{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XOROX3D46P65TODD25CRJA6IRL","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":"b4abe084141323e30a86fda6c57c3aa12fcf9a18d4a753630daf6bf878b007e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-12T20:57:18Z","title_canon_sha256":"728610071cb9eadf395229ad90df37bcfecffb90a363fb135e0aa586ec85fc43"},"schema_version":"1.0","source":{"id":"1701.03502","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.03502","created_at":"2026-05-18T00:03:37Z"},{"alias_kind":"arxiv_version","alias_value":"1701.03502v2","created_at":"2026-05-18T00:03:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.03502","created_at":"2026-05-18T00:03:37Z"},{"alias_kind":"pith_short_12","alias_value":"XOROX3D46P65","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XOROX3D46P65TODD","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XOROX3D4","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:ce9f0f1febabc080fdc7fd0a26bde326afa590ecc334d0a69d67551a6c75ce46","target":"graph","created_at":"2026-05-18T00:03:37Z","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 fibers are subvarieties of the flag variety parametrized by partitions; they are central objects of study in geometric representation theory. Schubert varieties are subvarieties of the flag variety that induce a well-known basis for the cohomology of the flag variety. This paper relates these two varieties combinatorially. We prove that the Betti numbers of the Springer fiber associated to a partition with at most three rows or two columns are equal to the Betti numbers of a specific union of Schubert varieties.","authors_text":"Julianna Tymoczko, Martha Precup","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-12T20:57:18Z","title":"Springer fibers and Schubert points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03502","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":"sha256:893e5c70fc9896e6053b8f27ef8565936e22ccd4d0239de298e528309c9e5e6d","target":"record","created_at":"2026-05-18T00:03:37Z","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":"b4abe084141323e30a86fda6c57c3aa12fcf9a18d4a753630daf6bf878b007e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-12T20:57:18Z","title_canon_sha256":"728610071cb9eadf395229ad90df37bcfecffb90a363fb135e0aa586ec85fc43"},"schema_version":"1.0","source":{"id":"1701.03502","kind":"arxiv","version":2}},"canonical_sha256":"bba2ebec7cf3fdd9b863d7451483c88aeb9596f2a7f51ed6fa2db78462bbd1bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bba2ebec7cf3fdd9b863d7451483c88aeb9596f2a7f51ed6fa2db78462bbd1bc","first_computed_at":"2026-05-18T00:03:37.429919Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:37.429919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Br+McFfOg/DUeIhHkYF2Kr++ykeqFgsymhmJDjDq6d0qqQDL60Y2V9sVm8qgMM7LAmwYbm2A/byDOSuNhziEBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:37.430417Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.03502","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:893e5c70fc9896e6053b8f27ef8565936e22ccd4d0239de298e528309c9e5e6d","sha256:ce9f0f1febabc080fdc7fd0a26bde326afa590ecc334d0a69d67551a6c75ce46"],"state_sha256":"9ffd04f746cd08d03b07909d13b917f929c67ffad74b8cbcf0de994c8786a210"}