{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:SPDTU5JOAXYAVCWSKGCRWU5GIA","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":"9265314547ed4eeccf45c52ac6a7bfbcedf9bfaa75746163100075c5c723c999","cross_cats_sorted":["math.AG","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2021-08-19T16:40:21Z","title_canon_sha256":"cfd13f8fa2cc5484ceb4229e8f80c154247468a903fa108d57a86de15cf355ad"},"schema_version":"1.0","source":{"id":"2108.08779","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.08779","created_at":"2026-07-05T05:20:08Z"},{"alias_kind":"arxiv_version","alias_value":"2108.08779v5","created_at":"2026-07-05T05:20:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.08779","created_at":"2026-07-05T05:20:08Z"},{"alias_kind":"pith_short_12","alias_value":"SPDTU5JOAXYA","created_at":"2026-07-05T05:20:08Z"},{"alias_kind":"pith_short_16","alias_value":"SPDTU5JOAXYAVCWS","created_at":"2026-07-05T05:20:08Z"},{"alias_kind":"pith_short_8","alias_value":"SPDTU5JO","created_at":"2026-07-05T05:20:08Z"}],"graph_snapshots":[{"event_id":"sha256:2e45016909c7007885fd2689ab0015b01f21daff64190b64cb76c2affcd5fd8a","target":"graph","created_at":"2026-07-05T05:20:08Z","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/2108.08779/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the shuffle algebra associated to a doubled quiver (determined by 3-variable wheel conditions) is generated by elements of minimal degree. Together with results of Varagnolo-Vasserot and Yu Zhao, this implies that the aforementioned shuffle algebra is isomorphic to the localized K-theoretic Hall algebra associated to the quiver by Schiffmann-Vasserot. With small modifications, our theorems also hold under certain specializations of the equivariant parameters, which will allow us in Negu\\c{t}-Sala-Schiffmann to give a generators-and-relations description of the Hall algebra of any ","authors_text":"Andrei Negu\\c{t}","cross_cats":["math.AG","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2021-08-19T16:40:21Z","title":"Shuffle algebras for quivers and wheel conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.08779","kind":"arxiv","version":5},"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:c92e54f6ab2e0d7b0537c05f1754f74eb4d8fe78428ca5120368eff2faecf33c","target":"record","created_at":"2026-07-05T05:20:08Z","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":"9265314547ed4eeccf45c52ac6a7bfbcedf9bfaa75746163100075c5c723c999","cross_cats_sorted":["math.AG","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2021-08-19T16:40:21Z","title_canon_sha256":"cfd13f8fa2cc5484ceb4229e8f80c154247468a903fa108d57a86de15cf355ad"},"schema_version":"1.0","source":{"id":"2108.08779","kind":"arxiv","version":5}},"canonical_sha256":"93c73a752e05f00a8ad251851b53a640046bc1a1d9a13dd18f2edad701db9ded","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93c73a752e05f00a8ad251851b53a640046bc1a1d9a13dd18f2edad701db9ded","first_computed_at":"2026-07-05T05:20:08.237788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:20:08.237788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9GuHtFoTrKvABX4PwyJSjIJR1fISNDUjh3hz5QmHXKx9Emggip4ILj8cgi8rNs4jz9XD7hFxZN13wz5i1PTKAg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:20:08.238367Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.08779","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c92e54f6ab2e0d7b0537c05f1754f74eb4d8fe78428ca5120368eff2faecf33c","sha256:2e45016909c7007885fd2689ab0015b01f21daff64190b64cb76c2affcd5fd8a"],"state_sha256":"d22609373d90b73afe69a8821b6056b4c4c67d01bb42bbdf186994f7f329ad79"}