{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HFL5XKTRJR6VZJAI7WSJA4OS36","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":"60a0affe32d18b615ce30b9c67f19956e26baec98684f409887ac190e09cf5cb","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-07-05T03:26:49Z","title_canon_sha256":"1e0939c24d72856d1bf6e28570292b2750707f270aa334c66e5b1d818ca53294"},"schema_version":"1.0","source":{"id":"1007.0611","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0611","created_at":"2026-05-18T03:58:38Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0611v2","created_at":"2026-05-18T03:58:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0611","created_at":"2026-05-18T03:58:38Z"},{"alias_kind":"pith_short_12","alias_value":"HFL5XKTRJR6V","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HFL5XKTRJR6VZJAI","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HFL5XKTR","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:43ea7d395a34649c6665d8d19a2481d21a675b7be1b8a124e78e1e93ff3cf3a9","target":"graph","created_at":"2026-05-18T03:58:38Z","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":"Springer varieties appear in both geometric representation theory and knot theory. Motivated by knot theory and categorification Khovanov provides a topological construction of $(n/2, n/2)$ Springer varieties. We extend Khovanov's construction to all two-row Springer varieties. Using the combinatorial and diagrammatic properties of this construction we provide a particularly useful homology basis and construct the Springer representation using this basis. We also provide a skein-theoretic formulation of the representation in this case.","authors_text":"Heather M. Russell","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-07-05T03:26:49Z","title":"A topological construction for all two-row Springer varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0611","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":"sha256:800ef9f5317a1fb3023d38c31e3b78bc5db358072439c72168dedaae6479675b","target":"record","created_at":"2026-05-18T03:58:38Z","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":"60a0affe32d18b615ce30b9c67f19956e26baec98684f409887ac190e09cf5cb","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-07-05T03:26:49Z","title_canon_sha256":"1e0939c24d72856d1bf6e28570292b2750707f270aa334c66e5b1d818ca53294"},"schema_version":"1.0","source":{"id":"1007.0611","kind":"arxiv","version":2}},"canonical_sha256":"3957dbaa714c7d5ca408fda49071d2df88cfdd2cbc8d972e4e8f46c78b38bea6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3957dbaa714c7d5ca408fda49071d2df88cfdd2cbc8d972e4e8f46c78b38bea6","first_computed_at":"2026-05-18T03:58:38.421115Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:38.421115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6f1O1u9GADhPG3gZELppl3keaPnUgtJZe6UDKantFGWc+7VezowI2AJLhEc4IQ7DDH/Dm9RWXZ7Vle++kz8ZDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:38.421577Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.0611","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:800ef9f5317a1fb3023d38c31e3b78bc5db358072439c72168dedaae6479675b","sha256:43ea7d395a34649c6665d8d19a2481d21a675b7be1b8a124e78e1e93ff3cf3a9"],"state_sha256":"c49a720afea1e466a9c7185959b808702a3641da464e6233a0db3c97d8e5b2c5"}