{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:FUOC2LSM3LE7K5VD6APDMEUGJH","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":"7a185cf29b90c5e207b1cc1ee0b3e38cafd987ba1f70c746a5958d11d11366f0","cross_cats_sorted":[],"license":"","primary_cat":"math.OA","submitted_at":"2004-04-29T23:57:48Z","title_canon_sha256":"c1e98d311fcbfadd52852c9ab87de4684fa952b0981fef3b103764d86a988061"},"schema_version":"1.0","source":{"id":"math/0404542","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0404542","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"arxiv_version","alias_value":"math/0404542v1","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0404542","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"pith_short_12","alias_value":"FUOC2LSM3LE7","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"FUOC2LSM3LE7K5VD","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"FUOC2LSM","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:805f82577412243e5babf5985d51d7853341be91b5d7d694b57f8a273074641c","target":"graph","created_at":"2026-05-18T03:37:19Z","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":"In this paper we describe an operation on directed graphs which produces a graph with fewer vertices, such that the C*-algebra of the new graph is Morita equivalent to that of the original graph. We unify and generalize several related constructions, notably delays and desingularizations of directed graphs.","authors_text":"Daniel Gow, Tyrone Crisp","cross_cats":[],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"2004-04-29T23:57:48Z","title":"Contractible subgraphs and Morita equivalence of graph C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0404542","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:ae1875466e517f3173b9c314b98b32574739772d4d4c378cf78c096caebde668","target":"record","created_at":"2026-05-18T03:37:19Z","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":"7a185cf29b90c5e207b1cc1ee0b3e38cafd987ba1f70c746a5958d11d11366f0","cross_cats_sorted":[],"license":"","primary_cat":"math.OA","submitted_at":"2004-04-29T23:57:48Z","title_canon_sha256":"c1e98d311fcbfadd52852c9ab87de4684fa952b0981fef3b103764d86a988061"},"schema_version":"1.0","source":{"id":"math/0404542","kind":"arxiv","version":1}},"canonical_sha256":"2d1c2d2e4cdac9f576a3f01e36128649ecc1239fe666560669f7c6200a449a85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d1c2d2e4cdac9f576a3f01e36128649ecc1239fe666560669f7c6200a449a85","first_computed_at":"2026-05-18T03:37:19.408247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:19.408247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+2A3m3LARJZt6JHqK0z/E0NieW1xjbzrh4uOVZOjek2xh4/gfaOjFYnBC4nr9sjzUPAOiI+bB0v7RHNmxSZ8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:19.408758Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0404542","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae1875466e517f3173b9c314b98b32574739772d4d4c378cf78c096caebde668","sha256:805f82577412243e5babf5985d51d7853341be91b5d7d694b57f8a273074641c"],"state_sha256":"6e6babfc64c8707043e72d77379dab38e58c85cf1136deadb4c3ec79b57463f3"}