{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:YTYPBYGEDFHXI6VOFWONQEQJRX","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":"4b22b78ec17fa434cf130c9cd92614fa980d5f3e5a1269c4ddd1e48ba5d09959","cross_cats_sorted":["math.AC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-10-03T01:39:53Z","title_canon_sha256":"9ce96757715657c2bae1c4770240e3211f1b1fa72146c5bbe28a517f17041442"},"schema_version":"1.0","source":{"id":"2410.02135","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.02135","created_at":"2026-06-29T00:13:59Z"},{"alias_kind":"arxiv_version","alias_value":"2410.02135v3","created_at":"2026-06-29T00:13:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.02135","created_at":"2026-06-29T00:13:59Z"},{"alias_kind":"pith_short_12","alias_value":"YTYPBYGEDFHX","created_at":"2026-06-29T00:13:59Z"},{"alias_kind":"pith_short_16","alias_value":"YTYPBYGEDFHXI6VO","created_at":"2026-06-29T00:13:59Z"},{"alias_kind":"pith_short_8","alias_value":"YTYPBYGE","created_at":"2026-06-29T00:13:59Z"}],"graph_snapshots":[{"event_id":"sha256:1b789e4aa2949b7de5fdca3feb24ea6bd295b7dba0f6d15b3d30fc6b5bc29dd6","target":"graph","created_at":"2026-06-29T00:13:59Z","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/2410.02135/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a criterion for a collection of polynomials to be a universal Gr\\\"{o}bner basis for an ideal in terms of the multidegree of the closure of the corresponding affine variety in $(\\mathbb{P}^1)^N$. This criterion can be used to give simple proofs of several existing results on universal Gr\\\"{o}bner bases. We introduce fine Schubert polynomials, which record the multidegrees of the closures of matrix Schubert varieties in $(\\mathbb{P}^1)^{n^2}$. We compute the fine Schubert polynomials of permutations $w$ where the coefficients of the Schubert polynomials of $w$ and $w^{-1}$ are all either","authors_text":"Daoji Huang, Matt Larson","cross_cats":["math.AC","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-10-03T01:39:53Z","title":"Fine multidegrees, universal Grobner bases, and matrix Schubert varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.02135","kind":"arxiv","version":3},"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":"sha256:717ab15cf83dbd71da07352bf66d63c290c046e27d1f077416e120d12d57d23a","target":"record","created_at":"2026-06-29T00:13:59Z","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":"4b22b78ec17fa434cf130c9cd92614fa980d5f3e5a1269c4ddd1e48ba5d09959","cross_cats_sorted":["math.AC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-10-03T01:39:53Z","title_canon_sha256":"9ce96757715657c2bae1c4770240e3211f1b1fa72146c5bbe28a517f17041442"},"schema_version":"1.0","source":{"id":"2410.02135","kind":"arxiv","version":3}},"canonical_sha256":"c4f0f0e0c4194f747aae2d9cd812098dd411a8b61b8105efe165e71bd9605cef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4f0f0e0c4194f747aae2d9cd812098dd411a8b61b8105efe165e71bd9605cef","first_computed_at":"2026-06-29T00:13:59.250975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-29T00:13:59.250975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7LxUcol45AmdGdicffnm13lqUef8wjy7qzH7Tg72lNqQ+E9ijqJqqtLEsBm/Hk8zvtv4wfsspp2FUAkq6/sKCw==","signature_status":"signed_v1","signed_at":"2026-06-29T00:13:59.251477Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.02135","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:717ab15cf83dbd71da07352bf66d63c290c046e27d1f077416e120d12d57d23a","sha256:1b789e4aa2949b7de5fdca3feb24ea6bd295b7dba0f6d15b3d30fc6b5bc29dd6"],"state_sha256":"a08a00cac1ec66709528d653c2d85feae5ce49a4e21e8e0cbe2c2d93997949d9"}