{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:JS3HDAOJNDGZ2ENVFGLLVUN4XZ","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":"baf3d8c1ae0ba422f3424dea3ef72f9c35f762bc42db5d943213a5599e686f66","cross_cats_sorted":[],"license":"","primary_cat":"math.RT","submitted_at":"2006-05-23T18:39:35Z","title_canon_sha256":"0642df1a42776e08375cf8e670768aa9609cd54863a6f1db09b8cbf71c0ad71a"},"schema_version":"1.0","source":{"id":"math/0605628","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0605628","created_at":"2026-07-04T15:05:14Z"},{"alias_kind":"arxiv_version","alias_value":"math/0605628v3","created_at":"2026-07-04T15:05:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0605628","created_at":"2026-07-04T15:05:14Z"},{"alias_kind":"pith_short_12","alias_value":"JS3HDAOJNDGZ","created_at":"2026-07-04T15:05:14Z"},{"alias_kind":"pith_short_16","alias_value":"JS3HDAOJNDGZ2ENV","created_at":"2026-07-04T15:05:14Z"},{"alias_kind":"pith_short_8","alias_value":"JS3HDAOJ","created_at":"2026-07-04T15:05:14Z"}],"graph_snapshots":[{"event_id":"sha256:a60dd97671f120c1b6859f8e92930c716a50d385ad3d08428930048aa54b075e","target":"graph","created_at":"2026-07-04T15:05:14Z","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/0605628/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a weak version of Lusztig's conjecture on explicit description of the asymptotic Hecke algebras (both finite and affine), and explain its relation to Lusztig's classification of character sheaves.","authors_text":"Michael Finkelberg, Roman Bezrukavnikov, Victor Ostrik","cross_cats":[],"headline":"","license":"","primary_cat":"math.RT","submitted_at":"2006-05-23T18:39:35Z","title":"On tensor categories attached to cells in affine Weyl groups, III"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605628","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:fae405bab5963c4ccf0b7b2ce9f04d7360c1f4763d0fe0cb5c68d35096e3ddc7","target":"record","created_at":"2026-07-04T15:05:14Z","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":"baf3d8c1ae0ba422f3424dea3ef72f9c35f762bc42db5d943213a5599e686f66","cross_cats_sorted":[],"license":"","primary_cat":"math.RT","submitted_at":"2006-05-23T18:39:35Z","title_canon_sha256":"0642df1a42776e08375cf8e670768aa9609cd54863a6f1db09b8cbf71c0ad71a"},"schema_version":"1.0","source":{"id":"math/0605628","kind":"arxiv","version":3}},"canonical_sha256":"4cb67181c968cd9d11b52996bad1bcbe484092bfdc8c8e91783cff8fc2a56e9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4cb67181c968cd9d11b52996bad1bcbe484092bfdc8c8e91783cff8fc2a56e9c","first_computed_at":"2026-07-04T15:05:14.604899Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:05:14.604899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LAcc9OUF23LSECZgdoY1tduuBEIIZ66G88rhxssYDqBL8nzYGdHzGw1CXCbXnHgm36ut9sLIJeZDRDuh60prCA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:05:14.605228Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0605628","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fae405bab5963c4ccf0b7b2ce9f04d7360c1f4763d0fe0cb5c68d35096e3ddc7","sha256:a60dd97671f120c1b6859f8e92930c716a50d385ad3d08428930048aa54b075e"],"state_sha256":"5472883af8a471b01b6fd5d603bdb6657888081cf7051d945241d5101f6a5181"}