{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DURXHY5NASCSTLHRA5ZXWC24FF","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":"5df0feff9d38fec7731ed7eea779acfe01fe860f19f804b0ebb75435e4e4d420","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-06-17T12:58:27Z","title_canon_sha256":"79ed2bcba58c30640cbedc06bc2b64782ab6229ba3e84c4b98622c268c7d9151"},"schema_version":"1.0","source":{"id":"1306.3840","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3840","created_at":"2026-05-18T03:20:46Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3840v1","created_at":"2026-05-18T03:20:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3840","created_at":"2026-05-18T03:20:46Z"},{"alias_kind":"pith_short_12","alias_value":"DURXHY5NASCS","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DURXHY5NASCSTLHR","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DURXHY5N","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:5bc0321dc2742268835ef84392d31f39e2e859776484170559029ca3caac89a3","target":"graph","created_at":"2026-05-18T03:20:46Z","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":"For a free partial action of a group in a set we realize the associated partial skew group ring as an algebra of functions with finite support over an equivalence relation and we use this result to characterize the ideals in the partial skew group ring. This generalizes, to the purely algebraic setting, the known characterization of partial C*-crossed products as groupoid C*-algebras. For completeness we include a new proof of the C* result for free partial actions.","authors_text":"Daniel Gon\\c{c}alves, Viviane M. Beuter","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-06-17T12:58:27Z","title":"Partial crossed products as equivalence relation algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3840","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":"sha256:5a408cabfeee7860656cc136581d133fd8a71c1d96c38665316ef64376506bb1","target":"record","created_at":"2026-05-18T03:20:46Z","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":"5df0feff9d38fec7731ed7eea779acfe01fe860f19f804b0ebb75435e4e4d420","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-06-17T12:58:27Z","title_canon_sha256":"79ed2bcba58c30640cbedc06bc2b64782ab6229ba3e84c4b98622c268c7d9151"},"schema_version":"1.0","source":{"id":"1306.3840","kind":"arxiv","version":1}},"canonical_sha256":"1d2373e3ad048529acf107737b0b5c296e7c188e2bc553685250bf435357b0a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d2373e3ad048529acf107737b0b5c296e7c188e2bc553685250bf435357b0a6","first_computed_at":"2026-05-18T03:20:46.207968Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:46.207968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IUNXDHFxgCWinrNrudS1FLJgl8K+76btQt1XcCqB+tsdF5HB+KA9PDeDj+g6q0iWBGS7fJIMebo72tI9mXD5Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:46.208675Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.3840","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a408cabfeee7860656cc136581d133fd8a71c1d96c38665316ef64376506bb1","sha256:5bc0321dc2742268835ef84392d31f39e2e859776484170559029ca3caac89a3"],"state_sha256":"d02eaab600652d45edd137e79fd65195e119f53f4c18632c7aa8cd76b1e3c6a0"}