{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:OA4KZC3V4XKGD5YDFLGIVAS2HC","short_pith_number":"pith:OA4KZC3V","schema_version":"1.0","canonical_sha256":"7038ac8b75e5d461f7032acc8a825a388b3a658e3054e72a5c82e139b34137b7","source":{"kind":"arxiv","id":"2410.01037","version":4},"attestation_state":"computed","paper":{"title":"$g$-vectors and $DT$-$F$-polynomials for Grassmannians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Bernhard Keller, Sarjick Bakshi","submitted_at":"2024-10-01T19:54:52Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2410.01037","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-10-01T19:54:52Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"8a601e4f4cb6e69b23a2de27ef8470a407af99169d8b6d9571029b91ca0cc55c","abstract_canon_sha256":"cbb01fe70f4dddccd473915e9dff4b9424e02af22464ced0c9036a731e671fce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:04:05.180466Z","signature_b64":"KeJ6y9ozoJp0NexN2w0ZdkCDoURGBB56bJl+cfEKr66QLcBVo0ZbXjmnxxcCLuB9UoXI7eH+OOoqiE5OajVdCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7038ac8b75e5d461f7032acc8a825a388b3a658e3054e72a5c82e139b34137b7","last_reissued_at":"2026-05-20T00:04:05.179870Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:04:05.179870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$g$-vectors and $DT$-$F$-polynomials for Grassmannians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Bernhard Keller, Sarjick Bakshi","submitted_at":"2024-10-01T19:54:52Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.01037","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.01037/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2410.01037","created_at":"2026-05-20T00:04:05.179960+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.01037v4","created_at":"2026-05-20T00:04:05.179960+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.01037","created_at":"2026-05-20T00:04:05.179960+00:00"},{"alias_kind":"pith_short_12","alias_value":"OA4KZC3V4XKG","created_at":"2026-05-20T00:04:05.179960+00:00"},{"alias_kind":"pith_short_16","alias_value":"OA4KZC3V4XKGD5YD","created_at":"2026-05-20T00:04:05.179960+00:00"},{"alias_kind":"pith_short_8","alias_value":"OA4KZC3V","created_at":"2026-05-20T00:04:05.179960+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2410.01037","citing_title":"$g$-vectors and $DT$-$F$-polynomials for Grassmannians","ref_index":3,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OA4KZC3V4XKGD5YDFLGIVAS2HC","json":"https://pith.science/pith/OA4KZC3V4XKGD5YDFLGIVAS2HC.json","graph_json":"https://pith.science/api/pith-number/OA4KZC3V4XKGD5YDFLGIVAS2HC/graph.json","events_json":"https://pith.science/api/pith-number/OA4KZC3V4XKGD5YDFLGIVAS2HC/events.json","paper":"https://pith.science/paper/OA4KZC3V"},"agent_actions":{"view_html":"https://pith.science/pith/OA4KZC3V4XKGD5YDFLGIVAS2HC","download_json":"https://pith.science/pith/OA4KZC3V4XKGD5YDFLGIVAS2HC.json","view_paper":"https://pith.science/paper/OA4KZC3V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.01037&json=true","fetch_graph":"https://pith.science/api/pith-number/OA4KZC3V4XKGD5YDFLGIVAS2HC/graph.json","fetch_events":"https://pith.science/api/pith-number/OA4KZC3V4XKGD5YDFLGIVAS2HC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OA4KZC3V4XKGD5YDFLGIVAS2HC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OA4KZC3V4XKGD5YDFLGIVAS2HC/action/storage_attestation","attest_author":"https://pith.science/pith/OA4KZC3V4XKGD5YDFLGIVAS2HC/action/author_attestation","sign_citation":"https://pith.science/pith/OA4KZC3V4XKGD5YDFLGIVAS2HC/action/citation_signature","submit_replication":"https://pith.science/pith/OA4KZC3V4XKGD5YDFLGIVAS2HC/action/replication_record"}},"created_at":"2026-05-20T00:04:05.179960+00:00","updated_at":"2026-05-20T00:04:05.179960+00:00"}