{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:SGDZXK5QLUPRPJMIJJVENBREHI","short_pith_number":"pith:SGDZXK5Q","canonical_record":{"source":{"id":"1204.3366","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-04-16T05:39:31Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"b7eb9e27b0a9e691f2ae51b049610a8bd9b798888668ba5a1bd0d955367e54f0","abstract_canon_sha256":"08f7f46b27b9fdcbfc916799f6351185042999e6fd363c985be9c95c9ccfe8cd"},"schema_version":"1.0"},"canonical_sha256":"91879babb05d1f17a5884a6a4686243a17c9ba47758e54a9683d2efd13d2be55","source":{"kind":"arxiv","id":"1204.3366","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3366","created_at":"2026-05-18T03:57:51Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3366v1","created_at":"2026-05-18T03:57:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3366","created_at":"2026-05-18T03:57:51Z"},{"alias_kind":"pith_short_12","alias_value":"SGDZXK5QLUPR","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SGDZXK5QLUPRPJMI","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SGDZXK5Q","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:SGDZXK5QLUPRPJMIJJVENBREHI","target":"record","payload":{"canonical_record":{"source":{"id":"1204.3366","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-04-16T05:39:31Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"b7eb9e27b0a9e691f2ae51b049610a8bd9b798888668ba5a1bd0d955367e54f0","abstract_canon_sha256":"08f7f46b27b9fdcbfc916799f6351185042999e6fd363c985be9c95c9ccfe8cd"},"schema_version":"1.0"},"canonical_sha256":"91879babb05d1f17a5884a6a4686243a17c9ba47758e54a9683d2efd13d2be55","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:51.711044Z","signature_b64":"bSmr98CS7WyTZBuBcR1SzM9aPkVknfrEP9PStI5nU0W1r6as5fxmHKUQuSW7bvvzIFZmNCAZ45d2YlRF1FD1DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91879babb05d1f17a5884a6a4686243a17c9ba47758e54a9683d2efd13d2be55","last_reissued_at":"2026-05-18T03:57:51.710371Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:51.710371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.3366","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":"2026-05-18T03:57:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gcLn0F73MGgPZIKRTJKJnZldedWNAmeA+okLQRjJRhk1uKRLv9kTfk+qyfBQOHSI6qHMd63NpAifuEQjxzueAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T01:38:57.430887Z"},"content_sha256":"ed63b1ba12ddd2d3e1690e13d430437ef2ecfcd0f9f1c74aaa57cea15f8adb18","schema_version":"1.0","event_id":"sha256:ed63b1ba12ddd2d3e1690e13d430437ef2ecfcd0f9f1c74aaa57cea15f8adb18"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:SGDZXK5QLUPRPJMIJJVENBREHI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on the isomorphism conjectures for Leavitt path algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.RA","authors_text":"R. Hazrat","submitted_at":"2012-04-16T05:39:31Z","abstract_excerpt":"We relate two conjectures which have been raised for classification of Leavitt path algebras. For purely infinite simple unital Leavitt path algebras, it is conjectured that K_0 classifies them completely. For arbitrary Leavitt path algebras, it is conjectured that K^{\\gr}_0 classifies them completely \\cite{hazann}. We show that for two finite graphs with no sinks (which their associated Leavitt path algebras include the purely infinite simple ones) if their K^{\\gr}_0-groups of their Leavitt path algebras are isomorphic then their K_0-groups are isomorphic as well."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3366","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":"2026-05-18T03:57:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NjTCYbEVGWH/wQawJoDTayc9EU+boV0bD0w94yTbp/eZ7bWsZUil8yI5bqQ8V19ge/ekYIt17DKsJ/diLA6yDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T01:38:57.431229Z"},"content_sha256":"4b54c1fcfbb17cfcb0ba078e4c487549c6de1d51f14d3113543e3c19b29dda0b","schema_version":"1.0","event_id":"sha256:4b54c1fcfbb17cfcb0ba078e4c487549c6de1d51f14d3113543e3c19b29dda0b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SGDZXK5QLUPRPJMIJJVENBREHI/bundle.json","state_url":"https://pith.science/pith/SGDZXK5QLUPRPJMIJJVENBREHI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SGDZXK5QLUPRPJMIJJVENBREHI/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":"2026-06-27T01:38:57Z","links":{"resolver":"https://pith.science/pith/SGDZXK5QLUPRPJMIJJVENBREHI","bundle":"https://pith.science/pith/SGDZXK5QLUPRPJMIJJVENBREHI/bundle.json","state":"https://pith.science/pith/SGDZXK5QLUPRPJMIJJVENBREHI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SGDZXK5QLUPRPJMIJJVENBREHI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SGDZXK5QLUPRPJMIJJVENBREHI","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":"08f7f46b27b9fdcbfc916799f6351185042999e6fd363c985be9c95c9ccfe8cd","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-04-16T05:39:31Z","title_canon_sha256":"b7eb9e27b0a9e691f2ae51b049610a8bd9b798888668ba5a1bd0d955367e54f0"},"schema_version":"1.0","source":{"id":"1204.3366","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3366","created_at":"2026-05-18T03:57:51Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3366v1","created_at":"2026-05-18T03:57:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3366","created_at":"2026-05-18T03:57:51Z"},{"alias_kind":"pith_short_12","alias_value":"SGDZXK5QLUPR","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SGDZXK5QLUPRPJMI","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SGDZXK5Q","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:4b54c1fcfbb17cfcb0ba078e4c487549c6de1d51f14d3113543e3c19b29dda0b","target":"graph","created_at":"2026-05-18T03:57:51Z","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 relate two conjectures which have been raised for classification of Leavitt path algebras. For purely infinite simple unital Leavitt path algebras, it is conjectured that K_0 classifies them completely. For arbitrary Leavitt path algebras, it is conjectured that K^{\\gr}_0 classifies them completely \\cite{hazann}. We show that for two finite graphs with no sinks (which their associated Leavitt path algebras include the purely infinite simple ones) if their K^{\\gr}_0-groups of their Leavitt path algebras are isomorphic then their K_0-groups are isomorphic as well.","authors_text":"R. Hazrat","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-04-16T05:39:31Z","title":"A note on the isomorphism conjectures for Leavitt path algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3366","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:ed63b1ba12ddd2d3e1690e13d430437ef2ecfcd0f9f1c74aaa57cea15f8adb18","target":"record","created_at":"2026-05-18T03:57:51Z","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":"08f7f46b27b9fdcbfc916799f6351185042999e6fd363c985be9c95c9ccfe8cd","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-04-16T05:39:31Z","title_canon_sha256":"b7eb9e27b0a9e691f2ae51b049610a8bd9b798888668ba5a1bd0d955367e54f0"},"schema_version":"1.0","source":{"id":"1204.3366","kind":"arxiv","version":1}},"canonical_sha256":"91879babb05d1f17a5884a6a4686243a17c9ba47758e54a9683d2efd13d2be55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91879babb05d1f17a5884a6a4686243a17c9ba47758e54a9683d2efd13d2be55","first_computed_at":"2026-05-18T03:57:51.710371Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:51.710371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bSmr98CS7WyTZBuBcR1SzM9aPkVknfrEP9PStI5nU0W1r6as5fxmHKUQuSW7bvvzIFZmNCAZ45d2YlRF1FD1DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:51.711044Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3366","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed63b1ba12ddd2d3e1690e13d430437ef2ecfcd0f9f1c74aaa57cea15f8adb18","sha256:4b54c1fcfbb17cfcb0ba078e4c487549c6de1d51f14d3113543e3c19b29dda0b"],"state_sha256":"ca9423b6a031ae9a643f540de95188847fd436f56a9cd4a3b025b8bbed9c6056"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wf8DJZz7a24aUeRPfRbFBKa5n67dxuYjS02AB3TjNVFosPcHAYkZ9vsTOSbkY0+QKDolGJYQQu+E1vNG/VgTDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T01:38:57.433122Z","bundle_sha256":"92e70178d61124a73c531ecf3db7dfe2d6bae00063e3ea56b639603ece835068"}}