{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ISVLYEKX3AAYRV4TATXXRK62ZR","short_pith_number":"pith:ISVLYEKX","schema_version":"1.0","canonical_sha256":"44aabc1157d80188d79304ef78abdacc5e5e58329717943d29e54b809e1f74e6","source":{"kind":"arxiv","id":"1706.07839","version":2},"attestation_state":"computed","paper":{"title":"Multiplicity formulas for fundamental strings of representations of classical Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Emilio A. Lauret, Fiorela Rossi Bertone","submitted_at":"2017-06-23T19:14:03Z","abstract_excerpt":"We call the \\emph{$p$-fundamental string} of a complex simple Lie algebra to the sequence of irreducible representations having highest weights of the form $k\\omega_1+\\omega_p$ for $k\\geq0$, where $\\omega_j$ denotes the $j$-th fundamental weight of the associated root system. For a classical complex Lie algebra, we establish a closed explicit formula for the weight multiplicities of any representation in any $p$-fundamental string."},"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":"1706.07839","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-23T19:14:03Z","cross_cats_sorted":[],"title_canon_sha256":"b1296fe636a87e17ac04cf32adfd03e94ab37ca13a87d88e18f0eaf6d30f4b3f","abstract_canon_sha256":"c637d931354db37e72f8a20b9a91eeb1faece14685f688b86bf741880652a543"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:13.212282Z","signature_b64":"g6+xIGY8ulxnq5HZNN1Mk2RJu2XgTbVz0hMld0ZCgCdjvfFV4QKyJmjknJdM7otBXQSZoWytydjXwFMT8KHmAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44aabc1157d80188d79304ef78abdacc5e5e58329717943d29e54b809e1f74e6","last_reissued_at":"2026-05-18T00:29:13.211941Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:13.211941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiplicity formulas for fundamental strings of representations of classical Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Emilio A. Lauret, Fiorela Rossi Bertone","submitted_at":"2017-06-23T19:14:03Z","abstract_excerpt":"We call the \\emph{$p$-fundamental string} of a complex simple Lie algebra to the sequence of irreducible representations having highest weights of the form $k\\omega_1+\\omega_p$ for $k\\geq0$, where $\\omega_j$ denotes the $j$-th fundamental weight of the associated root system. For a classical complex Lie algebra, we establish a closed explicit formula for the weight multiplicities of any representation in any $p$-fundamental string."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07839","kind":"arxiv","version":2},"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":"1706.07839","created_at":"2026-05-18T00:29:13.211995+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.07839v2","created_at":"2026-05-18T00:29:13.211995+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07839","created_at":"2026-05-18T00:29:13.211995+00:00"},{"alias_kind":"pith_short_12","alias_value":"ISVLYEKX3AAY","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"ISVLYEKX3AAYRV4T","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"ISVLYEKX","created_at":"2026-05-18T12:31:21.493067+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/ISVLYEKX3AAYRV4TATXXRK62ZR","json":"https://pith.science/pith/ISVLYEKX3AAYRV4TATXXRK62ZR.json","graph_json":"https://pith.science/api/pith-number/ISVLYEKX3AAYRV4TATXXRK62ZR/graph.json","events_json":"https://pith.science/api/pith-number/ISVLYEKX3AAYRV4TATXXRK62ZR/events.json","paper":"https://pith.science/paper/ISVLYEKX"},"agent_actions":{"view_html":"https://pith.science/pith/ISVLYEKX3AAYRV4TATXXRK62ZR","download_json":"https://pith.science/pith/ISVLYEKX3AAYRV4TATXXRK62ZR.json","view_paper":"https://pith.science/paper/ISVLYEKX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.07839&json=true","fetch_graph":"https://pith.science/api/pith-number/ISVLYEKX3AAYRV4TATXXRK62ZR/graph.json","fetch_events":"https://pith.science/api/pith-number/ISVLYEKX3AAYRV4TATXXRK62ZR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ISVLYEKX3AAYRV4TATXXRK62ZR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ISVLYEKX3AAYRV4TATXXRK62ZR/action/storage_attestation","attest_author":"https://pith.science/pith/ISVLYEKX3AAYRV4TATXXRK62ZR/action/author_attestation","sign_citation":"https://pith.science/pith/ISVLYEKX3AAYRV4TATXXRK62ZR/action/citation_signature","submit_replication":"https://pith.science/pith/ISVLYEKX3AAYRV4TATXXRK62ZR/action/replication_record"}},"created_at":"2026-05-18T00:29:13.211995+00:00","updated_at":"2026-05-18T00:29:13.211995+00:00"}