{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TNMN77YLCVV7M7VHMG7CGISFLU","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":"04bc7a58498be726d0355caab75e63268580208ee171c7d183493d42cce389cb","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-07-02T18:43:57Z","title_canon_sha256":"627309383141a304a44af38dae2e2715c5855e99fbbedbea926e9abf35e4562f"},"schema_version":"1.0","source":{"id":"2607.02701","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.02701","created_at":"2026-07-07T00:16:09Z"},{"alias_kind":"arxiv_version","alias_value":"2607.02701v1","created_at":"2026-07-07T00:16:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02701","created_at":"2026-07-07T00:16:09Z"},{"alias_kind":"pith_short_12","alias_value":"TNMN77YLCVV7","created_at":"2026-07-07T00:16:09Z"},{"alias_kind":"pith_short_16","alias_value":"TNMN77YLCVV7M7VH","created_at":"2026-07-07T00:16:09Z"},{"alias_kind":"pith_short_8","alias_value":"TNMN77YL","created_at":"2026-07-07T00:16:09Z"}],"graph_snapshots":[{"event_id":"sha256:5b12365a8f2e056742f5cc58105af127e659a482ada0ddb7ca43f26bcc13fdca","target":"graph","created_at":"2026-07-07T00:16:09Z","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/2607.02701/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present an embedded (in $G/B$) degeneration of Lusztig varieties (which generalize type $A$ Hessenberg varieties) to certain unions of Richardson varieties, giving a simultaneous reproof (and extension) of results of Anderson--Tymoczko, Harada--Horiguchi--Masuda--Park, and Kim. Although torus-equivariant, the degeneration is not Gr\\\"obner. In the case that the Lusztig variety is the permutahedral toric variety, this degeneration provides a subdivision of the permutahedron into Bruhat interval polytopes, and we prove a more general result showing equivariant degenerations of projective toric","authors_text":"Allen Knutson, Mario Sanchez, Melissa Sherman-Bennett","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-07-02T18:43:57Z","title":"Permutahedra, Lusztig varieties, degenerations, and subdivisions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02701","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:bfae45fb5ffeebb28d93a59a6c3e29a8d2804f7a2e3e96c8ea1d832156a88ff0","target":"record","created_at":"2026-07-07T00:16:09Z","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":"04bc7a58498be726d0355caab75e63268580208ee171c7d183493d42cce389cb","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-07-02T18:43:57Z","title_canon_sha256":"627309383141a304a44af38dae2e2715c5855e99fbbedbea926e9abf35e4562f"},"schema_version":"1.0","source":{"id":"2607.02701","kind":"arxiv","version":1}},"canonical_sha256":"9b58dfff0b156bf67ea761be2322455d0f550c67aadd1ffff8c6d2aa3ae7f9bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b58dfff0b156bf67ea761be2322455d0f550c67aadd1ffff8c6d2aa3ae7f9bb","first_computed_at":"2026-07-07T00:16:09.264634Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T00:16:09.264634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q99iYO8V3U1KmY1xZLO0ScDyxaQvC02VG75YEF976pzrQZCuGvOKUW1nn7f81lWYX4RhQN6a+2lBIz4t6JypBg==","signature_status":"signed_v1","signed_at":"2026-07-07T00:16:09.265289Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.02701","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfae45fb5ffeebb28d93a59a6c3e29a8d2804f7a2e3e96c8ea1d832156a88ff0","sha256:5b12365a8f2e056742f5cc58105af127e659a482ada0ddb7ca43f26bcc13fdca"],"state_sha256":"04f8936fe9acb27bcfeb318f152ee83435ded5815b0ff7ef0e938d91a95bd69d"}