{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:HNBHOEJYYQXRZX5IBHG2WHIDIN","short_pith_number":"pith:HNBHOEJY","schema_version":"1.0","canonical_sha256":"3b42771138c42f1cdfa809cdab1d03436ef4d6adc3ccbedbcc020c715c97b13a","source":{"kind":"arxiv","id":"1210.6464","version":1},"attestation_state":"computed","paper":{"title":"R\\'eflexions dans un cristal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Joel Kamnitzer, Pierre Baumann, St\\'ephane Gaussent","submitted_at":"2012-10-24T09:04:20Z","abstract_excerpt":"Let g = n^- + h + n^+ be a symmetrizable Kac-Moody algebra. Let B(\\infty) be the Kashiwara crystal of U_q(n^-), let \\lambda be a dominant integral weight, let T_\\lambda = {t_\\lambda} be the crystal with one element of weight \\lambda, and let B(\\lambda) \\subset B(\\infty) \\otimes T_\\lambda be the crystal of the integrable representation of highest weight \\lambda. We compute the descending string parameters of an element b \\otimes t_\\lambda in B(\\lambda) in terms of the Lusztig parameters of b."},"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":"1210.6464","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-24T09:04:20Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"a6941551814a4a8c59f31667109063f273a7af2811cdc934f67a91d0ea3cff3a","abstract_canon_sha256":"cec6d1d27c3950a0153d93dbd3d649748e95fb2f0e7699b00e87d07916c72b72"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:24.766633Z","signature_b64":"AL9RXcjclGIZwP1F51Ju23GpDW20P48EQrWeHLaedgQEHp5HIHJTzrGLrcAsuBuBWBmDeG/IJEqYTTD+/glnDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b42771138c42f1cdfa809cdab1d03436ef4d6adc3ccbedbcc020c715c97b13a","last_reissued_at":"2026-05-18T03:42:24.765746Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:24.765746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"R\\'eflexions dans un cristal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Joel Kamnitzer, Pierre Baumann, St\\'ephane Gaussent","submitted_at":"2012-10-24T09:04:20Z","abstract_excerpt":"Let g = n^- + h + n^+ be a symmetrizable Kac-Moody algebra. Let B(\\infty) be the Kashiwara crystal of U_q(n^-), let \\lambda be a dominant integral weight, let T_\\lambda = {t_\\lambda} be the crystal with one element of weight \\lambda, and let B(\\lambda) \\subset B(\\infty) \\otimes T_\\lambda be the crystal of the integrable representation of highest weight \\lambda. We compute the descending string parameters of an element b \\otimes t_\\lambda in B(\\lambda) in terms of the Lusztig parameters of b."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6464","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":""},"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":"1210.6464","created_at":"2026-05-18T03:42:24.765886+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.6464v1","created_at":"2026-05-18T03:42:24.765886+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6464","created_at":"2026-05-18T03:42:24.765886+00:00"},{"alias_kind":"pith_short_12","alias_value":"HNBHOEJYYQXR","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"HNBHOEJYYQXRZX5I","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"HNBHOEJY","created_at":"2026-05-18T12:27:09.501522+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/HNBHOEJYYQXRZX5IBHG2WHIDIN","json":"https://pith.science/pith/HNBHOEJYYQXRZX5IBHG2WHIDIN.json","graph_json":"https://pith.science/api/pith-number/HNBHOEJYYQXRZX5IBHG2WHIDIN/graph.json","events_json":"https://pith.science/api/pith-number/HNBHOEJYYQXRZX5IBHG2WHIDIN/events.json","paper":"https://pith.science/paper/HNBHOEJY"},"agent_actions":{"view_html":"https://pith.science/pith/HNBHOEJYYQXRZX5IBHG2WHIDIN","download_json":"https://pith.science/pith/HNBHOEJYYQXRZX5IBHG2WHIDIN.json","view_paper":"https://pith.science/paper/HNBHOEJY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.6464&json=true","fetch_graph":"https://pith.science/api/pith-number/HNBHOEJYYQXRZX5IBHG2WHIDIN/graph.json","fetch_events":"https://pith.science/api/pith-number/HNBHOEJYYQXRZX5IBHG2WHIDIN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HNBHOEJYYQXRZX5IBHG2WHIDIN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HNBHOEJYYQXRZX5IBHG2WHIDIN/action/storage_attestation","attest_author":"https://pith.science/pith/HNBHOEJYYQXRZX5IBHG2WHIDIN/action/author_attestation","sign_citation":"https://pith.science/pith/HNBHOEJYYQXRZX5IBHG2WHIDIN/action/citation_signature","submit_replication":"https://pith.science/pith/HNBHOEJYYQXRZX5IBHG2WHIDIN/action/replication_record"}},"created_at":"2026-05-18T03:42:24.765886+00:00","updated_at":"2026-05-18T03:42:24.765886+00:00"}