{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:P7YPUSC3ZYZ222CNJXBZBTX6AI","short_pith_number":"pith:P7YPUSC3","canonical_record":{"source":{"id":"2608.01231","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-08-02T13:28:32Z","cross_cats_sorted":[],"title_canon_sha256":"e61c5bcc9510d2781c2b0dc53a83d84bf127110a81cfab234e8776767d6bb89c","abstract_canon_sha256":"c25e351b76a573a3449a657871d4591dd38e120602e9a5b8dbae582ee812271c"},"schema_version":"1.0"},"canonical_sha256":"7ff0fa485bce33ad684d4dc390cefe023b98e443ffe64120239f190e41be5800","source":{"kind":"arxiv","id":"2608.01231","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:P7YPUSC3ZYZ222CNJXBZBTX6AI","target":"record","payload":{"canonical_record":{"source":{"id":"2608.01231","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-08-02T13:28:32Z","cross_cats_sorted":[],"title_canon_sha256":"e61c5bcc9510d2781c2b0dc53a83d84bf127110a81cfab234e8776767d6bb89c","abstract_canon_sha256":"c25e351b76a573a3449a657871d4591dd38e120602e9a5b8dbae582ee812271c"},"schema_version":"1.0"},"canonical_sha256":"7ff0fa485bce33ad684d4dc390cefe023b98e443ffe64120239f190e41be5800","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T02:02:14.326029Z","signature_b64":"MINdu5Xg5z5x59vFjee3FYlcesOzz/rxXaWJ5lgPhq11vwyngg8wWp/BWmjd7c8erdPNk9epMTwRIPSPfEf4CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ff0fa485bce33ad684d4dc390cefe023b98e443ffe64120239f190e41be5800","last_reissued_at":"2026-08-04T02:02:14.324497Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T02:02:14.324497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.01231","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-04T02:02:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6aAu4JYovEvsoAIqpIk1/HGRaVJ2rVdr4bua8geTL0OiN/us9qXGock/6+yepQ6jSNNc7je2NGOfTEvu+3+cCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T21:35:46.879185Z"},"content_sha256":"166096ea2c66e1383f7d89cd88179491900bba4b7ec4bf0e28240698df2be06c","schema_version":"1.0","event_id":"sha256:166096ea2c66e1383f7d89cd88179491900bba4b7ec4bf0e28240698df2be06c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:P7YPUSC3ZYZ222CNJXBZBTX6AI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Borel graphs generated by finitely many bounded-to-1 commuting Borel functions and hyperfinite equivalence relations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ruijun Wang","submitted_at":"2026-08-02T13:28:32Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.01231","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.01231/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-04T02:02:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sNjpa4IHeNghdBkU276PuGAGppnCQcGCvSA3P/xxCRRXBVSHTLDh+aEHNzdM4RZ6kO6SKYCPHO3QWXhRLwKODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T21:35:46.879517Z"},"content_sha256":"0a9bab6c6a688039b3419395ec09efd4580a3f82f7f117ad240b9b72027fcca6","schema_version":"1.0","event_id":"sha256:0a9bab6c6a688039b3419395ec09efd4580a3f82f7f117ad240b9b72027fcca6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P7YPUSC3ZYZ222CNJXBZBTX6AI/bundle.json","state_url":"https://pith.science/pith/P7YPUSC3ZYZ222CNJXBZBTX6AI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P7YPUSC3ZYZ222CNJXBZBTX6AI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-06T21:35:46Z","links":{"resolver":"https://pith.science/pith/P7YPUSC3ZYZ222CNJXBZBTX6AI","bundle":"https://pith.science/pith/P7YPUSC3ZYZ222CNJXBZBTX6AI/bundle.json","state":"https://pith.science/pith/P7YPUSC3ZYZ222CNJXBZBTX6AI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P7YPUSC3ZYZ222CNJXBZBTX6AI/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dNXx2PrSJaH0fZNSbDJDlAlfLzYSAlXvEfxibMNbROFbwjMqzsnp49B0ALeuiaWuS6pKqYq9tCkvQ2RaFJWnAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T21:35:46.882758Z","bundle_sha256":"5e58b0eb7b1afa756a63dd98c4022942efc26d965ad35473559e009f72303ee2"}}