{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:BIQGPFORK4AES2O773OIJ5QPAD","short_pith_number":"pith:BIQGPFOR","canonical_record":{"source":{"id":"0707.0038","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"2007-06-30T02:35:32Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"c3cd08edcffacee5cc8c6e1683b0b27d2df3bde1734e8e6d4b3954af9dbcdac6","abstract_canon_sha256":"2f2953f4a28675b3e08d1c1ecab3afd1271cb0768d49298b85036928b7d7cbf5"},"schema_version":"1.0"},"canonical_sha256":"0a206795d157004969dffedc84f60f00d8304a8ce704b38236ac7a1842d8fd92","source":{"kind":"arxiv","id":"0707.0038","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.0038","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"arxiv_version","alias_value":"0707.0038v2","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.0038","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"pith_short_12","alias_value":"BIQGPFORK4AE","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"BIQGPFORK4AES2O7","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"BIQGPFOR","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:BIQGPFORK4AES2O773OIJ5QPAD","target":"record","payload":{"canonical_record":{"source":{"id":"0707.0038","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"2007-06-30T02:35:32Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"c3cd08edcffacee5cc8c6e1683b0b27d2df3bde1734e8e6d4b3954af9dbcdac6","abstract_canon_sha256":"2f2953f4a28675b3e08d1c1ecab3afd1271cb0768d49298b85036928b7d7cbf5"},"schema_version":"1.0"},"canonical_sha256":"0a206795d157004969dffedc84f60f00d8304a8ce704b38236ac7a1842d8fd92","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:15.895681Z","signature_b64":"J1+b4cMu7mKbCr21iipIrsE+AXhZn26DHa2RwjUOoTOCAgATqE1A9+XTOKwogKuxf8HVckcRDKyxqWfkfX8XAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a206795d157004969dffedc84f60f00d8304a8ce704b38236ac7a1842d8fd92","last_reissued_at":"2026-05-18T04:09:15.895036Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:15.895036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0707.0038","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":"2026-05-18T04:09:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"csLDqSzwBOMfZliE+UEJINJPYCodWWWxDEPJr36sRnNXSA/cInA5atsXv+Mslay0nAxIJ420VQvLZtW1x9h9Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T10:53:18.259187Z"},"content_sha256":"075cda6ad2b132f2d4c8a411b65fc8237a984cfe235bb6173c509198a56e2123","schema_version":"1.0","event_id":"sha256:075cda6ad2b132f2d4c8a411b65fc8237a984cfe235bb6173c509198a56e2123"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:BIQGPFORK4AES2O773OIJ5QPAD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cluster-tilted algebras and slices","license":"","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Ibrahim Assem, Ralf Schiffler, Thomas Bruestle","submitted_at":"2007-06-30T02:35:32Z","abstract_excerpt":"We give a criterion allowing to verify whether or not two tilted algebras have the same relation-extension (thus correspond to the same cluster-tilted algebra). This criterion is in terms of a combinatorial configuration in the Auslander-Reiten quiver of the cluster-tilted algebra, which we call local slice."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.0038","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":""},"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":"2026-05-18T04:09:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tnNmNxmSaKsYDuYd7GhdIFiq3gyKsl2EGvfF5eWaXtbZchK7T2dj7SiSDzY6HYmFUr1QrBjfMV9PqWb73SA7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T10:53:18.259547Z"},"content_sha256":"85e43672fe18ed9d2d0813ebe6397561b0b48b268cd3b10079605022d763a2e9","schema_version":"1.0","event_id":"sha256:85e43672fe18ed9d2d0813ebe6397561b0b48b268cd3b10079605022d763a2e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BIQGPFORK4AES2O773OIJ5QPAD/bundle.json","state_url":"https://pith.science/pith/BIQGPFORK4AES2O773OIJ5QPAD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BIQGPFORK4AES2O773OIJ5QPAD/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":"2026-06-11T10:53:18Z","links":{"resolver":"https://pith.science/pith/BIQGPFORK4AES2O773OIJ5QPAD","bundle":"https://pith.science/pith/BIQGPFORK4AES2O773OIJ5QPAD/bundle.json","state":"https://pith.science/pith/BIQGPFORK4AES2O773OIJ5QPAD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BIQGPFORK4AES2O773OIJ5QPAD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:BIQGPFORK4AES2O773OIJ5QPAD","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":"2f2953f4a28675b3e08d1c1ecab3afd1271cb0768d49298b85036928b7d7cbf5","cross_cats_sorted":["math.RA"],"license":"","primary_cat":"math.RT","submitted_at":"2007-06-30T02:35:32Z","title_canon_sha256":"c3cd08edcffacee5cc8c6e1683b0b27d2df3bde1734e8e6d4b3954af9dbcdac6"},"schema_version":"1.0","source":{"id":"0707.0038","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.0038","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"arxiv_version","alias_value":"0707.0038v2","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.0038","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"pith_short_12","alias_value":"BIQGPFORK4AE","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"BIQGPFORK4AES2O7","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"BIQGPFOR","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:85e43672fe18ed9d2d0813ebe6397561b0b48b268cd3b10079605022d763a2e9","target":"graph","created_at":"2026-05-18T04:09:15Z","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 criterion allowing to verify whether or not two tilted algebras have the same relation-extension (thus correspond to the same cluster-tilted algebra). This criterion is in terms of a combinatorial configuration in the Auslander-Reiten quiver of the cluster-tilted algebra, which we call local slice.","authors_text":"Ibrahim Assem, Ralf Schiffler, Thomas Bruestle","cross_cats":["math.RA"],"headline":"","license":"","primary_cat":"math.RT","submitted_at":"2007-06-30T02:35:32Z","title":"Cluster-tilted algebras and slices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.0038","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":"sha256:075cda6ad2b132f2d4c8a411b65fc8237a984cfe235bb6173c509198a56e2123","target":"record","created_at":"2026-05-18T04:09:15Z","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":"2f2953f4a28675b3e08d1c1ecab3afd1271cb0768d49298b85036928b7d7cbf5","cross_cats_sorted":["math.RA"],"license":"","primary_cat":"math.RT","submitted_at":"2007-06-30T02:35:32Z","title_canon_sha256":"c3cd08edcffacee5cc8c6e1683b0b27d2df3bde1734e8e6d4b3954af9dbcdac6"},"schema_version":"1.0","source":{"id":"0707.0038","kind":"arxiv","version":2}},"canonical_sha256":"0a206795d157004969dffedc84f60f00d8304a8ce704b38236ac7a1842d8fd92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a206795d157004969dffedc84f60f00d8304a8ce704b38236ac7a1842d8fd92","first_computed_at":"2026-05-18T04:09:15.895036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:15.895036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J1+b4cMu7mKbCr21iipIrsE+AXhZn26DHa2RwjUOoTOCAgATqE1A9+XTOKwogKuxf8HVckcRDKyxqWfkfX8XAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:15.895681Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.0038","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:075cda6ad2b132f2d4c8a411b65fc8237a984cfe235bb6173c509198a56e2123","sha256:85e43672fe18ed9d2d0813ebe6397561b0b48b268cd3b10079605022d763a2e9"],"state_sha256":"c93ea8df3f591e93128e3933620b67a3da3a977823544fb3ef372356b18142a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LnR30ZD9+lKSWmb3l140bTXm5XfgTGHhE8dyofqCOMxz1k7lrQVAo9K9lPx0Dx2cR1LsJ9UVWdsi9e0QaoLSDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T10:53:18.261473Z","bundle_sha256":"c3a89a253f4aac11666d448cc11b2ca196c963fe1fbfcd29ad886ab2a579136d"}}