{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:GJJTZICMEY5VJ3SSN6ZTM6XUDQ","short_pith_number":"pith:GJJTZICM","canonical_record":{"source":{"id":"1806.05247","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-13T20:07:42Z","cross_cats_sorted":[],"title_canon_sha256":"28c8fb49d6a7fe26145b0820a4652a0f34d202ed40e396623213f390a40df740","abstract_canon_sha256":"de9cfc6809651680133ee2e7d6ff7721ff5ca5e6a783667e677cc30a59953d16"},"schema_version":"1.0"},"canonical_sha256":"32533ca04c263b54ee526fb3367af41c0e34638d09f697ea31eab923b5911c59","source":{"kind":"arxiv","id":"1806.05247","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05247","created_at":"2026-05-18T00:13:16Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05247v1","created_at":"2026-05-18T00:13:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05247","created_at":"2026-05-18T00:13:16Z"},{"alias_kind":"pith_short_12","alias_value":"GJJTZICMEY5V","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GJJTZICMEY5VJ3SS","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GJJTZICM","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:GJJTZICMEY5VJ3SSN6ZTM6XUDQ","target":"record","payload":{"canonical_record":{"source":{"id":"1806.05247","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-13T20:07:42Z","cross_cats_sorted":[],"title_canon_sha256":"28c8fb49d6a7fe26145b0820a4652a0f34d202ed40e396623213f390a40df740","abstract_canon_sha256":"de9cfc6809651680133ee2e7d6ff7721ff5ca5e6a783667e677cc30a59953d16"},"schema_version":"1.0"},"canonical_sha256":"32533ca04c263b54ee526fb3367af41c0e34638d09f697ea31eab923b5911c59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:16.670395Z","signature_b64":"SvcErYee1Mq9h5tw2vGMcY41AsWZ7tkePEDfE0FuZxe6c8cOA18NeVih0ZuHTmPbDjmghHQtkM2PB3ZvZTrJAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32533ca04c263b54ee526fb3367af41c0e34638d09f697ea31eab923b5911c59","last_reissued_at":"2026-05-18T00:13:16.669534Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:16.669534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.05247","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":"2026-05-18T00:13:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/AEaSx43LCvxWOjF1aMGs5lxnVWjI99ZhaWM2i08pAHwCqI+0KgdP88/bQ/7auE2zZyTP+XijCPOCXhDp4ZVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T16:50:05.763406Z"},"content_sha256":"85ebb1a8b92818b4435d08d580cea22e848c1bdb3673aceaed21b2585a876abd","schema_version":"1.0","event_id":"sha256:85ebb1a8b92818b4435d08d580cea22e848c1bdb3673aceaed21b2585a876abd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:GJJTZICMEY5VJ3SSN6ZTM6XUDQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reduced words for clans","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brendan Pawlowski, Brian Burks","submitted_at":"2018-06-13T20:07:42Z","abstract_excerpt":"Clans are combinatorial objects indexing the orbits of $GL(\\mathbb{C}^p) \\times GL(\\mathbb{C}^q)$ on the variety of flags in $\\mathbb{C}^{p+q}$. This geometry leads to a partial order on the set of clans analogous to weak Bruhat order on the symmetric group, and we study the saturated chains in this order. We prove an analogue of the Matsumoto-Tits theorem on reduced words in a Coxeter group. We also obtain enumerations of reduced word sets for particular clans in terms of standard tableaux and shifted standard tableaux."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05247","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":"2026-05-18T00:13:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nq6n+iseEoj9+CS9jzGVBoxuxRsLNLuAAiXeBWCkATdE3/skGdEm4HX5ZkMJwuMrT1Vj1f7JHsfb5UPuNrLjBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T16:50:05.763764Z"},"content_sha256":"8b2d6d76a2bd053abeb1e8a5398b6ccd8076d2290c2e4dba856b630c2703bbf3","schema_version":"1.0","event_id":"sha256:8b2d6d76a2bd053abeb1e8a5398b6ccd8076d2290c2e4dba856b630c2703bbf3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GJJTZICMEY5VJ3SSN6ZTM6XUDQ/bundle.json","state_url":"https://pith.science/pith/GJJTZICMEY5VJ3SSN6ZTM6XUDQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GJJTZICMEY5VJ3SSN6ZTM6XUDQ/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":"2026-05-21T16:50:05Z","links":{"resolver":"https://pith.science/pith/GJJTZICMEY5VJ3SSN6ZTM6XUDQ","bundle":"https://pith.science/pith/GJJTZICMEY5VJ3SSN6ZTM6XUDQ/bundle.json","state":"https://pith.science/pith/GJJTZICMEY5VJ3SSN6ZTM6XUDQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GJJTZICMEY5VJ3SSN6ZTM6XUDQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GJJTZICMEY5VJ3SSN6ZTM6XUDQ","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":"de9cfc6809651680133ee2e7d6ff7721ff5ca5e6a783667e677cc30a59953d16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-13T20:07:42Z","title_canon_sha256":"28c8fb49d6a7fe26145b0820a4652a0f34d202ed40e396623213f390a40df740"},"schema_version":"1.0","source":{"id":"1806.05247","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05247","created_at":"2026-05-18T00:13:16Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05247v1","created_at":"2026-05-18T00:13:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05247","created_at":"2026-05-18T00:13:16Z"},{"alias_kind":"pith_short_12","alias_value":"GJJTZICMEY5V","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GJJTZICMEY5VJ3SS","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GJJTZICM","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:8b2d6d76a2bd053abeb1e8a5398b6ccd8076d2290c2e4dba856b630c2703bbf3","target":"graph","created_at":"2026-05-18T00:13:16Z","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":"Clans are combinatorial objects indexing the orbits of $GL(\\mathbb{C}^p) \\times GL(\\mathbb{C}^q)$ on the variety of flags in $\\mathbb{C}^{p+q}$. This geometry leads to a partial order on the set of clans analogous to weak Bruhat order on the symmetric group, and we study the saturated chains in this order. We prove an analogue of the Matsumoto-Tits theorem on reduced words in a Coxeter group. We also obtain enumerations of reduced word sets for particular clans in terms of standard tableaux and shifted standard tableaux.","authors_text":"Brendan Pawlowski, Brian Burks","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-13T20:07:42Z","title":"Reduced words for clans"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05247","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":"sha256:85ebb1a8b92818b4435d08d580cea22e848c1bdb3673aceaed21b2585a876abd","target":"record","created_at":"2026-05-18T00:13:16Z","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":"de9cfc6809651680133ee2e7d6ff7721ff5ca5e6a783667e677cc30a59953d16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-13T20:07:42Z","title_canon_sha256":"28c8fb49d6a7fe26145b0820a4652a0f34d202ed40e396623213f390a40df740"},"schema_version":"1.0","source":{"id":"1806.05247","kind":"arxiv","version":1}},"canonical_sha256":"32533ca04c263b54ee526fb3367af41c0e34638d09f697ea31eab923b5911c59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32533ca04c263b54ee526fb3367af41c0e34638d09f697ea31eab923b5911c59","first_computed_at":"2026-05-18T00:13:16.669534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:16.669534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SvcErYee1Mq9h5tw2vGMcY41AsWZ7tkePEDfE0FuZxe6c8cOA18NeVih0ZuHTmPbDjmghHQtkM2PB3ZvZTrJAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:16.670395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.05247","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85ebb1a8b92818b4435d08d580cea22e848c1bdb3673aceaed21b2585a876abd","sha256:8b2d6d76a2bd053abeb1e8a5398b6ccd8076d2290c2e4dba856b630c2703bbf3"],"state_sha256":"6f39e77d614148954b169f82755448b80d8d5d5e90004e92c37a3a33affc9036"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A6Nv14TsUYum+0hC/ZgMiEvJZD0utEYmEOuQ25jkZUI3jugPxezTw0Nnt+2g3QkJ0hajYsfavyvoC52YPUDlCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T16:50:05.765773Z","bundle_sha256":"464279114018e0a97ac2416ab0b36b504f53cced66bd6c65bb80a4edb5a66805"}}