{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HYJAGLJAGRECJKOGZTA4Z3USN6","short_pith_number":"pith:HYJAGLJA","canonical_record":{"source":{"id":"1401.1407","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-01-07T14:55:12Z","cross_cats_sorted":[],"title_canon_sha256":"5b86a4327f011f50a295dab2e24bc92ee0d70fe3903372d4a663fde28de21917","abstract_canon_sha256":"cbcce3f15ffb279a054b344dbea3438eb90f75efd6dfe863fdaff289fdd5c742"},"schema_version":"1.0"},"canonical_sha256":"3e12032d20344824a9c6ccc1ccee926fbc4a7db31cbb56bfcfaa4b105e208312","source":{"kind":"arxiv","id":"1401.1407","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1407","created_at":"2026-05-18T03:03:08Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1407v1","created_at":"2026-05-18T03:03:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1407","created_at":"2026-05-18T03:03:08Z"},{"alias_kind":"pith_short_12","alias_value":"HYJAGLJAGREC","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"HYJAGLJAGRECJKOG","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"HYJAGLJA","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HYJAGLJAGRECJKOGZTA4Z3USN6","target":"record","payload":{"canonical_record":{"source":{"id":"1401.1407","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-01-07T14:55:12Z","cross_cats_sorted":[],"title_canon_sha256":"5b86a4327f011f50a295dab2e24bc92ee0d70fe3903372d4a663fde28de21917","abstract_canon_sha256":"cbcce3f15ffb279a054b344dbea3438eb90f75efd6dfe863fdaff289fdd5c742"},"schema_version":"1.0"},"canonical_sha256":"3e12032d20344824a9c6ccc1ccee926fbc4a7db31cbb56bfcfaa4b105e208312","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:08.478815Z","signature_b64":"ahSY8qYeGwZ4efqAnk36wJGKsrUbfmNO879laA0CE3PKcm3WADbIHxRLwLdEZkEU62TetIn8OpHZWNdnlVwWAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e12032d20344824a9c6ccc1ccee926fbc4a7db31cbb56bfcfaa4b105e208312","last_reissued_at":"2026-05-18T03:03:08.478042Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:08.478042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.1407","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":"2026-05-18T03:03:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+wwFhHOrtN89Db+w18UjKVH1s1TvAiWsU4XlJ+XDY3zT+JKTSG623VLO6X5LFDNi8ADKCJWYiKKQ8rUtjSj7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:54:21.363287Z"},"content_sha256":"a6e9e9ca46c41941616a9c309b378dd8b87edad1146986276bac25f9b67d3ccc","schema_version":"1.0","event_id":"sha256:a6e9e9ca46c41941616a9c309b378dd8b87edad1146986276bac25f9b67d3ccc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HYJAGLJAGRECJKOGZTA4Z3USN6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Representations of reductive normal algebraic monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Stephen Doty","submitted_at":"2014-01-07T14:55:12Z","abstract_excerpt":"The rational representation theory of a reductive normal algebraic monoid (with one-dimensional center) forms a highest weight category, in the sense of Cline, Parshall, and Scott. This is a fundamental fact about the representation theory of reductive normal algebraic monoids. We survey how this result was obtained, and treat some natural examples coming from classical groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1407","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":"2026-05-18T03:03:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dmYqVsW2lq4E5R3FyX1Y4IMd498zjScJuK9L7kFSagZjiWQuTVzDhiPA7MuC/67pnZJKtVWFpFW8A4p94pREAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:54:21.363914Z"},"content_sha256":"76717ee04f1155b6ac6dc3085d1bc2e755f61c47614e0dabf5c12e1c7498b7cb","schema_version":"1.0","event_id":"sha256:76717ee04f1155b6ac6dc3085d1bc2e755f61c47614e0dabf5c12e1c7498b7cb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HYJAGLJAGRECJKOGZTA4Z3USN6/bundle.json","state_url":"https://pith.science/pith/HYJAGLJAGRECJKOGZTA4Z3USN6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HYJAGLJAGRECJKOGZTA4Z3USN6/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":"2026-06-07T09:54:21Z","links":{"resolver":"https://pith.science/pith/HYJAGLJAGRECJKOGZTA4Z3USN6","bundle":"https://pith.science/pith/HYJAGLJAGRECJKOGZTA4Z3USN6/bundle.json","state":"https://pith.science/pith/HYJAGLJAGRECJKOGZTA4Z3USN6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HYJAGLJAGRECJKOGZTA4Z3USN6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HYJAGLJAGRECJKOGZTA4Z3USN6","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":"cbcce3f15ffb279a054b344dbea3438eb90f75efd6dfe863fdaff289fdd5c742","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-01-07T14:55:12Z","title_canon_sha256":"5b86a4327f011f50a295dab2e24bc92ee0d70fe3903372d4a663fde28de21917"},"schema_version":"1.0","source":{"id":"1401.1407","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1407","created_at":"2026-05-18T03:03:08Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1407v1","created_at":"2026-05-18T03:03:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1407","created_at":"2026-05-18T03:03:08Z"},{"alias_kind":"pith_short_12","alias_value":"HYJAGLJAGREC","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"HYJAGLJAGRECJKOG","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"HYJAGLJA","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:76717ee04f1155b6ac6dc3085d1bc2e755f61c47614e0dabf5c12e1c7498b7cb","target":"graph","created_at":"2026-05-18T03:03:08Z","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":"The rational representation theory of a reductive normal algebraic monoid (with one-dimensional center) forms a highest weight category, in the sense of Cline, Parshall, and Scott. This is a fundamental fact about the representation theory of reductive normal algebraic monoids. We survey how this result was obtained, and treat some natural examples coming from classical groups.","authors_text":"Stephen Doty","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-01-07T14:55:12Z","title":"Representations of reductive normal algebraic monoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1407","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:a6e9e9ca46c41941616a9c309b378dd8b87edad1146986276bac25f9b67d3ccc","target":"record","created_at":"2026-05-18T03:03:08Z","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":"cbcce3f15ffb279a054b344dbea3438eb90f75efd6dfe863fdaff289fdd5c742","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-01-07T14:55:12Z","title_canon_sha256":"5b86a4327f011f50a295dab2e24bc92ee0d70fe3903372d4a663fde28de21917"},"schema_version":"1.0","source":{"id":"1401.1407","kind":"arxiv","version":1}},"canonical_sha256":"3e12032d20344824a9c6ccc1ccee926fbc4a7db31cbb56bfcfaa4b105e208312","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e12032d20344824a9c6ccc1ccee926fbc4a7db31cbb56bfcfaa4b105e208312","first_computed_at":"2026-05-18T03:03:08.478042Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:08.478042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ahSY8qYeGwZ4efqAnk36wJGKsrUbfmNO879laA0CE3PKcm3WADbIHxRLwLdEZkEU62TetIn8OpHZWNdnlVwWAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:08.478815Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.1407","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6e9e9ca46c41941616a9c309b378dd8b87edad1146986276bac25f9b67d3ccc","sha256:76717ee04f1155b6ac6dc3085d1bc2e755f61c47614e0dabf5c12e1c7498b7cb"],"state_sha256":"988b66e72e28b1146e36afc109c873612edb8ce69fa2c97205c014310d727bb3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"stxH/Cw1gLNFsHV6fRad4J9xkrzrTgcQH0jIeVXjpdY7Hg52nvtSpNwHVSac6Cg0VjJK6/EGEJ6pndvEBfYBDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T09:54:21.366972Z","bundle_sha256":"6ee070f1c32db744f557ae3c1cc019827d31e419b71aebdf496e776de6a5aa88"}}