{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:K3DEKW6QHVMNCVF3ISUE2BZVIK","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":"ff6ccf6ef8f43183ac57ebc1418e1b6e88d1fdbb9381672523b46f150b770312","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-02-13T17:33:58Z","title_canon_sha256":"b21e73c3c305a68e28d335260672c0a498c372c21e950bd9d6f6c76ccc1d6897"},"schema_version":"1.0","source":{"id":"0802.1872","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.1872","created_at":"2026-05-18T02:20:50Z"},{"alias_kind":"arxiv_version","alias_value":"0802.1872v2","created_at":"2026-05-18T02:20:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.1872","created_at":"2026-05-18T02:20:50Z"},{"alias_kind":"pith_short_12","alias_value":"K3DEKW6QHVMN","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"K3DEKW6QHVMNCVF3","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"K3DEKW6Q","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:a41451e757e5fa126186ef56130ab1fcba2d027137486961ad8164eb779785f8","target":"graph","created_at":"2026-05-18T02:20:50Z","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 survey recent progress on the realization problem for von Neumann regular rings, which asks whether every countable conical refinement monoid can be realized as the monoid of isoclasses of finitely generated projective right $R$-modules over a von Neumann regular ring $R$.","authors_text":"Pere Ara","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-02-13T17:33:58Z","title":"The realization problem for von Neumann regular rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.1872","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":"sha256:4616498c39ecb89818b7a4a5576815998ff3626d53fb3af5ebc7ee3ab2eae93c","target":"record","created_at":"2026-05-18T02:20:50Z","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":"ff6ccf6ef8f43183ac57ebc1418e1b6e88d1fdbb9381672523b46f150b770312","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-02-13T17:33:58Z","title_canon_sha256":"b21e73c3c305a68e28d335260672c0a498c372c21e950bd9d6f6c76ccc1d6897"},"schema_version":"1.0","source":{"id":"0802.1872","kind":"arxiv","version":2}},"canonical_sha256":"56c6455bd03d58d154bb44a84d073542aa642060a98be3c713772ab6252c931c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56c6455bd03d58d154bb44a84d073542aa642060a98be3c713772ab6252c931c","first_computed_at":"2026-05-18T02:20:50.261002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:50.261002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QRQcF/JW4rBDaSvyYxC4Lv++FyWEZWLnDeggcbHvJ4SU1wQL8+5t4mMEwTrEoTtJop6uoSYgSCdPl3HYUWkfBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:50.261599Z","signed_message":"canonical_sha256_bytes"},"source_id":"0802.1872","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4616498c39ecb89818b7a4a5576815998ff3626d53fb3af5ebc7ee3ab2eae93c","sha256:a41451e757e5fa126186ef56130ab1fcba2d027137486961ad8164eb779785f8"],"state_sha256":"914fddefb8cab6f74b0b8ac7adb37b75a7b9b3fac575ca34140a0fa8e1d8df56"}