{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6AMAB6UBZMWT44FYL36EUSFG7H","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":"d2a2eccea37a2be2f69888fbb4066d4f45a29e1703a788024eac18f592b2e5ce","cross_cats_sorted":["math.GR","math.KT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-07-22T17:39:07Z","title_canon_sha256":"525b18cfb6110c3a118ddd528cc3a1efc35cca894216ba87fc67647d757082f7"},"schema_version":"1.0","source":{"id":"1007.3952","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.3952","created_at":"2026-05-18T03:26:10Z"},{"alias_kind":"arxiv_version","alias_value":"1007.3952v5","created_at":"2026-05-18T03:26:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.3952","created_at":"2026-05-18T03:26:10Z"},{"alias_kind":"pith_short_12","alias_value":"6AMAB6UBZMWT","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6AMAB6UBZMWT44FY","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6AMAB6UB","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:a3268c939ef0ce28cdebdc5a2523e6ed900aeb1eb61d5a124016945c127ef0a7","target":"graph","created_at":"2026-05-18T03:26:10Z","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"},"paper":{"abstract_excerpt":"We calculate the K-theory of the Cuntz-Krieger algebra ${\\cal O}_E$ associated with an infinite, locally finite graph, via the Bass-Hashimoto operator. The formulae we get express the Grothendieck group and the Whitehead group in purely graph theoretic terms.\n  We consider the category of finite (black-and-white, bi-directed) subgraphs with certain graph homomorphisms and construct a continuous functor to abelian groups. In this category $K_0$ is an inductive limit of $K$-groups of finite graphs, which were calculated in \\cite{MM}.\n  In the case of an infinite graph with the finite Betti numbe","authors_text":"Natalia Iyudu","cross_cats":["math.GR","math.KT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-07-22T17:39:07Z","title":"K-theory of locally finite graph $C^*$-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3952","kind":"arxiv","version":5},"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":"sha256:01da78510bb85f99ed204f029aff7b78302038195417c727b33524554a0b3b9d","target":"record","created_at":"2026-05-18T03:26:10Z","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":"d2a2eccea37a2be2f69888fbb4066d4f45a29e1703a788024eac18f592b2e5ce","cross_cats_sorted":["math.GR","math.KT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-07-22T17:39:07Z","title_canon_sha256":"525b18cfb6110c3a118ddd528cc3a1efc35cca894216ba87fc67647d757082f7"},"schema_version":"1.0","source":{"id":"1007.3952","kind":"arxiv","version":5}},"canonical_sha256":"f01800fa81cb2d3e70b85efc4a48a6f9e486dc546986ac91a981613640afe21f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f01800fa81cb2d3e70b85efc4a48a6f9e486dc546986ac91a981613640afe21f","first_computed_at":"2026-05-18T03:26:10.633238Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:10.633238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I7YHBRLroJQJb7xHF3aef5H5ISjmlwjvGOGYpbwgp6HYQPoZDSB/yn3+LTJkajOWFbau4DMyXGBhsl3jO3gbAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:10.634019Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.3952","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01da78510bb85f99ed204f029aff7b78302038195417c727b33524554a0b3b9d","sha256:a3268c939ef0ce28cdebdc5a2523e6ed900aeb1eb61d5a124016945c127ef0a7"],"state_sha256":"bb66c84b8a5e4b8bd69935ef347dac1eba9bce6926ae7fab409b0625b8682972"}