{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ISVLYEKX3AAYRV4TATXXRK62ZR","short_pith_number":"pith:ISVLYEKX","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"},"canonical_sha256":"44aabc1157d80188d79304ef78abdacc5e5e58329717943d29e54b809e1f74e6","source":{"kind":"arxiv","id":"1706.07839","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07839","created_at":"2026-05-18T00:29:13Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07839v2","created_at":"2026-05-18T00:29:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07839","created_at":"2026-05-18T00:29:13Z"},{"alias_kind":"pith_short_12","alias_value":"ISVLYEKX3AAY","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"ISVLYEKX3AAYRV4T","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"ISVLYEKX","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ISVLYEKX3AAYRV4TATXXRK62ZR","target":"record","payload":{"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"},"canonical_sha256":"44aabc1157d80188d79304ef78abdacc5e5e58329717943d29e54b809e1f74e6","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"},"source_kind":"arxiv","source_id":"1706.07839","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9394E1sUfgqK0j+SMQoLZPuQu2t0oV+UwlXcoQBjLTgH4QV/bHo0spRhWoe11D04gknVicdGcrVFdD7nn+z9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:05:53.602641Z"},"content_sha256":"3d0d62765700400800c5b7b1c8da5d3924010b02a3c2edc82a6a2b24c4bf4807","schema_version":"1.0","event_id":"sha256:3d0d62765700400800c5b7b1c8da5d3924010b02a3c2edc82a6a2b24c4bf4807"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ISVLYEKX3AAYRV4TATXXRK62ZR","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hvgfhXBCl14uWdw2bEEMP1pWW6m+n/VCAwJXnnMtO6QohGy1jS1JbHS5QrHL8ywm5sajpm+fOGVt4E6VuhkfDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:05:53.603017Z"},"content_sha256":"5ae19f3f0bde61a5ce191f44103962145f26580371f7322f3cfe4b5b8aecb070","schema_version":"1.0","event_id":"sha256:5ae19f3f0bde61a5ce191f44103962145f26580371f7322f3cfe4b5b8aecb070"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ISVLYEKX3AAYRV4TATXXRK62ZR/bundle.json","state_url":"https://pith.science/pith/ISVLYEKX3AAYRV4TATXXRK62ZR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ISVLYEKX3AAYRV4TATXXRK62ZR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T04:05:53Z","links":{"resolver":"https://pith.science/pith/ISVLYEKX3AAYRV4TATXXRK62ZR","bundle":"https://pith.science/pith/ISVLYEKX3AAYRV4TATXXRK62ZR/bundle.json","state":"https://pith.science/pith/ISVLYEKX3AAYRV4TATXXRK62ZR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ISVLYEKX3AAYRV4TATXXRK62ZR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ISVLYEKX3AAYRV4TATXXRK62ZR","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":"c637d931354db37e72f8a20b9a91eeb1faece14685f688b86bf741880652a543","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-23T19:14:03Z","title_canon_sha256":"b1296fe636a87e17ac04cf32adfd03e94ab37ca13a87d88e18f0eaf6d30f4b3f"},"schema_version":"1.0","source":{"id":"1706.07839","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07839","created_at":"2026-05-18T00:29:13Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07839v2","created_at":"2026-05-18T00:29:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07839","created_at":"2026-05-18T00:29:13Z"},{"alias_kind":"pith_short_12","alias_value":"ISVLYEKX3AAY","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"ISVLYEKX3AAYRV4T","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"ISVLYEKX","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:5ae19f3f0bde61a5ce191f44103962145f26580371f7322f3cfe4b5b8aecb070","target":"graph","created_at":"2026-05-18T00:29:13Z","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"},"paper":{"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.","authors_text":"Emilio A. Lauret, Fiorela Rossi Bertone","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-23T19:14:03Z","title":"Multiplicity formulas for fundamental strings of representations of classical Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07839","kind":"arxiv","version":2},"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":"sha256:3d0d62765700400800c5b7b1c8da5d3924010b02a3c2edc82a6a2b24c4bf4807","target":"record","created_at":"2026-05-18T00:29:13Z","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":"c637d931354db37e72f8a20b9a91eeb1faece14685f688b86bf741880652a543","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-23T19:14:03Z","title_canon_sha256":"b1296fe636a87e17ac04cf32adfd03e94ab37ca13a87d88e18f0eaf6d30f4b3f"},"schema_version":"1.0","source":{"id":"1706.07839","kind":"arxiv","version":2}},"canonical_sha256":"44aabc1157d80188d79304ef78abdacc5e5e58329717943d29e54b809e1f74e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44aabc1157d80188d79304ef78abdacc5e5e58329717943d29e54b809e1f74e6","first_computed_at":"2026-05-18T00:29:13.211941Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:13.211941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g6+xIGY8ulxnq5HZNN1Mk2RJu2XgTbVz0hMld0ZCgCdjvfFV4QKyJmjknJdM7otBXQSZoWytydjXwFMT8KHmAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:13.212282Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.07839","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d0d62765700400800c5b7b1c8da5d3924010b02a3c2edc82a6a2b24c4bf4807","sha256:5ae19f3f0bde61a5ce191f44103962145f26580371f7322f3cfe4b5b8aecb070"],"state_sha256":"58a8c832bf950110c68adc4ca42d8ab4a8fdefd5b68b56696557a3f6fbb66fd2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FdlJVuZeRPLNHu9FL1AeozKBXcVjLWtT0qYqYjflBW60z/lXIT1/Hq1zATik/sOsSlvHvavKfzJitPEuzZOLCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T04:05:53.605328Z","bundle_sha256":"45abc44d18ee2a1e4c416f321c73ba3b678e6806bf5b6863037b9e37e7eeec10"}}