/pith/6XA6OVYQXVR5AQ4EGONDTDBXL6/bundle.json","state":"https://pith.science/pith/6XA6OVYQXVR5AQ4EGONDTDBXL6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6XA6OVYQXVR5AQ4EGONDTDBXL6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6XA6OVYQXVR5AQ4EGONDTDBXL6","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":"e932cb1a6f36fbc868cad387ba95d21f96afcf8971f19f8f0ba9041434ce2f42","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-02-19T02:38:25Z","title_canon_sha256":"aef8162bb60ffd0f032dbfdf7d63c088d7328a87e754da4c08028cda9a95ef71"},"schema_version":"1.0","source":{"id":"1102.3952","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3952","created_at":"2026-05-18T03:43:27Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3952v2","created_at":"2026-05-18T03:43:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3952","created_at":"2026-05-18T03:43:27Z"},{"alias_kind":"pith_short_12","alias_value":"6XA6OVYQXVR5","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6XA6OVYQXVR5AQ4E","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6XA6OVYQ","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:80b037b855b8cff6b23faaa84517c46b3a8ce1f7e737eddbbf0701458e5e90ce","target":"graph","created_at":"2026-05-18T03:43:27Z","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 purpose of this paper is to study a categorification of the $n$-th tensor power of the spin representation of $U(\\mf{so}(7,\\C))$ by using certain singular blocks and projective functors of the BGG category of the complex Lie algebra $\\mf{gl}_n$.","authors_text":"Shilin Yang, Yongjun Xu","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-02-19T02:38:25Z","title":"A Categorification of the Spin Representation of $U(\\mf{so}(7,\\C))$ via Projective Functors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3952","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":"sha256:11602e19abfa301ea1e5af848fa080e661c367a79469da607e79f43733364a81","target":"record","created_at":"2026-05-18T03:43:27Z","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":"e932cb1a6f36fbc868cad387ba95d21f96afcf8971f19f8f0ba9041434ce2f42","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-02-19T02:38:25Z","title_canon_sha256":"aef8162bb60ffd0f032dbfdf7d63c088d7328a87e754da4c08028cda9a95ef71"},"schema_version":"1.0","source":{"id":"1102.3952","kind":"arxiv","version":2}},"canonical_sha256":"f5c1e75710bd63d04384339a398c375fba930052a51bad8e683536ed9978468f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5c1e75710bd63d04384339a398c375fba930052a51bad8e683536ed9978468f","first_computed_at":"2026-05-18T03:43:27.442424Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:27.442424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/xkL0hFaxCdtuh8+KENDHCfiWI92+8jl1WLwY1h3w53FyR2NjyyDfIgycsczbdZazIOnHjgX2xSj02Y/JxhhBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:27.443001Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.3952","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11602e19abfa301ea1e5af848fa080e661c367a79469da607e79f43733364a81","sha256:80b037b855b8cff6b23faaa84517c46b3a8ce1f7e737eddbbf0701458e5e90ce"],"state_sha256":"53e15a38a6b82b261fb19638c54293cfbeb4662154ed0046a6321d47c443a3f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/1UXOrcMvKmRZYmft5xcTxcf1pnRnODM8huNkYKyPddlzeWBZGbyhlsvjsJ8bXRSmBWNBs4XrzD1TXOE2r+jBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T07:13:51.002420Z","bundle_sha256":"89f6a3276630192b86b592bcc9ace47e6e82c708d2e4b6dd917e4c91103ab829"}}