{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:OA4KZC3V4XKGD5YDFLGIVAS2HC","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":"cbb01fe70f4dddccd473915e9dff4b9424e02af22464ced0c9036a731e671fce","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-10-01T19:54:52Z","title_canon_sha256":"8a601e4f4cb6e69b23a2de27ef8470a407af99169d8b6d9571029b91ca0cc55c"},"schema_version":"1.0","source":{"id":"2410.01037","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.01037","created_at":"2026-05-20T00:04:05Z"},{"alias_kind":"arxiv_version","alias_value":"2410.01037v4","created_at":"2026-05-20T00:04:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.01037","created_at":"2026-05-20T00:04:05Z"},{"alias_kind":"pith_short_12","alias_value":"OA4KZC3V4XKG","created_at":"2026-05-20T00:04:05Z"},{"alias_kind":"pith_short_16","alias_value":"OA4KZC3V4XKGD5YD","created_at":"2026-05-20T00:04:05Z"},{"alias_kind":"pith_short_8","alias_value":"OA4KZC3V","created_at":"2026-05-20T00:04:05Z"}],"graph_snapshots":[{"event_id":"sha256:b3dc4bc11c795eb6d40bdce7918ec006f87547d6c7ebd6686ee4d48197440ade","target":"graph","created_at":"2026-05-20T00:04:05Z","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/2410.01037/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We review $\\mathrm{Hom}$-infinite Frobenius categorification of cluster algebras with coefficients and use it to give two applications of Jensen--King--Su's Frobenius categorification of the Grassmannian: 1) we determine the $g$-vectors of the Pl\\\"ucker coordinates with respect to the triangular initial seed and 2) we express the $F$-polynomials associated with the Donaldson--Thomas transformation in terms of $3$-dimensional Young diagrams thus providing a new proof for a theorem of Daping Weng.","authors_text":"Bernhard Keller, Sarjick Bakshi","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-10-01T19:54:52Z","title":"$g$-vectors and $DT$-$F$-polynomials for Grassmannians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.01037","kind":"arxiv","version":4},"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":"sha256:437176c76ed232abfa6035cb4d7a67d644d78cbc18000920a62637d6566d4cef","target":"record","created_at":"2026-05-20T00:04:05Z","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":"cbb01fe70f4dddccd473915e9dff4b9424e02af22464ced0c9036a731e671fce","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-10-01T19:54:52Z","title_canon_sha256":"8a601e4f4cb6e69b23a2de27ef8470a407af99169d8b6d9571029b91ca0cc55c"},"schema_version":"1.0","source":{"id":"2410.01037","kind":"arxiv","version":4}},"canonical_sha256":"7038ac8b75e5d461f7032acc8a825a388b3a658e3054e72a5c82e139b34137b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7038ac8b75e5d461f7032acc8a825a388b3a658e3054e72a5c82e139b34137b7","first_computed_at":"2026-05-20T00:04:05.179870Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:04:05.179870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KeJ6y9ozoJp0NexN2w0ZdkCDoURGBB56bJl+cfEKr66QLcBVo0ZbXjmnxxcCLuB9UoXI7eH+OOoqiE5OajVdCA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:04:05.180466Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.01037","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:437176c76ed232abfa6035cb4d7a67d644d78cbc18000920a62637d6566d4cef","sha256:b3dc4bc11c795eb6d40bdce7918ec006f87547d6c7ebd6686ee4d48197440ade"],"state_sha256":"e5d6d6f78d64b5a1ad501d28775fa1f62c077af08c78261992f0e2308b2e8311"}