{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:M3UJOLTQVG6HP4RCIWQLIDODQJ","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":"2722153e1cf374f24fea30c695b64953e3fba4091b76dc237adc1272de508f01","cross_cats_sorted":["math.GN","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-01-12T11:34:59Z","title_canon_sha256":"d340b5eb32b4e16e9bc4cf8c9fd2e066a50daa46a9c4c3680d030604531d0ae0"},"schema_version":"1.0","source":{"id":"1501.02606","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02606","created_at":"2026-05-18T00:15:24Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02606v6","created_at":"2026-05-18T00:15:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02606","created_at":"2026-05-18T00:15:24Z"},{"alias_kind":"pith_short_12","alias_value":"M3UJOLTQVG6H","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"M3UJOLTQVG6HP4RC","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"M3UJOLTQ","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:c5a1023e1fb976916771d2216a687b6c9b44b82f533a73a83b16a6c2e464fdb6","target":"graph","created_at":"2026-05-18T00:15:24Z","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":"It is shown that, in the Gromov space of isometry classes of pointed proper metric spaces, the equivalence relations defined by existence of coarse quasi-isometries or being at finite Gromov-Hausdorff distance, cannot be reduced to the equivalence relation defined by any Polish action.","authors_text":"Alberto Candel, Jes\\'us A. \\'Alvarez L\\'opez","cross_cats":["math.GN","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-01-12T11:34:59Z","title":"Non-reduction of relations in the Gromov space to Polish actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02606","kind":"arxiv","version":6},"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":"sha256:7fdce859b79a5a7330bcec593266ff966bf0f5c330c6250a666dea9f7ad8b407","target":"record","created_at":"2026-05-18T00:15:24Z","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":"2722153e1cf374f24fea30c695b64953e3fba4091b76dc237adc1272de508f01","cross_cats_sorted":["math.GN","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-01-12T11:34:59Z","title_canon_sha256":"d340b5eb32b4e16e9bc4cf8c9fd2e066a50daa46a9c4c3680d030604531d0ae0"},"schema_version":"1.0","source":{"id":"1501.02606","kind":"arxiv","version":6}},"canonical_sha256":"66e8972e70a9bc77f22245a0b40dc3825bca90ce4932e7eda99bfbb26744e5c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66e8972e70a9bc77f22245a0b40dc3825bca90ce4932e7eda99bfbb26744e5c2","first_computed_at":"2026-05-18T00:15:24.974858Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:24.974858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qFXDuRGyDCVuCGwVjSlMm3JLxhtrKpEWsHajo/52LTWRb/2whAs2dsrtdA2aLceiBwhWsuRhkGDSfiIlwmDCDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:24.975444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.02606","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7fdce859b79a5a7330bcec593266ff966bf0f5c330c6250a666dea9f7ad8b407","sha256:c5a1023e1fb976916771d2216a687b6c9b44b82f533a73a83b16a6c2e464fdb6"],"state_sha256":"671aa73d7bd651e920c1ff9e240142935adbced17f757a2b3214de39ede101a4"}