{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:LYK3FSMDZY4X52CV3RESKWVHH7","short_pith_number":"pith:LYK3FSMD","canonical_record":{"source":{"id":"1409.7554","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-26T12:28:06Z","cross_cats_sorted":[],"title_canon_sha256":"0b6539a57b317c2fe15784c29d20da1e2f5a52ddd10c11d37297b9a49b3001cf","abstract_canon_sha256":"66348e4cb980b2e8de3dfd5fd675079b4320416da91ca788fa876e533bd0358a"},"schema_version":"1.0"},"canonical_sha256":"5e15b2c983ce397ee855dc49255aa73fff4b979008c1aa3977e506600bb8a9fa","source":{"kind":"arxiv","id":"1409.7554","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7554","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7554v1","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7554","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"LYK3FSMDZY4X","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LYK3FSMDZY4X52CV","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LYK3FSMD","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:LYK3FSMDZY4X52CV3RESKWVHH7","target":"record","payload":{"canonical_record":{"source":{"id":"1409.7554","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-26T12:28:06Z","cross_cats_sorted":[],"title_canon_sha256":"0b6539a57b317c2fe15784c29d20da1e2f5a52ddd10c11d37297b9a49b3001cf","abstract_canon_sha256":"66348e4cb980b2e8de3dfd5fd675079b4320416da91ca788fa876e533bd0358a"},"schema_version":"1.0"},"canonical_sha256":"5e15b2c983ce397ee855dc49255aa73fff4b979008c1aa3977e506600bb8a9fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:52.434031Z","signature_b64":"cEuE9jWbPd+adfHM6rQT2OKWezQSuKYj8DLsuQMeXI6p94ba35m0lITZat/21iBscNHMdkPYCpfLCOVSomytDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e15b2c983ce397ee855dc49255aa73fff4b979008c1aa3977e506600bb8a9fa","last_reissued_at":"2026-05-18T02:41:52.433565Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:52.433565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.7554","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QwuPO5/gVlxkkY42WPsgWnZJah0JQuvFCqpUdpBbwhYVddFE04l10Ljl8fH9XN+kVy/o7MxDCz4YvZbeq6wqAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:08:30.808204Z"},"content_sha256":"3b3d2d05fb1e850de9299dcd9dfb3b5447833d7b28817b30ef126e1e4ecef862","schema_version":"1.0","event_id":"sha256:3b3d2d05fb1e850de9299dcd9dfb3b5447833d7b28817b30ef126e1e4ecef862"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:LYK3FSMDZY4X52CV3RESKWVHH7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On compositions associated to Frobenius parabolic and seaweed subalgebras of $\\mathrm{sl}_{n}(\\Bbbk )$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Michel Duflo, Rupert W.T. Yu","submitted_at":"2014-09-26T12:28:06Z","abstract_excerpt":"By using a free monoid of operators on the set of compositions (resp. pairs of compositions), we establish in this paper a bijective correspondence between Frobenius standard parabolic (resp. seaweed) subalgebras and certain elements of this monoid. We prove via this correspondence a conjecture of one of the authors on the number of Frobenius standard parabolic (resp. seaweed) subalgebras of $\\mathrm{sl}_{n}(\\Bbbk )$ associated to compositions (resp. pairs of compositions) with $n-t$ parts (resp. parts in total)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7554","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2eNXAGcjwkHZhQiMjB3wMQnQmyVBwYrVxEqsIeUPw5EqK30u+IFJJ0V+ny9vODPB0vj3cEkXX7y5wwv8p8lnBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:08:30.808818Z"},"content_sha256":"9a237c27630969242327ad1f9c74fe336d4f8bcfea22fd1c11a1fea4a0ac9285","schema_version":"1.0","event_id":"sha256:9a237c27630969242327ad1f9c74fe336d4f8bcfea22fd1c11a1fea4a0ac9285"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LYK3FSMDZY4X52CV3RESKWVHH7/bundle.json","state_url":"https://pith.science/pith/LYK3FSMDZY4X52CV3RESKWVHH7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LYK3FSMDZY4X52CV3RESKWVHH7/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":"2026-06-07T22:08:30Z","links":{"resolver":"https://pith.science/pith/LYK3FSMDZY4X52CV3RESKWVHH7","bundle":"https://pith.science/pith/LYK3FSMDZY4X52CV3RESKWVHH7/bundle.json","state":"https://pith.science/pith/LYK3FSMDZY4X52CV3RESKWVHH7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LYK3FSMDZY4X52CV3RESKWVHH7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LYK3FSMDZY4X52CV3RESKWVHH7","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":"66348e4cb980b2e8de3dfd5fd675079b4320416da91ca788fa876e533bd0358a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-26T12:28:06Z","title_canon_sha256":"0b6539a57b317c2fe15784c29d20da1e2f5a52ddd10c11d37297b9a49b3001cf"},"schema_version":"1.0","source":{"id":"1409.7554","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7554","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7554v1","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7554","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"LYK3FSMDZY4X","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LYK3FSMDZY4X52CV","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LYK3FSMD","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:9a237c27630969242327ad1f9c74fe336d4f8bcfea22fd1c11a1fea4a0ac9285","target":"graph","created_at":"2026-05-18T02:41:52Z","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":"By using a free monoid of operators on the set of compositions (resp. pairs of compositions), we establish in this paper a bijective correspondence between Frobenius standard parabolic (resp. seaweed) subalgebras and certain elements of this monoid. We prove via this correspondence a conjecture of one of the authors on the number of Frobenius standard parabolic (resp. seaweed) subalgebras of $\\mathrm{sl}_{n}(\\Bbbk )$ associated to compositions (resp. pairs of compositions) with $n-t$ parts (resp. parts in total).","authors_text":"Michel Duflo, Rupert W.T. Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-26T12:28:06Z","title":"On compositions associated to Frobenius parabolic and seaweed subalgebras of $\\mathrm{sl}_{n}(\\Bbbk )$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7554","kind":"arxiv","version":1},"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":"sha256:3b3d2d05fb1e850de9299dcd9dfb3b5447833d7b28817b30ef126e1e4ecef862","target":"record","created_at":"2026-05-18T02:41:52Z","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":"66348e4cb980b2e8de3dfd5fd675079b4320416da91ca788fa876e533bd0358a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-26T12:28:06Z","title_canon_sha256":"0b6539a57b317c2fe15784c29d20da1e2f5a52ddd10c11d37297b9a49b3001cf"},"schema_version":"1.0","source":{"id":"1409.7554","kind":"arxiv","version":1}},"canonical_sha256":"5e15b2c983ce397ee855dc49255aa73fff4b979008c1aa3977e506600bb8a9fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e15b2c983ce397ee855dc49255aa73fff4b979008c1aa3977e506600bb8a9fa","first_computed_at":"2026-05-18T02:41:52.433565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:52.433565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cEuE9jWbPd+adfHM6rQT2OKWezQSuKYj8DLsuQMeXI6p94ba35m0lITZat/21iBscNHMdkPYCpfLCOVSomytDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:52.434031Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.7554","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b3d2d05fb1e850de9299dcd9dfb3b5447833d7b28817b30ef126e1e4ecef862","sha256:9a237c27630969242327ad1f9c74fe336d4f8bcfea22fd1c11a1fea4a0ac9285"],"state_sha256":"ec47547c4de540e3240f631322c1cb1fb63f2b53ce319c6369d585e7400860fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eIXpaOR9uHqkKgzE7rSyYtX999F/pn+WbJh5sahUTkO9vMmsEp6gd8dtnk9+/38HUf8Z5Soaazns9AXR4369Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T22:08:30.812160Z","bundle_sha256":"54b80fb3ae64ab5eae6eddc7a0f3b03e7b61de8a9eed63c05ea215d834eb99df"}}