{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FEC6G5H5S4RH462B7L3QP3M4XQ","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":"81d3643579dc1fd7a2be4e6e88d1cc0f539754cda2fb3ab5ab669ca10e92e80a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-21T21:58:27Z","title_canon_sha256":"6eca5e0d2204fc123cd7323b4c320015a2d93f76d07deab70775d9e254b944d2"},"schema_version":"1.0","source":{"id":"1901.07094","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.07094","created_at":"2026-05-17T23:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1901.07094v2","created_at":"2026-05-17T23:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.07094","created_at":"2026-05-17T23:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"FEC6G5H5S4RH","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"FEC6G5H5S4RH462B","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"FEC6G5H5","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:c1d8aa547321797e870bda6385efff39127c2571ee25ade26d1c48ac5a976673","target":"graph","created_at":"2026-05-17T23:43:09Z","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 characterize properly purely infinite Steinberg algebras $A_K(\\mathcal{G})$ for strongly effective, ample Hausdorff groupoids $\\mathcal{G}$. As an application, when $\\Lambda$ is a strongly aperiodic $k$-graph, we show that the notions of pure infiniteness and proper pure infiniteness are equivalent for the Kumjian-Pask algebra $\\text{KP}_K(\\Lambda)$, which may be determined by the proper infiniteness of vertex idempotents. In particular, for unital cases, we give simple graph-theoretic criteria for the (proper) pure infiniteness of $\\text{KP}_K(\\Lambda)$.\n  Furthermore, since","authors_text":"Hossein Larki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-21T21:58:27Z","title":"Non-simple purely infinite Steinberg Algebras with applications to Kumjian-Pask algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07094","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":"sha256:019176d33e1420f14e3fdbee64c329a142e7c6c7359f28019323cda09c74c20e","target":"record","created_at":"2026-05-17T23:43:09Z","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":"81d3643579dc1fd7a2be4e6e88d1cc0f539754cda2fb3ab5ab669ca10e92e80a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-21T21:58:27Z","title_canon_sha256":"6eca5e0d2204fc123cd7323b4c320015a2d93f76d07deab70775d9e254b944d2"},"schema_version":"1.0","source":{"id":"1901.07094","kind":"arxiv","version":2}},"canonical_sha256":"2905e374fd97227e7b41faf707ed9cbc0470c6ad72dfec9e97703d67bd6ae6fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2905e374fd97227e7b41faf707ed9cbc0470c6ad72dfec9e97703d67bd6ae6fd","first_computed_at":"2026-05-17T23:43:09.154607Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:09.154607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FcUrx75LDQLKmPBJXAmr4+Itn6rZ3a9ya+VTozp4Pscx0fBkT0PhmLAO/JogxQ4KmNgmIoIX0oESX0NzbZ+zCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:09.155056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.07094","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:019176d33e1420f14e3fdbee64c329a142e7c6c7359f28019323cda09c74c20e","sha256:c1d8aa547321797e870bda6385efff39127c2571ee25ade26d1c48ac5a976673"],"state_sha256":"2570e4c87e5e95462bd9d0055a6191170c0fcf3e14115b43762212f6ac3827a4"}