{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:P4GEK6UR3YPH7QU4YL3CR3WPUI","short_pith_number":"pith:P4GEK6UR","canonical_record":{"source":{"id":"math/0401314","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"2004-01-23T15:19:50Z","cross_cats_sorted":[],"title_canon_sha256":"77c8fa6153d20804835a611d4836690edb336b3d7f23224659ce50762d835487","abstract_canon_sha256":"89df9a76cbd8d6a1fcfb2410f6944167f84b53104e5a0018e72815b3a4fc1df8"},"schema_version":"1.0"},"canonical_sha256":"7f0c457a91de1e7fc29cc2f628eecfa221c07dde07571ca7c18d761a08276e85","source":{"kind":"arxiv","id":"math/0401314","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0401314","created_at":"2026-07-04T14:38:10Z"},{"alias_kind":"arxiv_version","alias_value":"math/0401314v2","created_at":"2026-07-04T14:38:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0401314","created_at":"2026-07-04T14:38:10Z"},{"alias_kind":"pith_short_12","alias_value":"P4GEK6UR3YPH","created_at":"2026-07-04T14:38:10Z"},{"alias_kind":"pith_short_16","alias_value":"P4GEK6UR3YPH7QU4","created_at":"2026-07-04T14:38:10Z"},{"alias_kind":"pith_short_8","alias_value":"P4GEK6UR","created_at":"2026-07-04T14:38:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:P4GEK6UR3YPH7QU4YL3CR3WPUI","target":"record","payload":{"canonical_record":{"source":{"id":"math/0401314","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"2004-01-23T15:19:50Z","cross_cats_sorted":[],"title_canon_sha256":"77c8fa6153d20804835a611d4836690edb336b3d7f23224659ce50762d835487","abstract_canon_sha256":"89df9a76cbd8d6a1fcfb2410f6944167f84b53104e5a0018e72815b3a4fc1df8"},"schema_version":"1.0"},"canonical_sha256":"7f0c457a91de1e7fc29cc2f628eecfa221c07dde07571ca7c18d761a08276e85","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:38:10.979409Z","signature_b64":"ypdzXttN5ZLf+bRvbcwvufq0EWd7WXS9ESlxnmWN+7BxdW8/iFviE6rL45nKKyLMggV0+79aGD+hXJZAq6wECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f0c457a91de1e7fc29cc2f628eecfa221c07dde07571ca7c18d761a08276e85","last_reissued_at":"2026-07-04T14:38:10.979023Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:38:10.979023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0401314","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":"2026-07-04T14:38:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RhBSszuhvwkdPxhG7C3vYgdSczU6VZi0mhV98Hu8SdkYXqw3Au85xjMX4FRnoLwSZ6Rhl1gpbnJdQBRUCtuNBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T14:06:30.238589Z"},"content_sha256":"fe8537d72a5394a24f386465fad1990010cda0bc792a236f0197aec69bfbf353","schema_version":"1.0","event_id":"sha256:fe8537d72a5394a24f386465fad1990010cda0bc792a236f0197aec69bfbf353"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:P4GEK6UR3YPH7QU4YL3CR3WPUI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Partition Algebras","license":"","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Arun Ram, Tom Halverson","submitted_at":"2004-01-23T15:19:50Z","abstract_excerpt":"The partition algebras are algebras of diagrams (which contain the group algebra of the symmetric group and the Brauer algebra) such that the multiplication is given by a combinatorial rule and such that the structure constants of the algebra depend polynomially on a parameter. This is a survey paper which proves the primary results in the theory of partition algebras. Some of the results in this paper are new. This paper gives: (a) a presentation of the partition algebras by generators and relations, (b) shows that each partition algebra has an ideal which is isomorphic to a basic constructio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0401314","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0401314/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:38:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wQCD+2fg5AiXvA6ZqmysWJbUcZotvN6Vo3p6lf/H+we4Z/sgG9RkxyzF4ocKdD/DuTnweeSwYpPwYAIifjbRDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T14:06:30.239189Z"},"content_sha256":"73e58981b3887df96b14ab514da1fdc91e4af66d3277a3c9985fb422bf72e48e","schema_version":"1.0","event_id":"sha256:73e58981b3887df96b14ab514da1fdc91e4af66d3277a3c9985fb422bf72e48e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P4GEK6UR3YPH7QU4YL3CR3WPUI/bundle.json","state_url":"https://pith.science/pith/P4GEK6UR3YPH7QU4YL3CR3WPUI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P4GEK6UR3YPH7QU4YL3CR3WPUI/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":"2026-08-22T14:06:30Z","links":{"resolver":"https://pith.science/pith/P4GEK6UR3YPH7QU4YL3CR3WPUI","bundle":"https://pith.science/pith/P4GEK6UR3YPH7QU4YL3CR3WPUI/bundle.json","state":"https://pith.science/pith/P4GEK6UR3YPH7QU4YL3CR3WPUI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P4GEK6UR3YPH7QU4YL3CR3WPUI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:P4GEK6UR3YPH7QU4YL3CR3WPUI","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":"89df9a76cbd8d6a1fcfb2410f6944167f84b53104e5a0018e72815b3a4fc1df8","cross_cats_sorted":[],"license":"","primary_cat":"math.RT","submitted_at":"2004-01-23T15:19:50Z","title_canon_sha256":"77c8fa6153d20804835a611d4836690edb336b3d7f23224659ce50762d835487"},"schema_version":"1.0","source":{"id":"math/0401314","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0401314","created_at":"2026-07-04T14:38:10Z"},{"alias_kind":"arxiv_version","alias_value":"math/0401314v2","created_at":"2026-07-04T14:38:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0401314","created_at":"2026-07-04T14:38:10Z"},{"alias_kind":"pith_short_12","alias_value":"P4GEK6UR3YPH","created_at":"2026-07-04T14:38:10Z"},{"alias_kind":"pith_short_16","alias_value":"P4GEK6UR3YPH7QU4","created_at":"2026-07-04T14:38:10Z"},{"alias_kind":"pith_short_8","alias_value":"P4GEK6UR","created_at":"2026-07-04T14:38:10Z"}],"graph_snapshots":[{"event_id":"sha256:73e58981b3887df96b14ab514da1fdc91e4af66d3277a3c9985fb422bf72e48e","target":"graph","created_at":"2026-07-04T14:38:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0401314/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The partition algebras are algebras of diagrams (which contain the group algebra of the symmetric group and the Brauer algebra) such that the multiplication is given by a combinatorial rule and such that the structure constants of the algebra depend polynomially on a parameter. This is a survey paper which proves the primary results in the theory of partition algebras. Some of the results in this paper are new. This paper gives: (a) a presentation of the partition algebras by generators and relations, (b) shows that each partition algebra has an ideal which is isomorphic to a basic constructio","authors_text":"Arun Ram, Tom Halverson","cross_cats":[],"headline":"","license":"","primary_cat":"math.RT","submitted_at":"2004-01-23T15:19:50Z","title":"Partition Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0401314","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:fe8537d72a5394a24f386465fad1990010cda0bc792a236f0197aec69bfbf353","target":"record","created_at":"2026-07-04T14:38:10Z","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":"89df9a76cbd8d6a1fcfb2410f6944167f84b53104e5a0018e72815b3a4fc1df8","cross_cats_sorted":[],"license":"","primary_cat":"math.RT","submitted_at":"2004-01-23T15:19:50Z","title_canon_sha256":"77c8fa6153d20804835a611d4836690edb336b3d7f23224659ce50762d835487"},"schema_version":"1.0","source":{"id":"math/0401314","kind":"arxiv","version":2}},"canonical_sha256":"7f0c457a91de1e7fc29cc2f628eecfa221c07dde07571ca7c18d761a08276e85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f0c457a91de1e7fc29cc2f628eecfa221c07dde07571ca7c18d761a08276e85","first_computed_at":"2026-07-04T14:38:10.979023Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:38:10.979023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ypdzXttN5ZLf+bRvbcwvufq0EWd7WXS9ESlxnmWN+7BxdW8/iFviE6rL45nKKyLMggV0+79aGD+hXJZAq6wECg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:38:10.979409Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0401314","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe8537d72a5394a24f386465fad1990010cda0bc792a236f0197aec69bfbf353","sha256:73e58981b3887df96b14ab514da1fdc91e4af66d3277a3c9985fb422bf72e48e"],"state_sha256":"3e13c269bc6f3fe0d696efcdcd96233b21b7017692e4a6f5249f0a16f9df2157"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PGE0XUMBhqvuSOg1ZQwLkpoK+qh4XaxCh2E983EGrl0KiY9nwm5MfIW/AEYw5NS8iSrUBI8mH97HjBIK9FJuBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T14:06:30.244593Z","bundle_sha256":"3504168646ccba9005d3cc974b5330ef097ba574ebde8e24fbbb8e62ef24abb9"}}