{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:E3VNGLPGT6R5ID3VOQMDGX7Y5J","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":"f511f9728441a8eef8b2945c11311a39d278ef62d081e42fd79d48825f4233f6","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-08-05T16:58:37Z","title_canon_sha256":"ed1827a6ad339964079a7b13be95ffaf2a998a199d0d50b322149cf363868f00"},"schema_version":"1.0","source":{"id":"2408.02633","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.02633","created_at":"2026-07-05T08:52:15Z"},{"alias_kind":"arxiv_version","alias_value":"2408.02633v1","created_at":"2026-07-05T08:52:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.02633","created_at":"2026-07-05T08:52:15Z"},{"alias_kind":"pith_short_12","alias_value":"E3VNGLPGT6R5","created_at":"2026-07-05T08:52:15Z"},{"alias_kind":"pith_short_16","alias_value":"E3VNGLPGT6R5ID3V","created_at":"2026-07-05T08:52:15Z"},{"alias_kind":"pith_short_8","alias_value":"E3VNGLPG","created_at":"2026-07-05T08:52:15Z"}],"graph_snapshots":[{"event_id":"sha256:9a0c7eb08fa8f63260d653fe8f7568c36409fe88f6f4aafe7b3e3b7ab11ee7be","target":"graph","created_at":"2026-07-05T08:52:15Z","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/2408.02633/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is about the positive part $U_q^+$ of the $q$-deformed enveloping algebra $U_q(\\widehat{\\mathfrak{sl}}_2)$. The algebra $U_q^+$ admits an embedding, due to Rosso, into a $q$-shuffle algebra $\\mathbb{V}$. The underlying vector space of $\\mathbb{V}$ is the free algebra on two generators $x,y$. Therefore, the algebra $\\mathbb{V}$ has a basis consisting of the words in $x,y$. Let $U$ denote the image of $U_q^+$ under the Rosso embedding. In our first main result, we find all the words in $x,y$ that are contained in $U$. One type of solution is called alternating. The alternating words h","authors_text":"Chenwei Ruan","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-08-05T16:58:37Z","title":"Doubly alternating words in the positive part of $U_q(\\widehat{\\mathfrak{sl}}_2)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.02633","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":"sha256:57f50f5a91e0194e815194db6583a792a4b9a917707f0d09abb08f8346319e34","target":"record","created_at":"2026-07-05T08:52:15Z","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":"f511f9728441a8eef8b2945c11311a39d278ef62d081e42fd79d48825f4233f6","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-08-05T16:58:37Z","title_canon_sha256":"ed1827a6ad339964079a7b13be95ffaf2a998a199d0d50b322149cf363868f00"},"schema_version":"1.0","source":{"id":"2408.02633","kind":"arxiv","version":1}},"canonical_sha256":"26ead32de69fa3d40f757418335ff8ea79020ef24b320d194d5f50f2b578477f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26ead32de69fa3d40f757418335ff8ea79020ef24b320d194d5f50f2b578477f","first_computed_at":"2026-07-05T08:52:15.541099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:52:15.541099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xor7WiR0dhD421+zUF4ZNH68hcjUZi4kbuvXcR3XrNQVowZcjwsImKX0Kn/eZuRfVphLriJijXAlF/TK+ehvDA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:52:15.541535Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.02633","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57f50f5a91e0194e815194db6583a792a4b9a917707f0d09abb08f8346319e34","sha256:9a0c7eb08fa8f63260d653fe8f7568c36409fe88f6f4aafe7b3e3b7ab11ee7be"],"state_sha256":"2354d1fd05154ded18543202af88841d90bd93139f2561aaa17eb3d45fdd428f"}