{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:MZ2PXD2TRW6NHJQRSEYSIHABBM","short_pith_number":"pith:MZ2PXD2T","canonical_record":{"source":{"id":"1202.2704","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-02-13T12:28:25Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"3d28a8540c0e0aa6f89d8436e4749ed56aeb5b19ae7ea6ce4f87d013f44072d3","abstract_canon_sha256":"5bf59ab9ce0aa71a0c98f97d4b47deb4e188438a9a25ac64a22cb03a9fa1d15a"},"schema_version":"1.0"},"canonical_sha256":"6674fb8f538dbcd3a6119131241c010b3f775fc8379679396260583e22e364bd","source":{"kind":"arxiv","id":"1202.2704","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2704","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2704v1","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2704","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"pith_short_12","alias_value":"MZ2PXD2TRW6N","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MZ2PXD2TRW6NHJQR","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MZ2PXD2T","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:MZ2PXD2TRW6NHJQRSEYSIHABBM","target":"record","payload":{"canonical_record":{"source":{"id":"1202.2704","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-02-13T12:28:25Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"3d28a8540c0e0aa6f89d8436e4749ed56aeb5b19ae7ea6ce4f87d013f44072d3","abstract_canon_sha256":"5bf59ab9ce0aa71a0c98f97d4b47deb4e188438a9a25ac64a22cb03a9fa1d15a"},"schema_version":"1.0"},"canonical_sha256":"6674fb8f538dbcd3a6119131241c010b3f775fc8379679396260583e22e364bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:25.876239Z","signature_b64":"HoMzay1cc/lpD61GwoiEJxnxpownPlEG2mzQ5R6Kef39hhupLWaoT7D1CMxitDN90iw4SWRATIDLMXWuBYS5Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6674fb8f538dbcd3a6119131241c010b3f775fc8379679396260583e22e364bd","last_reissued_at":"2026-05-18T04:02:25.875712Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:25.875712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.2704","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":"2026-05-18T04:02:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I6PB6IR7s5FvY/yP4sck2sx6XB4bmf+mc5h2lIoybmo5LGacs8r8kwqvqXehi9falT2vV0uyjCXoBH4QtYMsAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:00:43.581401Z"},"content_sha256":"92233aaeaa4ba8f1bb18194a644252de1fc3be3e597959c94350371439cffde7","schema_version":"1.0","event_id":"sha256:92233aaeaa4ba8f1bb18194a644252de1fc3be3e597959c94350371439cffde7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:MZ2PXD2TRW6NHJQRSEYSIHABBM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Leavitt path algebras as partial skew group rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.RA","authors_text":"Daniel Gon\\c{c}alves, Danilo Royer","submitted_at":"2012-02-13T12:28:25Z","abstract_excerpt":"We realize Leavitt path algebras as partial skew group rings and give new proofs, based on partial skew group ring theory, of the Cuntz-Krieger uniqueness theorem and simplicity criteria for Leavitt path algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2704","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":"2026-05-18T04:02:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GOVUdktf+bUiMhr90JTC4eFXSgrqfKAR2yFTf88iEsrsdcIG1yAvdQlR60Bm2hztgEGUxEnzlZRY5FaML+nwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:00:43.582070Z"},"content_sha256":"0a37f6b25d649b19b856cbd625a9de9b5f7758e8b870e932299ccd005af32351","schema_version":"1.0","event_id":"sha256:0a37f6b25d649b19b856cbd625a9de9b5f7758e8b870e932299ccd005af32351"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MZ2PXD2TRW6NHJQRSEYSIHABBM/bundle.json","state_url":"https://pith.science/pith/MZ2PXD2TRW6NHJQRSEYSIHABBM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MZ2PXD2TRW6NHJQRSEYSIHABBM/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":"2026-06-02T06:00:43Z","links":{"resolver":"https://pith.science/pith/MZ2PXD2TRW6NHJQRSEYSIHABBM","bundle":"https://pith.science/pith/MZ2PXD2TRW6NHJQRSEYSIHABBM/bundle.json","state":"https://pith.science/pith/MZ2PXD2TRW6NHJQRSEYSIHABBM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MZ2PXD2TRW6NHJQRSEYSIHABBM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MZ2PXD2TRW6NHJQRSEYSIHABBM","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":"5bf59ab9ce0aa71a0c98f97d4b47deb4e188438a9a25ac64a22cb03a9fa1d15a","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-02-13T12:28:25Z","title_canon_sha256":"3d28a8540c0e0aa6f89d8436e4749ed56aeb5b19ae7ea6ce4f87d013f44072d3"},"schema_version":"1.0","source":{"id":"1202.2704","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2704","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2704v1","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2704","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"pith_short_12","alias_value":"MZ2PXD2TRW6N","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MZ2PXD2TRW6NHJQR","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MZ2PXD2T","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:0a37f6b25d649b19b856cbd625a9de9b5f7758e8b870e932299ccd005af32351","target":"graph","created_at":"2026-05-18T04:02:25Z","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 realize Leavitt path algebras as partial skew group rings and give new proofs, based on partial skew group ring theory, of the Cuntz-Krieger uniqueness theorem and simplicity criteria for Leavitt path algebras.","authors_text":"Daniel Gon\\c{c}alves, Danilo Royer","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-02-13T12:28:25Z","title":"Leavitt path algebras as partial skew group rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2704","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":"sha256:92233aaeaa4ba8f1bb18194a644252de1fc3be3e597959c94350371439cffde7","target":"record","created_at":"2026-05-18T04:02:25Z","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":"5bf59ab9ce0aa71a0c98f97d4b47deb4e188438a9a25ac64a22cb03a9fa1d15a","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-02-13T12:28:25Z","title_canon_sha256":"3d28a8540c0e0aa6f89d8436e4749ed56aeb5b19ae7ea6ce4f87d013f44072d3"},"schema_version":"1.0","source":{"id":"1202.2704","kind":"arxiv","version":1}},"canonical_sha256":"6674fb8f538dbcd3a6119131241c010b3f775fc8379679396260583e22e364bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6674fb8f538dbcd3a6119131241c010b3f775fc8379679396260583e22e364bd","first_computed_at":"2026-05-18T04:02:25.875712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:25.875712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HoMzay1cc/lpD61GwoiEJxnxpownPlEG2mzQ5R6Kef39hhupLWaoT7D1CMxitDN90iw4SWRATIDLMXWuBYS5Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:25.876239Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2704","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92233aaeaa4ba8f1bb18194a644252de1fc3be3e597959c94350371439cffde7","sha256:0a37f6b25d649b19b856cbd625a9de9b5f7758e8b870e932299ccd005af32351"],"state_sha256":"387310bd2fbe8c14cc1c0b7960fcd67c44f71d3b412195932808dd355d9014c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iTKT3PMtU0fLViLuhWIOXOYN5urmS8v/RMgK8gH0BT6gghXWuUWaVkM66ftkpvg3Hw23KDRro60QFyyrfV/UBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T06:00:43.584725Z","bundle_sha256":"0b74d056f00494efda2ddaa48f14f52daa7a62c33513f8ec88239b8f21bb324e"}}