{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:3HRURC473VWKNYCDGRRTT3DGLF","short_pith_number":"pith:3HRURC47","schema_version":"1.0","canonical_sha256":"d9e3488b9fdd6ca6e043346339ec665969c85a34b1e84e0c9832e695dbfb5653","source":{"kind":"arxiv","id":"2312.09986","version":2},"attestation_state":"computed","paper":{"title":"Computing the $q$-Multiplicity of the Positive Roots of $\\mathfrak{sl}_{r+1}(\\mathbb{C})$ and Products of Fibonacci Numbers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Kimberly J. Harry","submitted_at":"2023-12-15T17:58:26Z","abstract_excerpt":"Using Kostant's weight multiplicity formula, we describe and enumerate the terms contributing a nonzero value to the multiplicity of a positive root $\\mu$ in the adjoint representation of $\\mathfrak{sl}_{r+1}(\\mathbb{C})$, which we denote $L(\\tilde{\\alpha})$, where $\\tilde{\\alpha}$ is the highest root of $\\mathfrak{sl}_{r+1}(\\mathbb{C})$. We prove that the number of terms contributing a nonzero value in the multiplicity of the positive root $\\mu=\\alpha_i+\\alpha_{i+1}+\\cdots+\\alpha_j$ with $1\\leq i\\leq j\\leq r$ in $L(\\tilde{\\alpha})$ is given by the product $F_{i}\\cdot F_{r-j+1}$, where $F_n$ i"},"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":"2312.09986","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2023-12-15T17:58:26Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"86365c240ec9734bb3bbdfb6f93367a7ef01eccce105960caf82e20b992892a5","abstract_canon_sha256":"29b0532a459949e694902bd3652166a4997e30222f754d2e8a5b1f3821792a8f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:55:32.639864Z","signature_b64":"IkjIkg9YI7ZmTUj6TyjEMA2rj/Dn8cMrHRAM1pmFjvlqCWqKbIJpiHWifH7pOjgs5L3oLs+QsYA3CYO1t1rUBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9e3488b9fdd6ca6e043346339ec665969c85a34b1e84e0c9832e695dbfb5653","last_reissued_at":"2026-07-05T08:55:32.639425Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:55:32.639425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing the $q$-Multiplicity of the Positive Roots of $\\mathfrak{sl}_{r+1}(\\mathbb{C})$ and Products of Fibonacci Numbers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Kimberly J. Harry","submitted_at":"2023-12-15T17:58:26Z","abstract_excerpt":"Using Kostant's weight multiplicity formula, we describe and enumerate the terms contributing a nonzero value to the multiplicity of a positive root $\\mu$ in the adjoint representation of $\\mathfrak{sl}_{r+1}(\\mathbb{C})$, which we denote $L(\\tilde{\\alpha})$, where $\\tilde{\\alpha}$ is the highest root of $\\mathfrak{sl}_{r+1}(\\mathbb{C})$. We prove that the number of terms contributing a nonzero value in the multiplicity of the positive root $\\mu=\\alpha_i+\\alpha_{i+1}+\\cdots+\\alpha_j$ with $1\\leq i\\leq j\\leq r$ in $L(\\tilde{\\alpha})$ is given by the product $F_{i}\\cdot F_{r-j+1}$, where $F_n$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.09986","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.09986/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":"2312.09986","created_at":"2026-07-05T08:55:32.639480+00:00"},{"alias_kind":"arxiv_version","alias_value":"2312.09986v2","created_at":"2026-07-05T08:55:32.639480+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.09986","created_at":"2026-07-05T08:55:32.639480+00:00"},{"alias_kind":"pith_short_12","alias_value":"3HRURC473VWK","created_at":"2026-07-05T08:55:32.639480+00:00"},{"alias_kind":"pith_short_16","alias_value":"3HRURC473VWKNYCD","created_at":"2026-07-05T08:55:32.639480+00:00"},{"alias_kind":"pith_short_8","alias_value":"3HRURC47","created_at":"2026-07-05T08:55:32.639480+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/3HRURC473VWKNYCDGRRTT3DGLF","json":"https://pith.science/pith/3HRURC473VWKNYCDGRRTT3DGLF.json","graph_json":"https://pith.science/api/pith-number/3HRURC473VWKNYCDGRRTT3DGLF/graph.json","events_json":"https://pith.science/api/pith-number/3HRURC473VWKNYCDGRRTT3DGLF/events.json","paper":"https://pith.science/paper/3HRURC47"},"agent_actions":{"view_html":"https://pith.science/pith/3HRURC473VWKNYCDGRRTT3DGLF","download_json":"https://pith.science/pith/3HRURC473VWKNYCDGRRTT3DGLF.json","view_paper":"https://pith.science/paper/3HRURC47","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2312.09986&json=true","fetch_graph":"https://pith.science/api/pith-number/3HRURC473VWKNYCDGRRTT3DGLF/graph.json","fetch_events":"https://pith.science/api/pith-number/3HRURC473VWKNYCDGRRTT3DGLF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3HRURC473VWKNYCDGRRTT3DGLF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3HRURC473VWKNYCDGRRTT3DGLF/action/storage_attestation","attest_author":"https://pith.science/pith/3HRURC473VWKNYCDGRRTT3DGLF/action/author_attestation","sign_citation":"https://pith.science/pith/3HRURC473VWKNYCDGRRTT3DGLF/action/citation_signature","submit_replication":"https://pith.science/pith/3HRURC473VWKNYCDGRRTT3DGLF/action/replication_record"}},"created_at":"2026-07-05T08:55:32.639480+00:00","updated_at":"2026-07-05T08:55:32.639480+00:00"}