{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:K2BWNQX3XI4GOSH6M2BKSOROJR","short_pith_number":"pith:K2BWNQX3","canonical_record":{"source":{"id":"1701.00605","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-01-03T09:01:09Z","cross_cats_sorted":[],"title_canon_sha256":"24ae3dc1c72f09770a82b03c1f343da88d79e3c38ff80d757c3ccada5cd66cde","abstract_canon_sha256":"86cbf1dfe585bfb8a5a5398beea80073a8e8d6de20b47ed74978d79aedcf25d2"},"schema_version":"1.0"},"canonical_sha256":"568366c2fbba386748fe6682a93a2e4c7fbd1d0b102036626863e4a3b5ec88a1","source":{"kind":"arxiv","id":"1701.00605","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00605","created_at":"2026-05-18T00:28:25Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00605v2","created_at":"2026-05-18T00:28:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00605","created_at":"2026-05-18T00:28:25Z"},{"alias_kind":"pith_short_12","alias_value":"K2BWNQX3XI4G","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"K2BWNQX3XI4GOSH6","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"K2BWNQX3","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:K2BWNQX3XI4GOSH6M2BKSOROJR","target":"record","payload":{"canonical_record":{"source":{"id":"1701.00605","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-01-03T09:01:09Z","cross_cats_sorted":[],"title_canon_sha256":"24ae3dc1c72f09770a82b03c1f343da88d79e3c38ff80d757c3ccada5cd66cde","abstract_canon_sha256":"86cbf1dfe585bfb8a5a5398beea80073a8e8d6de20b47ed74978d79aedcf25d2"},"schema_version":"1.0"},"canonical_sha256":"568366c2fbba386748fe6682a93a2e4c7fbd1d0b102036626863e4a3b5ec88a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:25.826114Z","signature_b64":"BRWlHJoKsX5GjRjNE00DzmDZ8FSkl0e6FYzjf5ZYsxhdnKjAHA2Bwn7Ddwr5LuRFGedEfcc28haAaIyrvAY6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"568366c2fbba386748fe6682a93a2e4c7fbd1d0b102036626863e4a3b5ec88a1","last_reissued_at":"2026-05-18T00:28:25.825484Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:25.825484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.00605","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":"2026-05-18T00:28:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FRHpBPbvqfla4aqNAiSzJzVWIlRrEFoK9trfTlZBlfiRP2XLLIB1zWDv5IOIOI98jYfeoYMX/CZo+ZCuWJrkCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:57:04.971041Z"},"content_sha256":"c4b12cb56bf39deeac8ab3e166d3241599081b302ea1f7f1967ec2f9e741bedb","schema_version":"1.0","event_id":"sha256:c4b12cb56bf39deeac8ab3e166d3241599081b302ea1f7f1967ec2f9e741bedb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:K2BWNQX3XI4GOSH6M2BKSOROJR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On monomial linearisation and supercharacters of pattern subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Qiong Guo, Richard Dipper","submitted_at":"2017-01-03T09:01:09Z","abstract_excerpt":"Column closed pattern subgroups $U$ of the finite upper unitriangular groups $U_n(q)$ are defined as sets of matrices in $U_n(q)$ having zeros in a prescribed set of columns besides the diagonal ones. We explain Jedlitschky's construction of monomial linearisation and apply this to $C U$ yielding a generalisation of Yan's coadjoint cluster representations. Then we give a complete classification of the resulting supercharacters, by describing the resulting orbits and determining the Hom-spaces between orbit modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00605","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":"2026-05-18T00:28:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U7O1TDlq1QwqQhubyvF44O5b965d7aRF2+pwEPZ1SdCH+SkKsWofrVpetokbGWTWDRikq2vwPw8BAha/7X5gAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:57:04.971392Z"},"content_sha256":"599bf6849211f826c4e51154364cb0fcd567c986891f8c1c9b0d2c33daae911e","schema_version":"1.0","event_id":"sha256:599bf6849211f826c4e51154364cb0fcd567c986891f8c1c9b0d2c33daae911e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K2BWNQX3XI4GOSH6M2BKSOROJR/bundle.json","state_url":"https://pith.science/pith/K2BWNQX3XI4GOSH6M2BKSOROJR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K2BWNQX3XI4GOSH6M2BKSOROJR/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":"2026-06-23T02:57:04Z","links":{"resolver":"https://pith.science/pith/K2BWNQX3XI4GOSH6M2BKSOROJR","bundle":"https://pith.science/pith/K2BWNQX3XI4GOSH6M2BKSOROJR/bundle.json","state":"https://pith.science/pith/K2BWNQX3XI4GOSH6M2BKSOROJR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K2BWNQX3XI4GOSH6M2BKSOROJR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:K2BWNQX3XI4GOSH6M2BKSOROJR","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":"86cbf1dfe585bfb8a5a5398beea80073a8e8d6de20b47ed74978d79aedcf25d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-01-03T09:01:09Z","title_canon_sha256":"24ae3dc1c72f09770a82b03c1f343da88d79e3c38ff80d757c3ccada5cd66cde"},"schema_version":"1.0","source":{"id":"1701.00605","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00605","created_at":"2026-05-18T00:28:25Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00605v2","created_at":"2026-05-18T00:28:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00605","created_at":"2026-05-18T00:28:25Z"},{"alias_kind":"pith_short_12","alias_value":"K2BWNQX3XI4G","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"K2BWNQX3XI4GOSH6","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"K2BWNQX3","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:599bf6849211f826c4e51154364cb0fcd567c986891f8c1c9b0d2c33daae911e","target":"graph","created_at":"2026-05-18T00:28:25Z","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":"Column closed pattern subgroups $U$ of the finite upper unitriangular groups $U_n(q)$ are defined as sets of matrices in $U_n(q)$ having zeros in a prescribed set of columns besides the diagonal ones. We explain Jedlitschky's construction of monomial linearisation and apply this to $C U$ yielding a generalisation of Yan's coadjoint cluster representations. Then we give a complete classification of the resulting supercharacters, by describing the resulting orbits and determining the Hom-spaces between orbit modules.","authors_text":"Qiong Guo, Richard Dipper","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-01-03T09:01:09Z","title":"On monomial linearisation and supercharacters of pattern subgroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00605","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:c4b12cb56bf39deeac8ab3e166d3241599081b302ea1f7f1967ec2f9e741bedb","target":"record","created_at":"2026-05-18T00:28:25Z","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":"86cbf1dfe585bfb8a5a5398beea80073a8e8d6de20b47ed74978d79aedcf25d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-01-03T09:01:09Z","title_canon_sha256":"24ae3dc1c72f09770a82b03c1f343da88d79e3c38ff80d757c3ccada5cd66cde"},"schema_version":"1.0","source":{"id":"1701.00605","kind":"arxiv","version":2}},"canonical_sha256":"568366c2fbba386748fe6682a93a2e4c7fbd1d0b102036626863e4a3b5ec88a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"568366c2fbba386748fe6682a93a2e4c7fbd1d0b102036626863e4a3b5ec88a1","first_computed_at":"2026-05-18T00:28:25.825484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:25.825484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BRWlHJoKsX5GjRjNE00DzmDZ8FSkl0e6FYzjf5ZYsxhdnKjAHA2Bwn7Ddwr5LuRFGedEfcc28haAaIyrvAY6DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:25.826114Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.00605","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4b12cb56bf39deeac8ab3e166d3241599081b302ea1f7f1967ec2f9e741bedb","sha256:599bf6849211f826c4e51154364cb0fcd567c986891f8c1c9b0d2c33daae911e"],"state_sha256":"d287c87ab0978df1d732e1625975b4c85051c6a90aed02bde0d804401a294f46"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qYbeEe9dKYoGsecqUP3cSFsYhnLAn+Uovu5O6qFJWMnkZpfw2wk/GG6C9JQjz16Za/wksrGIWaZR2Jx5izZHBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T02:57:04.973249Z","bundle_sha256":"a7a4d0df1709d85759781a382adf3b68d57ab0acaf21b5ed9c95f7da0fe30a28"}}