{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:FY7F4TTQ3FCBKYLFB7PWCN2LLX","short_pith_number":"pith:FY7F4TTQ","canonical_record":{"source":{"id":"1002.4642","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-02-24T21:59:45Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1be8d98c10d6edb13de30311504a71e4b6750c340461da808d68d2774a6c28b2","abstract_canon_sha256":"3cd055b73c2a3079e2966d073f75d466fecb9629480dd82eb26cd923fc5014b1"},"schema_version":"1.0"},"canonical_sha256":"2e3e5e4e70d9441561650fdf61374b5dccde4093b1aae78a57470640ff379b81","source":{"kind":"arxiv","id":"1002.4642","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.4642","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"arxiv_version","alias_value":"1002.4642v3","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.4642","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"pith_short_12","alias_value":"FY7F4TTQ3FCB","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FY7F4TTQ3FCBKYLF","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FY7F4TTQ","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:FY7F4TTQ3FCBKYLFB7PWCN2LLX","target":"record","payload":{"canonical_record":{"source":{"id":"1002.4642","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-02-24T21:59:45Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1be8d98c10d6edb13de30311504a71e4b6750c340461da808d68d2774a6c28b2","abstract_canon_sha256":"3cd055b73c2a3079e2966d073f75d466fecb9629480dd82eb26cd923fc5014b1"},"schema_version":"1.0"},"canonical_sha256":"2e3e5e4e70d9441561650fdf61374b5dccde4093b1aae78a57470640ff379b81","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:05.114120Z","signature_b64":"i4fscDHzspkPc19V4+U4fiVB76KCSHC2WuCqoT5E+sX0WEGUeaAj19/HQ0Hb9tjJmGbcltCOYVa456GdxFjxBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e3e5e4e70d9441561650fdf61374b5dccde4093b1aae78a57470640ff379b81","last_reissued_at":"2026-05-18T04:41:05.113701Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:05.113701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.4642","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:41:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oWt98qdVmhcILmPBTXei3uG6Wt59eZThjBicxFLt+Ygn+YoMhTw0FE1VJq0F1GWmbl1ZZuYiwrSze1a0KZtoAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:22:40.807481Z"},"content_sha256":"9d65650b868ff2d075ffb2cec6f6b8309acd19bb13ef099be15de4b93b0e3454","schema_version":"1.0","event_id":"sha256:9d65650b868ff2d075ffb2cec6f6b8309acd19bb13ef099be15de4b93b0e3454"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:FY7F4TTQ3FCBKYLFB7PWCN2LLX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A bideterminant basis for a reductive monoid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Rudolf Tange","submitted_at":"2010-02-24T21:59:45Z","abstract_excerpt":"We use the rational tableaux introduced by Stembridge to give a bideterminant basis for a normal reductive monoid and for its variety of noninvertible elements. We also obtain a bideterminant basis for the full coordinate ring of the general linear group and for all its truncations with respect to saturated sets. Finally, we deduce an alternative proof of the double centraliser theorem for the rational Schur algebra and the walled Brauer algebra over an arbitrary infinite base field which was first obtained by Dipper, Doty and Stoll."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4642","kind":"arxiv","version":3},"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":"2026-05-18T04:41:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZLyG9cuN6pxMb38w4KnrucIp6KYQF2vYj3At608WNPSSnkddo0i/AT2P7weEzIS1TjUspxlTqKmqQHwbWyqTAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:22:40.807832Z"},"content_sha256":"8a91da94ded0bdc63e7b5e5c5f6e3c4f50172c3b199e93ac63c1af667b0b61ce","schema_version":"1.0","event_id":"sha256:8a91da94ded0bdc63e7b5e5c5f6e3c4f50172c3b199e93ac63c1af667b0b61ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FY7F4TTQ3FCBKYLFB7PWCN2LLX/bundle.json","state_url":"https://pith.science/pith/FY7F4TTQ3FCBKYLFB7PWCN2LLX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FY7F4TTQ3FCBKYLFB7PWCN2LLX/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":"2026-05-28T03:22:40Z","links":{"resolver":"https://pith.science/pith/FY7F4TTQ3FCBKYLFB7PWCN2LLX","bundle":"https://pith.science/pith/FY7F4TTQ3FCBKYLFB7PWCN2LLX/bundle.json","state":"https://pith.science/pith/FY7F4TTQ3FCBKYLFB7PWCN2LLX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FY7F4TTQ3FCBKYLFB7PWCN2LLX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:FY7F4TTQ3FCBKYLFB7PWCN2LLX","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":"3cd055b73c2a3079e2966d073f75d466fecb9629480dd82eb26cd923fc5014b1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-02-24T21:59:45Z","title_canon_sha256":"1be8d98c10d6edb13de30311504a71e4b6750c340461da808d68d2774a6c28b2"},"schema_version":"1.0","source":{"id":"1002.4642","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.4642","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"arxiv_version","alias_value":"1002.4642v3","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.4642","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"pith_short_12","alias_value":"FY7F4TTQ3FCB","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FY7F4TTQ3FCBKYLF","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FY7F4TTQ","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:8a91da94ded0bdc63e7b5e5c5f6e3c4f50172c3b199e93ac63c1af667b0b61ce","target":"graph","created_at":"2026-05-18T04:41:05Z","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 use the rational tableaux introduced by Stembridge to give a bideterminant basis for a normal reductive monoid and for its variety of noninvertible elements. We also obtain a bideterminant basis for the full coordinate ring of the general linear group and for all its truncations with respect to saturated sets. Finally, we deduce an alternative proof of the double centraliser theorem for the rational Schur algebra and the walled Brauer algebra over an arbitrary infinite base field which was first obtained by Dipper, Doty and Stoll.","authors_text":"Rudolf Tange","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-02-24T21:59:45Z","title":"A bideterminant basis for a reductive monoid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4642","kind":"arxiv","version":3},"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":"sha256:9d65650b868ff2d075ffb2cec6f6b8309acd19bb13ef099be15de4b93b0e3454","target":"record","created_at":"2026-05-18T04:41:05Z","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":"3cd055b73c2a3079e2966d073f75d466fecb9629480dd82eb26cd923fc5014b1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-02-24T21:59:45Z","title_canon_sha256":"1be8d98c10d6edb13de30311504a71e4b6750c340461da808d68d2774a6c28b2"},"schema_version":"1.0","source":{"id":"1002.4642","kind":"arxiv","version":3}},"canonical_sha256":"2e3e5e4e70d9441561650fdf61374b5dccde4093b1aae78a57470640ff379b81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e3e5e4e70d9441561650fdf61374b5dccde4093b1aae78a57470640ff379b81","first_computed_at":"2026-05-18T04:41:05.113701Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:05.113701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i4fscDHzspkPc19V4+U4fiVB76KCSHC2WuCqoT5E+sX0WEGUeaAj19/HQ0Hb9tjJmGbcltCOYVa456GdxFjxBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:05.114120Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.4642","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d65650b868ff2d075ffb2cec6f6b8309acd19bb13ef099be15de4b93b0e3454","sha256:8a91da94ded0bdc63e7b5e5c5f6e3c4f50172c3b199e93ac63c1af667b0b61ce"],"state_sha256":"85765232d5798c88b661fb83e9987a4c30b829b37d272234d636655043ccdfc6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GG7PEuKhcW5u5zgR/wJuikvqc3j7v0tCWFRK/kvToGz5f5sN9a7FxBuYPsRdSzDJdn7EhiNrMwnzfdVUy7THCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:22:40.809810Z","bundle_sha256":"c520d4908407a46da9d6e74560475812019a28ae0120a9a2d57b30df6be2dcfa"}}