{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:P7YPUSC3ZYZ222CNJXBZBTX6AI","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":"c25e351b76a573a3449a657871d4591dd38e120602e9a5b8dbae582ee812271c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-08-02T13:28:32Z","title_canon_sha256":"e61c5bcc9510d2781c2b0dc53a83d84bf127110a81cfab234e8776767d6bb89c"},"schema_version":"1.0","source":{"id":"2608.01231","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.01231","created_at":"2026-08-04T02:02:14Z"},{"alias_kind":"arxiv_version","alias_value":"2608.01231v1","created_at":"2026-08-04T02:02:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.01231","created_at":"2026-08-04T02:02:14Z"},{"alias_kind":"pith_short_12","alias_value":"P7YPUSC3ZYZ2","created_at":"2026-08-04T02:02:14Z"},{"alias_kind":"pith_short_16","alias_value":"P7YPUSC3ZYZ222CN","created_at":"2026-08-04T02:02:14Z"},{"alias_kind":"pith_short_8","alias_value":"P7YPUSC3","created_at":"2026-08-04T02:02:14Z"}],"graph_snapshots":[{"event_id":"sha256:0a9bab6c6a688039b3419395ec09efd4580a3f82f7f117ad240b9b72027fcca6","target":"graph","created_at":"2026-08-04T02:02:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.01231/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that a Borel graph generated by finitely many bounded-to-1 commuting functions is hyperfinite. This recovers a theorem in the forthcoming paper by Naryshkin, Shinko, Weilacher and Yu.","authors_text":"Ruijun Wang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-08-02T13:28:32Z","title":"Borel graphs generated by finitely many bounded-to-1 commuting Borel functions and hyperfinite equivalence relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.01231","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":"sha256:166096ea2c66e1383f7d89cd88179491900bba4b7ec4bf0e28240698df2be06c","target":"record","created_at":"2026-08-04T02:02:14Z","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":"c25e351b76a573a3449a657871d4591dd38e120602e9a5b8dbae582ee812271c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-08-02T13:28:32Z","title_canon_sha256":"e61c5bcc9510d2781c2b0dc53a83d84bf127110a81cfab234e8776767d6bb89c"},"schema_version":"1.0","source":{"id":"2608.01231","kind":"arxiv","version":1}},"canonical_sha256":"7ff0fa485bce33ad684d4dc390cefe023b98e443ffe64120239f190e41be5800","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ff0fa485bce33ad684d4dc390cefe023b98e443ffe64120239f190e41be5800","first_computed_at":"2026-08-04T02:02:14.324497Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-04T02:02:14.324497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MINdu5Xg5z5x59vFjee3FYlcesOzz/rxXaWJ5lgPhq11vwyngg8wWp/BWmjd7c8erdPNk9epMTwRIPSPfEf4CA==","signature_status":"signed_v1","signed_at":"2026-08-04T02:02:14.326029Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.01231","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:166096ea2c66e1383f7d89cd88179491900bba4b7ec4bf0e28240698df2be06c","sha256:0a9bab6c6a688039b3419395ec09efd4580a3f82f7f117ad240b9b72027fcca6"],"state_sha256":"32cfccf5714a92eb60edfa262f1b917b761b3219403e5e7b04112620407ca27e"}