{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:MMXYGNVPTXM62KFN3GRNO7I2T5","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":"37726ee2429a9ed70e3fd10b5c6d7716a304295f314402706f33c452208549c9","cross_cats_sorted":["math.RT"],"license":"","primary_cat":"math.QA","submitted_at":"2000-02-21T16:33:08Z","title_canon_sha256":"5dc4e4389e1d44935d48845783747b7431a961e7b325098f61728a245eeddc43"},"schema_version":"1.0","source":{"id":"math/0002170","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0002170","created_at":"2026-07-04T14:34:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0002170v1","created_at":"2026-07-04T14:34:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0002170","created_at":"2026-07-04T14:34:23Z"},{"alias_kind":"pith_short_12","alias_value":"MMXYGNVPTXM6","created_at":"2026-07-04T14:34:23Z"},{"alias_kind":"pith_short_16","alias_value":"MMXYGNVPTXM62KFN","created_at":"2026-07-04T14:34:23Z"},{"alias_kind":"pith_short_8","alias_value":"MMXYGNVP","created_at":"2026-07-04T14:34:23Z"}],"graph_snapshots":[{"event_id":"sha256:ca7620ac195dd8b7115375fea2ad04cfea5185212fb87ce151d318026a3af0d4","target":"graph","created_at":"2026-07-04T14:34:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0002170/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Explicit formulas for the symmetrizer and the antisymmetrizer of the Birman-Wenzl-Murakami algebras BWM(r,q)_n are given.","authors_text":"Axel Sch\\\"uler, Istv\\'an Heckenberger","cross_cats":["math.RT"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2000-02-21T16:33:08Z","title":"Symmetrizer and Antisymmetrizer of the Birman-Wenzl-Murakami Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0002170","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":"sha256:0f1bd1e9d54aa8dd3202e61ecdd2634aae9de49e452d0cb2e296378979d0d9d3","target":"record","created_at":"2026-07-04T14:34:23Z","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":"37726ee2429a9ed70e3fd10b5c6d7716a304295f314402706f33c452208549c9","cross_cats_sorted":["math.RT"],"license":"","primary_cat":"math.QA","submitted_at":"2000-02-21T16:33:08Z","title_canon_sha256":"5dc4e4389e1d44935d48845783747b7431a961e7b325098f61728a245eeddc43"},"schema_version":"1.0","source":{"id":"math/0002170","kind":"arxiv","version":1}},"canonical_sha256":"632f8336af9dd9ed28add9a2d77d1a9f6437066ab58b32b8614b3fa4f0bcd554","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"632f8336af9dd9ed28add9a2d77d1a9f6437066ab58b32b8614b3fa4f0bcd554","first_computed_at":"2026-07-04T14:34:23.162004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:34:23.162004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ouAm7lzGqLLDF/tah5HSaM9EAzB6pECG92i20OJLQxai+DSAaUwcLpg+i3Ei7mg+3hq68B6nejmXUYZUNu+OAw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:34:23.162403Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0002170","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f1bd1e9d54aa8dd3202e61ecdd2634aae9de49e452d0cb2e296378979d0d9d3","sha256:ca7620ac195dd8b7115375fea2ad04cfea5185212fb87ce151d318026a3af0d4"],"state_sha256":"70005ca70731a94e92db52a0769493863f8701a3309193f932f2390df44cba58"}