{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZTD7EMUJVON7277T625ZCD5ZSZ","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":"2b23a06677aa81d6053bea7acd5d88e4ba9da1204c16a412b748e91644100fe2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-21T22:53:06Z","title_canon_sha256":"03f099e3ddfb9b63deefab210c725eb103ec95e4c0b6bfa096eb502a0f9d1e4b"},"schema_version":"1.0","source":{"id":"1407.5685","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5685","created_at":"2026-05-18T01:20:22Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5685v2","created_at":"2026-05-18T01:20:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5685","created_at":"2026-05-18T01:20:22Z"},{"alias_kind":"pith_short_12","alias_value":"ZTD7EMUJVON7","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZTD7EMUJVON7277T","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZTD7EMUJ","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:fbc8970fe720a7aaac62e17b6f519f7316a311335c7ec8be8e70a07116bde540","target":"graph","created_at":"2026-05-18T01:20:22Z","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 provide geometric constructions of modules over the graded Cherednik algebra $\\mathfrak{H}^{gr}_\\nu$ and the rational Cherednik algebra $\\mathfrak{H}^{rat}_\\nu$ attached to a simple algebraic group $\\mathbb{G}$ together with a pinned automorphism $\\theta$. These modules are realized on the cohomology of affine Springer fibers (of finite type) that admit $\\mathbb{C}^*$-actions. In the rational Cherednik algebra case, the standard grading on these modules is derived from the perverse filtration on the cohomology of affine Springer fibers coming from its global analog: Hitchin fibers. When $\\t","authors_text":"Alexei Oblomkov, Zhiwei Yun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-21T22:53:06Z","title":"Geometric representations of graded and rational Cherednik algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5685","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":"sha256:183b693ad554ab05da3ff3a6e73ca113a1944b992ac789d1d5b86d91091dd8bf","target":"record","created_at":"2026-05-18T01:20:22Z","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":"2b23a06677aa81d6053bea7acd5d88e4ba9da1204c16a412b748e91644100fe2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-21T22:53:06Z","title_canon_sha256":"03f099e3ddfb9b63deefab210c725eb103ec95e4c0b6bfa096eb502a0f9d1e4b"},"schema_version":"1.0","source":{"id":"1407.5685","kind":"arxiv","version":2}},"canonical_sha256":"ccc7f23289ab9bfd7ff3f6bb910fb99652c123c370144b693c5805dadd80a50d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccc7f23289ab9bfd7ff3f6bb910fb99652c123c370144b693c5805dadd80a50d","first_computed_at":"2026-05-18T01:20:22.371217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:22.371217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gxoLw3HreE2O+5qaxqVZuHRYbh1VCaPujaJ/loO81Hwy1rOi8kiUn8ip+hfZkAVr6S7qjrjVgiti0NKhhkOGCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:22.371747Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.5685","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:183b693ad554ab05da3ff3a6e73ca113a1944b992ac789d1d5b86d91091dd8bf","sha256:fbc8970fe720a7aaac62e17b6f519f7316a311335c7ec8be8e70a07116bde540"],"state_sha256":"95f465903c5dc7e6187d7f0f819386abcc716b4c11f53288e96480260388324d"}