{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:JZHZZEA7V3UWRSYPWTDSWPCRU2","short_pith_number":"pith:JZHZZEA7","canonical_record":{"source":{"id":"1109.1489","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-07T15:29:27Z","cross_cats_sorted":[],"title_canon_sha256":"281b729484f19e41d3fb204509e4b7f0986c1b903a137303dcaf44186e47f6d2","abstract_canon_sha256":"6486808da2633979f3dd73b5600d57f3324120ee61f6ef5ee11edf1e02f2eb69"},"schema_version":"1.0"},"canonical_sha256":"4e4f9c901faee968cb0fb4c72b3c51a681fcc447be852fd3e4e8b4127834754f","source":{"kind":"arxiv","id":"1109.1489","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1489","created_at":"2026-05-18T04:13:55Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1489v1","created_at":"2026-05-18T04:13:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1489","created_at":"2026-05-18T04:13:55Z"},{"alias_kind":"pith_short_12","alias_value":"JZHZZEA7V3UW","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JZHZZEA7V3UWRSYP","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JZHZZEA7","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:JZHZZEA7V3UWRSYPWTDSWPCRU2","target":"record","payload":{"canonical_record":{"source":{"id":"1109.1489","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-07T15:29:27Z","cross_cats_sorted":[],"title_canon_sha256":"281b729484f19e41d3fb204509e4b7f0986c1b903a137303dcaf44186e47f6d2","abstract_canon_sha256":"6486808da2633979f3dd73b5600d57f3324120ee61f6ef5ee11edf1e02f2eb69"},"schema_version":"1.0"},"canonical_sha256":"4e4f9c901faee968cb0fb4c72b3c51a681fcc447be852fd3e4e8b4127834754f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:55.591113Z","signature_b64":"qZMVBgg27+kh8yHshh8qKt7ULx4jKg/zJNScTUE2fdYOd+dEVJ8efPXN87GAKqQRjRkV9WAsV1I41FgP7Z8CDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e4f9c901faee968cb0fb4c72b3c51a681fcc447be852fd3e4e8b4127834754f","last_reissued_at":"2026-05-18T04:13:55.590709Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:55.590709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.1489","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":"2026-05-18T04:13:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"he5dRGtKwHI3VxWjlCrQ1vLAh6pt77fe+yCiGpiRmnHDpdAVCNXA7Ujk1S0MweEjCqz4/b1feHGsTbBpQA4pAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:14:00.502933Z"},"content_sha256":"78feb6903f7c7f495c0839365471640c04a23d16cef0e174f68b42d7938727b9","schema_version":"1.0","event_id":"sha256:78feb6903f7c7f495c0839365471640c04a23d16cef0e174f68b42d7938727b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:JZHZZEA7V3UWRSYPWTDSWPCRU2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A semisimple series for $q$-Weyl and $q$-Specht modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Brian Parshall, Leonard Scott","submitted_at":"2011-09-07T15:29:27Z","abstract_excerpt":"In a previous paper, the authors studied the radical filtration of a Weyl module $\\Delta_\\zeta(\\lambda)$ for quantum enveloping algebras $U_\\zeta(\\overset\\circ{\\mathfrak g})$ associated to a finite dimensional complex semisimple Lie algebra $\\overset\\circ{\\mathfrak g}$. There $\\zeta^2=\\sqrt[e]{1}$ and $\\lambda$ was, initially, required to be $e$-regular. Some additional restrictions on $e$ were required---e.g., $e>h$, the Coxeter number, and $e$ odd.\n  Translation to a facet gave an explicit semisimple series for all quantum Weyl modules with singular, as well as regular, weights. That is, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1489","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":"2026-05-18T04:13:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N5lylzzZrR2wjcBENb9JNOeMrzGPo5O/3OYs2YB3beAJEVmBvpR77SCOvZLQjQDHEMSXSf/acB8cS1P2pusTAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:14:00.503273Z"},"content_sha256":"aad0d02a11cd6985f92112918553715105a78c42225efd79a070cd4ce7328371","schema_version":"1.0","event_id":"sha256:aad0d02a11cd6985f92112918553715105a78c42225efd79a070cd4ce7328371"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JZHZZEA7V3UWRSYPWTDSWPCRU2/bundle.json","state_url":"https://pith.science/pith/JZHZZEA7V3UWRSYPWTDSWPCRU2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JZHZZEA7V3UWRSYPWTDSWPCRU2/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":"2026-05-31T06:14:00Z","links":{"resolver":"https://pith.science/pith/JZHZZEA7V3UWRSYPWTDSWPCRU2","bundle":"https://pith.science/pith/JZHZZEA7V3UWRSYPWTDSWPCRU2/bundle.json","state":"https://pith.science/pith/JZHZZEA7V3UWRSYPWTDSWPCRU2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JZHZZEA7V3UWRSYPWTDSWPCRU2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JZHZZEA7V3UWRSYPWTDSWPCRU2","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":"6486808da2633979f3dd73b5600d57f3324120ee61f6ef5ee11edf1e02f2eb69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-07T15:29:27Z","title_canon_sha256":"281b729484f19e41d3fb204509e4b7f0986c1b903a137303dcaf44186e47f6d2"},"schema_version":"1.0","source":{"id":"1109.1489","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1489","created_at":"2026-05-18T04:13:55Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1489v1","created_at":"2026-05-18T04:13:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1489","created_at":"2026-05-18T04:13:55Z"},{"alias_kind":"pith_short_12","alias_value":"JZHZZEA7V3UW","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JZHZZEA7V3UWRSYP","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JZHZZEA7","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:aad0d02a11cd6985f92112918553715105a78c42225efd79a070cd4ce7328371","target":"graph","created_at":"2026-05-18T04:13:55Z","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":"In a previous paper, the authors studied the radical filtration of a Weyl module $\\Delta_\\zeta(\\lambda)$ for quantum enveloping algebras $U_\\zeta(\\overset\\circ{\\mathfrak g})$ associated to a finite dimensional complex semisimple Lie algebra $\\overset\\circ{\\mathfrak g}$. There $\\zeta^2=\\sqrt[e]{1}$ and $\\lambda$ was, initially, required to be $e$-regular. Some additional restrictions on $e$ were required---e.g., $e>h$, the Coxeter number, and $e$ odd.\n  Translation to a facet gave an explicit semisimple series for all quantum Weyl modules with singular, as well as regular, weights. That is, the","authors_text":"Brian Parshall, Leonard Scott","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-07T15:29:27Z","title":"A semisimple series for $q$-Weyl and $q$-Specht modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1489","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":"sha256:78feb6903f7c7f495c0839365471640c04a23d16cef0e174f68b42d7938727b9","target":"record","created_at":"2026-05-18T04:13:55Z","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":"6486808da2633979f3dd73b5600d57f3324120ee61f6ef5ee11edf1e02f2eb69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-07T15:29:27Z","title_canon_sha256":"281b729484f19e41d3fb204509e4b7f0986c1b903a137303dcaf44186e47f6d2"},"schema_version":"1.0","source":{"id":"1109.1489","kind":"arxiv","version":1}},"canonical_sha256":"4e4f9c901faee968cb0fb4c72b3c51a681fcc447be852fd3e4e8b4127834754f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e4f9c901faee968cb0fb4c72b3c51a681fcc447be852fd3e4e8b4127834754f","first_computed_at":"2026-05-18T04:13:55.590709Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:55.590709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qZMVBgg27+kh8yHshh8qKt7ULx4jKg/zJNScTUE2fdYOd+dEVJ8efPXN87GAKqQRjRkV9WAsV1I41FgP7Z8CDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:55.591113Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.1489","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78feb6903f7c7f495c0839365471640c04a23d16cef0e174f68b42d7938727b9","sha256:aad0d02a11cd6985f92112918553715105a78c42225efd79a070cd4ce7328371"],"state_sha256":"d4af9c841bd3ab75be573ec3be02d912a8ae9933a82c9585fc2d5a2c66298e09"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A1Ibvh6oWR+pe7l6Qg49CVY0rRWLG60iGeAhRcxcM4c9Uj1iqpwZIMNI0uzCZXevRcoQGGQWmF6YgBDgnPa1AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:14:00.505203Z","bundle_sha256":"a313b1b265e76f382ec9ad9f18dfd7b70356d2f75ac8bc1ee2c6e9db00ca63c6"}}