{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:TINXLQHQLIYJQGOU4NVZGF3OP7","short_pith_number":"pith:TINXLQHQ","schema_version":"1.0","canonical_sha256":"9a1b75c0f05a309819d4e36b93176e7fe899ea5f44f466853bd5c7dbdb193738","source":{"kind":"arxiv","id":"2606.00421","version":1},"attestation_state":"computed","paper":{"title":"Kleshchev multipartitions, affine Mirkovi\\'c-Vilonen polytopes, and representations of KLR algebras in type ${\\tt A}^{(1)}_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Bella Deborah Uwase, Corinne Moscariello, Jack Isaac, Lucas Walton, Robert Muth, Samantha Allen","submitted_at":"2026-05-29T23:16:06Z","abstract_excerpt":"We construct explicit isomorphisms between three models for the $B(\\infty)$ crystal in type ${\\tt A}_1^{(1)}$: affine Mirkovi\\'c--Vilonen polytopes, Kleshchev multipartitions, and a new model we call upper ledge diagrams. We also present some clarifying results on these crystals, giving a direct method for completing an affine MV polytope from the data of one of its boundary root partitions, and a non-iterative recognition theorem which characterizes Kleshchev multipartitions in type ${\\tt A}_1^{(1)}$. We apply these results to the representation theory of KLR algebras, where they yield a comb"},"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":"2606.00421","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-05-29T23:16:06Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"72275a35d31e1b70b252179c7d56d73d19efb32638014a3d00310143ead30c8c","abstract_canon_sha256":"016ad44c3fae3a90e8c1576e3fb526ab58c1da7ba77826db9b1791c2a753b173"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:03:54.107457Z","signature_b64":"1VwL7hsVV+wfWAc2Xw8XXKfqxUOiEldxNIowjtVj47BPauzN6a2fARz19xnnMpAaBwoOFqzSXP82nHzWQ8gLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a1b75c0f05a309819d4e36b93176e7fe899ea5f44f466853bd5c7dbdb193738","last_reissued_at":"2026-06-02T01:03:54.107034Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:03:54.107034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kleshchev multipartitions, affine Mirkovi\\'c-Vilonen polytopes, and representations of KLR algebras in type ${\\tt A}^{(1)}_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Bella Deborah Uwase, Corinne Moscariello, Jack Isaac, Lucas Walton, Robert Muth, Samantha Allen","submitted_at":"2026-05-29T23:16:06Z","abstract_excerpt":"We construct explicit isomorphisms between three models for the $B(\\infty)$ crystal in type ${\\tt A}_1^{(1)}$: affine Mirkovi\\'c--Vilonen polytopes, Kleshchev multipartitions, and a new model we call upper ledge diagrams. We also present some clarifying results on these crystals, giving a direct method for completing an affine MV polytope from the data of one of its boundary root partitions, and a non-iterative recognition theorem which characterizes Kleshchev multipartitions in type ${\\tt A}_1^{(1)}$. We apply these results to the representation theory of KLR algebras, where they yield a comb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00421","kind":"arxiv","version":1},"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/2606.00421/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":"2606.00421","created_at":"2026-06-02T01:03:54.107088+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.00421v1","created_at":"2026-06-02T01:03:54.107088+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00421","created_at":"2026-06-02T01:03:54.107088+00:00"},{"alias_kind":"pith_short_12","alias_value":"TINXLQHQLIYJ","created_at":"2026-06-02T01:03:54.107088+00:00"},{"alias_kind":"pith_short_16","alias_value":"TINXLQHQLIYJQGOU","created_at":"2026-06-02T01:03:54.107088+00:00"},{"alias_kind":"pith_short_8","alias_value":"TINXLQHQ","created_at":"2026-06-02T01:03:54.107088+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TINXLQHQLIYJQGOU4NVZGF3OP7","json":"https://pith.science/pith/TINXLQHQLIYJQGOU4NVZGF3OP7.json","graph_json":"https://pith.science/api/pith-number/TINXLQHQLIYJQGOU4NVZGF3OP7/graph.json","events_json":"https://pith.science/api/pith-number/TINXLQHQLIYJQGOU4NVZGF3OP7/events.json","paper":"https://pith.science/paper/TINXLQHQ"},"agent_actions":{"view_html":"https://pith.science/pith/TINXLQHQLIYJQGOU4NVZGF3OP7","download_json":"https://pith.science/pith/TINXLQHQLIYJQGOU4NVZGF3OP7.json","view_paper":"https://pith.science/paper/TINXLQHQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.00421&json=true","fetch_graph":"https://pith.science/api/pith-number/TINXLQHQLIYJQGOU4NVZGF3OP7/graph.json","fetch_events":"https://pith.science/api/pith-number/TINXLQHQLIYJQGOU4NVZGF3OP7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TINXLQHQLIYJQGOU4NVZGF3OP7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TINXLQHQLIYJQGOU4NVZGF3OP7/action/storage_attestation","attest_author":"https://pith.science/pith/TINXLQHQLIYJQGOU4NVZGF3OP7/action/author_attestation","sign_citation":"https://pith.science/pith/TINXLQHQLIYJQGOU4NVZGF3OP7/action/citation_signature","submit_replication":"https://pith.science/pith/TINXLQHQLIYJQGOU4NVZGF3OP7/action/replication_record"}},"created_at":"2026-06-02T01:03:54.107088+00:00","updated_at":"2026-06-02T01:03:54.107088+00:00"}