{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NJRIM7LWVTHIWOU457W44HB5DM","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":"af6d54de1a28a6f60cf84dfb97ec75a0583eceee88b2ace04ae75a78835aab54","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-03-15T13:07:54Z","title_canon_sha256":"434852be26a36979267481f5f5b3bf3fea3b240762cb5993ed3e87f9d1a6eeed"},"schema_version":"1.0","source":{"id":"1403.3799","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3799","created_at":"2026-05-18T01:22:24Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3799v2","created_at":"2026-05-18T01:22:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3799","created_at":"2026-05-18T01:22:24Z"},{"alias_kind":"pith_short_12","alias_value":"NJRIM7LWVTHI","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NJRIM7LWVTHIWOU4","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NJRIM7LW","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:67bf30b0b86af2d7e88151ea220e825f622d7ecdf246f98e19d07da35e4086b7","target":"graph","created_at":"2026-05-18T01:22:24Z","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":"This paper continues our investigation into the question of when a homotopy $\\omega = \\{\\omega_t\\}_{t \\in [0,1]}$ of 2-cocycles on a locally compact Hausdorff groupoid $\\mathcal{G}$ gives rise to an isomorphism of the $K$-theory groups of the twisted groupoid $C^*$-algebras: $K_*(C^*(\\mathcal{G}, \\omega_0)) \\cong K_*(C^*(\\mathcal{G}, \\omega_1)).$ In particular, we build on work by Kumjian, Pask, and Sims to show that if $\\mathcal{G} = \\mathcal{G}_\\Lambda$ is the infinite path groupoid associated to a row-finite higher-rank graph $\\Lambda$ with no sources, and $\\{c_t\\}_{t \\in [0,1]}$ is a homot","authors_text":"Elizabeth Gillaspy","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-03-15T13:07:54Z","title":"$K$-theory and homotopies of 2-cocycles on higher-rank graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3799","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":"sha256:2ac935ed71ae5c3e2dd11b9f84aa0e08780ec49d05262d0c96c3d738c5b36a76","target":"record","created_at":"2026-05-18T01:22:24Z","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":"af6d54de1a28a6f60cf84dfb97ec75a0583eceee88b2ace04ae75a78835aab54","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-03-15T13:07:54Z","title_canon_sha256":"434852be26a36979267481f5f5b3bf3fea3b240762cb5993ed3e87f9d1a6eeed"},"schema_version":"1.0","source":{"id":"1403.3799","kind":"arxiv","version":2}},"canonical_sha256":"6a62867d76acce8b3a9cefedce1c3d1b3fdb45bc061eb0460c47ed216062e3cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a62867d76acce8b3a9cefedce1c3d1b3fdb45bc061eb0460c47ed216062e3cb","first_computed_at":"2026-05-18T01:22:24.275161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:24.275161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g68CPgCBbv7GieSrYbi9ZanNfcpdhrBWInY95uL6+6mKxqkGUTi/aER2M0G3LRSja+GiJ+Ond65iF97itbk1Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:24.275912Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.3799","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ac935ed71ae5c3e2dd11b9f84aa0e08780ec49d05262d0c96c3d738c5b36a76","sha256:67bf30b0b86af2d7e88151ea220e825f622d7ecdf246f98e19d07da35e4086b7"],"state_sha256":"491def3a7b6dde76db50d4f89d23ddb6da456bf438ed8f63be26f967396c47df"}