{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MFQXE6APW3KL6UXTV2EQJQKLG4","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":"2930d0fed84a1b7025ffdf771d2686ba799a69f7bb927da2db05616a88d1b3c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-06-01T12:46:21Z","title_canon_sha256":"fe9fc804a724c7c8da0d6c24f6b448b9334889bb10c379e74a6f1a90e8403dfe"},"schema_version":"1.0","source":{"id":"1706.00276","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00276","created_at":"2026-05-18T00:43:14Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00276v1","created_at":"2026-05-18T00:43:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00276","created_at":"2026-05-18T00:43:14Z"},{"alias_kind":"pith_short_12","alias_value":"MFQXE6APW3KL","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MFQXE6APW3KL6UXT","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MFQXE6AP","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:3131494a73bd746b6d0245d4ad56ec7f8f6af355a40571e9cb7cc4bf53228bcd","target":"graph","created_at":"2026-05-18T00:43:14Z","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"},"paper":{"abstract_excerpt":"For every countable group $G$, there are $2^{\\omega}$ distinct classes of coarsely equivalent subsets of $G$.","authors_text":"Igor Protasov, Ksenia Protasova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-06-01T12:46:21Z","title":"Counting coarse subsets of a countable group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00276","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":"sha256:2df54ab2bf76f59156420aca6598b7665de3aa1bcf08fbc9bb66904d107e95da","target":"record","created_at":"2026-05-18T00:43:14Z","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":"2930d0fed84a1b7025ffdf771d2686ba799a69f7bb927da2db05616a88d1b3c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-06-01T12:46:21Z","title_canon_sha256":"fe9fc804a724c7c8da0d6c24f6b448b9334889bb10c379e74a6f1a90e8403dfe"},"schema_version":"1.0","source":{"id":"1706.00276","kind":"arxiv","version":1}},"canonical_sha256":"616172780fb6d4bf52f3ae8904c14b3703bce5665939971638d293b0b077c9fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"616172780fb6d4bf52f3ae8904c14b3703bce5665939971638d293b0b077c9fe","first_computed_at":"2026-05-18T00:43:14.504116Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:14.504116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z/P0fRmX9+1BmWGkHVwcYEPKeasTqggvZhtLKdCj+RQTT7YcdwDA1FLlE1dGkEYHKX24LTdt4f9rS8+HSZwbDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:14.504818Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.00276","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2df54ab2bf76f59156420aca6598b7665de3aa1bcf08fbc9bb66904d107e95da","sha256:3131494a73bd746b6d0245d4ad56ec7f8f6af355a40571e9cb7cc4bf53228bcd"],"state_sha256":"3abd45047a56d64b029113d4b2450fb6dc5a4083531415ce0517adb705e06112"}