{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:GUAJPMDJ4TLJJRC6BJXA7QGE7M","short_pith_number":"pith:GUAJPMDJ","canonical_record":{"source":{"id":"1310.2489","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-09T14:20:43Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"65d8eedc32310d74ea7b5f8129436f946bf711e769a043d91976345b0053da67","abstract_canon_sha256":"a1b119a36ff0f5188637ab143344b58c19d996375969516e15ff2942e96cacbd"},"schema_version":"1.0"},"canonical_sha256":"350097b069e4d694c45e0a6e0fc0c4fb029c83a19f2d2d3f4c1cb2f781ac3490","source":{"kind":"arxiv","id":"1310.2489","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.2489","created_at":"2026-05-18T01:36:20Z"},{"alias_kind":"arxiv_version","alias_value":"1310.2489v3","created_at":"2026-05-18T01:36:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2489","created_at":"2026-05-18T01:36:20Z"},{"alias_kind":"pith_short_12","alias_value":"GUAJPMDJ4TLJ","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GUAJPMDJ4TLJJRC6","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GUAJPMDJ","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:GUAJPMDJ4TLJJRC6BJXA7QGE7M","target":"record","payload":{"canonical_record":{"source":{"id":"1310.2489","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-09T14:20:43Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"65d8eedc32310d74ea7b5f8129436f946bf711e769a043d91976345b0053da67","abstract_canon_sha256":"a1b119a36ff0f5188637ab143344b58c19d996375969516e15ff2942e96cacbd"},"schema_version":"1.0"},"canonical_sha256":"350097b069e4d694c45e0a6e0fc0c4fb029c83a19f2d2d3f4c1cb2f781ac3490","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:20.994189Z","signature_b64":"SDlXTQlRUX2SR5e53DXP9+0hXk6nN/zDg9gQS4p7oQKMr+cf1ZakGmOoDN+LA9I9tLAdYlrqNCE6qYcpb9tpAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"350097b069e4d694c45e0a6e0fc0c4fb029c83a19f2d2d3f4c1cb2f781ac3490","last_reissued_at":"2026-05-18T01:36:20.993607Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:20.993607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.2489","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":"2026-05-18T01:36:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lo6hvfZKqNRfb03oU+F0yyC68bokfoWbcBC9duzWVylLBa2Pe4wIlJICa9o5doAEKdEp+SOt0d6dWfvSw/ZBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T06:37:16.174751Z"},"content_sha256":"68b55ea5b5c4df30a38176dfcec0a46eb28ba05299c5d53f4650e6a16a2e3aff","schema_version":"1.0","event_id":"sha256:68b55ea5b5c4df30a38176dfcec0a46eb28ba05299c5d53f4650e6a16a2e3aff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:GUAJPMDJ4TLJJRC6BJXA7QGE7M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On algebraic fusions of association schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Daniel Kalmanovich, Eli Shamovich","submitted_at":"2013-10-09T14:20:43Z","abstract_excerpt":"We give a complete description of the irreducible representations of algebraic fusions of association schemes, in terms of the irreducible representations of a Schur cover of the corresponding group of algebraic automorphisms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2489","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":"2026-05-18T01:36:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YE29maYNsVzcHAMuASZB9AjSagrOgOfLTzuH3RLX9eMWIttuYpkEazvMGcyfik4eTp6P7eDWpCX8TvrnUv0GBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T06:37:16.175103Z"},"content_sha256":"5fd8a8af2b0fb5a7a37695e2a3cb8ef66317efbf29e63b62a43f3953f9f2c006","schema_version":"1.0","event_id":"sha256:5fd8a8af2b0fb5a7a37695e2a3cb8ef66317efbf29e63b62a43f3953f9f2c006"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GUAJPMDJ4TLJJRC6BJXA7QGE7M/bundle.json","state_url":"https://pith.science/pith/GUAJPMDJ4TLJJRC6BJXA7QGE7M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GUAJPMDJ4TLJJRC6BJXA7QGE7M/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":"2026-07-02T06:37:16Z","links":{"resolver":"https://pith.science/pith/GUAJPMDJ4TLJJRC6BJXA7QGE7M","bundle":"https://pith.science/pith/GUAJPMDJ4TLJJRC6BJXA7QGE7M/bundle.json","state":"https://pith.science/pith/GUAJPMDJ4TLJJRC6BJXA7QGE7M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GUAJPMDJ4TLJJRC6BJXA7QGE7M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GUAJPMDJ4TLJJRC6BJXA7QGE7M","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":"a1b119a36ff0f5188637ab143344b58c19d996375969516e15ff2942e96cacbd","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-09T14:20:43Z","title_canon_sha256":"65d8eedc32310d74ea7b5f8129436f946bf711e769a043d91976345b0053da67"},"schema_version":"1.0","source":{"id":"1310.2489","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.2489","created_at":"2026-05-18T01:36:20Z"},{"alias_kind":"arxiv_version","alias_value":"1310.2489v3","created_at":"2026-05-18T01:36:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2489","created_at":"2026-05-18T01:36:20Z"},{"alias_kind":"pith_short_12","alias_value":"GUAJPMDJ4TLJ","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GUAJPMDJ4TLJJRC6","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GUAJPMDJ","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:5fd8a8af2b0fb5a7a37695e2a3cb8ef66317efbf29e63b62a43f3953f9f2c006","target":"graph","created_at":"2026-05-18T01:36:20Z","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 give a complete description of the irreducible representations of algebraic fusions of association schemes, in terms of the irreducible representations of a Schur cover of the corresponding group of algebraic automorphisms.","authors_text":"Daniel Kalmanovich, Eli Shamovich","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-09T14:20:43Z","title":"On algebraic fusions of association schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2489","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":"sha256:68b55ea5b5c4df30a38176dfcec0a46eb28ba05299c5d53f4650e6a16a2e3aff","target":"record","created_at":"2026-05-18T01:36:20Z","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":"a1b119a36ff0f5188637ab143344b58c19d996375969516e15ff2942e96cacbd","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-09T14:20:43Z","title_canon_sha256":"65d8eedc32310d74ea7b5f8129436f946bf711e769a043d91976345b0053da67"},"schema_version":"1.0","source":{"id":"1310.2489","kind":"arxiv","version":3}},"canonical_sha256":"350097b069e4d694c45e0a6e0fc0c4fb029c83a19f2d2d3f4c1cb2f781ac3490","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"350097b069e4d694c45e0a6e0fc0c4fb029c83a19f2d2d3f4c1cb2f781ac3490","first_computed_at":"2026-05-18T01:36:20.993607Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:20.993607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SDlXTQlRUX2SR5e53DXP9+0hXk6nN/zDg9gQS4p7oQKMr+cf1ZakGmOoDN+LA9I9tLAdYlrqNCE6qYcpb9tpAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:20.994189Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.2489","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68b55ea5b5c4df30a38176dfcec0a46eb28ba05299c5d53f4650e6a16a2e3aff","sha256:5fd8a8af2b0fb5a7a37695e2a3cb8ef66317efbf29e63b62a43f3953f9f2c006"],"state_sha256":"4665ba9b73968f99f6e9c5f79f115e95aff37e5c004f95ed2061c760835f58bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ALRzKLIxjd4ynshPrE+nwdT6RNalKP3NnsUq41gNVtiayK6KXm5YjuNRSktCTxIaDKorqMPq96DANFbqcizsAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T06:37:16.177056Z","bundle_sha256":"85df1fc81246f11b2a31b65b2db61343e97f2eeb032f9c72cd285859cf94cd5e"}}