{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OOLNDWR6OMJJ2EMLS2EYRURR2B","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":"f36782ce0da4bf7ca0fa38ac2378239402ea6c9c18607a3dcd8ef1a3a4cf9b29","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-12-11T15:30:12Z","title_canon_sha256":"7fc51bffb78a19e173d36a2728651cf1b69a9778eb91bff8b2fca7a168fe2d71"},"schema_version":"1.0","source":{"id":"1812.04468","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.04468","created_at":"2026-05-17T23:58:31Z"},{"alias_kind":"arxiv_version","alias_value":"1812.04468v1","created_at":"2026-05-17T23:58:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.04468","created_at":"2026-05-17T23:58:31Z"},{"alias_kind":"pith_short_12","alias_value":"OOLNDWR6OMJJ","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OOLNDWR6OMJJ2EML","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OOLNDWR6","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:db060f18c0cf94fa6a0d3e0f86d2a409da98d3b6641d900bc717a3640f01c787","target":"graph","created_at":"2026-05-17T23:58:31Z","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 give some lower bounds on the Shelah rank of varieties in the free group whose coordinate groups are hyperbolic towers.","authors_text":"Chlo\\'e Perin, Javier de la Nuez Gonz\\'alez, Rizos Sklinos","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-12-11T15:30:12Z","title":"Some lower bounds on Shelah rank in the free group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04468","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":"sha256:1514754a62b6c0a2e1b6831c6c8e229b102968f20f36542d7857d65fdd98ae4c","target":"record","created_at":"2026-05-17T23:58:31Z","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":"f36782ce0da4bf7ca0fa38ac2378239402ea6c9c18607a3dcd8ef1a3a4cf9b29","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-12-11T15:30:12Z","title_canon_sha256":"7fc51bffb78a19e173d36a2728651cf1b69a9778eb91bff8b2fca7a168fe2d71"},"schema_version":"1.0","source":{"id":"1812.04468","kind":"arxiv","version":1}},"canonical_sha256":"7396d1da3e73129d118b968988d231d044ac38406d93a8deaa8909ad0b7d1ab0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7396d1da3e73129d118b968988d231d044ac38406d93a8deaa8909ad0b7d1ab0","first_computed_at":"2026-05-17T23:58:31.976444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:31.976444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p4cZWXLCmQV5uRuGXk66T14pAm35EG8LET4nc6cqnfkb/L7mH665u7saghxyEjvRbGIV4K3FO7MMsYQ8zZyJDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:31.977141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.04468","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1514754a62b6c0a2e1b6831c6c8e229b102968f20f36542d7857d65fdd98ae4c","sha256:db060f18c0cf94fa6a0d3e0f86d2a409da98d3b6641d900bc717a3640f01c787"],"state_sha256":"40111be2c33985bb08aecd9ee810570021c607fbb494a0b53073e8b90939923b"}