{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TWPEYDNAR7RSY5AMG6C7BPJWMB","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":"4df14099b0e6a6f0242ab782e04164eeb66aeccc88bc9441ea26e4bf6ed0dc2d","cross_cats_sorted":["math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-01-30T13:44:53Z","title_canon_sha256":"d6269c6735282260aad14d3760c2f8f0a26fd9c84a54c57d47a888201074c2b1"},"schema_version":"1.0","source":{"id":"1901.11020","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.11020","created_at":"2026-05-17T23:55:02Z"},{"alias_kind":"arxiv_version","alias_value":"1901.11020v1","created_at":"2026-05-17T23:55:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.11020","created_at":"2026-05-17T23:55:02Z"},{"alias_kind":"pith_short_12","alias_value":"TWPEYDNAR7RS","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"TWPEYDNAR7RSY5AM","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"TWPEYDNA","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:9c616015b04c243764fca18a67a8ff45d3a710b687b170353540109120427cc9","target":"graph","created_at":"2026-05-17T23:55:02Z","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 continue, generalize and expand our study of linear degenerations of flag varieties from [G. Cerulli Irelli, X. Fang, E. Feigin, G. Fourier, M. Reineke, Math. Z. 287 (2017), no. 1-2, 615-654]. We realize partial flag varieties as quiver Grassmannians for equi-oriented type A quivers and construct linear degenerations by varying the corresponding quiver representation. We prove that there exists the deepest flat degeneration and the deepest flat irreducible degeneration: the former is the partial analogue of the mf-degenerate flag variety and the latter coincides with the partial PBW-degener","authors_text":"Evgeny Feigin, Ghislain Fourier, Giovanni Cerulli Irelli, Markus Reineke, Xin Fang","cross_cats":["math.CO","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-01-30T13:44:53Z","title":"Linear degenerations of flag varieties: partial flags, defining equations, and group actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.11020","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:c7c7fd63b271480d07c74767db8c269f9cec892dc4d608a1603e87a8a362178b","target":"record","created_at":"2026-05-17T23:55:02Z","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":"4df14099b0e6a6f0242ab782e04164eeb66aeccc88bc9441ea26e4bf6ed0dc2d","cross_cats_sorted":["math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-01-30T13:44:53Z","title_canon_sha256":"d6269c6735282260aad14d3760c2f8f0a26fd9c84a54c57d47a888201074c2b1"},"schema_version":"1.0","source":{"id":"1901.11020","kind":"arxiv","version":1}},"canonical_sha256":"9d9e4c0da08fe32c740c3785f0bd3660708e2d78998132cbd123afddca35deb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d9e4c0da08fe32c740c3785f0bd3660708e2d78998132cbd123afddca35deb2","first_computed_at":"2026-05-17T23:55:02.802296Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:02.802296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p7X5/+C5Dxecp3U4ihtveziwv81JumlGR01plHQWn+5OTU1xoKD5TFf4xFDxHFiHI7kQ1h1SIZUVLgiC8LInDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:02.803019Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.11020","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7c7fd63b271480d07c74767db8c269f9cec892dc4d608a1603e87a8a362178b","sha256:9c616015b04c243764fca18a67a8ff45d3a710b687b170353540109120427cc9"],"state_sha256":"fe0aa6eac609f0acee94dfc1c85fa3c9eee0864e5c68138241b36e3f1d4555ee"}