{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:UI66OSZ7YCAR3HUBY72BK3JSLF","short_pith_number":"pith:UI66OSZ7","canonical_record":{"source":{"id":"1312.0586","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-12-02T20:40:44Z","cross_cats_sorted":["math.GR","math.GT"],"title_canon_sha256":"9c1e9c780d711154b44faae60f7a246b58346585d5c8943334dcc499502b09e7","abstract_canon_sha256":"2d85af9e6bce9b65a8dd9619646f13e0711d2478a7de757a7ebca1d9a55e627f"},"schema_version":"1.0"},"canonical_sha256":"a23de74b3fc0811d9e81c7f4156d325943ba3c70bc46940f1381db9294b0afe7","source":{"kind":"arxiv","id":"1312.0586","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0586","created_at":"2026-05-18T00:42:52Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0586v2","created_at":"2026-05-18T00:42:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0586","created_at":"2026-05-18T00:42:52Z"},{"alias_kind":"pith_short_12","alias_value":"UI66OSZ7YCAR","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UI66OSZ7YCAR3HUB","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UI66OSZ7","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:UI66OSZ7YCAR3HUBY72BK3JSLF","target":"record","payload":{"canonical_record":{"source":{"id":"1312.0586","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-12-02T20:40:44Z","cross_cats_sorted":["math.GR","math.GT"],"title_canon_sha256":"9c1e9c780d711154b44faae60f7a246b58346585d5c8943334dcc499502b09e7","abstract_canon_sha256":"2d85af9e6bce9b65a8dd9619646f13e0711d2478a7de757a7ebca1d9a55e627f"},"schema_version":"1.0"},"canonical_sha256":"a23de74b3fc0811d9e81c7f4156d325943ba3c70bc46940f1381db9294b0afe7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:52.093914Z","signature_b64":"j9Wq577d2K3lAS9C+3lZrX6OKjaQXY6Of39McmjFtC6zg8FywIoT1t46RbOyGLbxqDdQB4sJOvokJJpswbqUCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a23de74b3fc0811d9e81c7f4156d325943ba3c70bc46940f1381db9294b0afe7","last_reissued_at":"2026-05-18T00:42:52.093333Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:52.093333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.0586","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W+30jQWKIxnteyQqc6rSFXJxSLdwCUksoNd18iGYv/u9XY8nxi0JmJhmHm9S9gPyqXUinXSfqkxLs2+iilssDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:09:23.148831Z"},"content_sha256":"232c3c82d57934a4fba0c355f7a90aaaac341585db8c585f9e6991a032d52429","schema_version":"1.0","event_id":"sha256:232c3c82d57934a4fba0c355f7a90aaaac341585db8c585f9e6991a032d52429"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:UI66OSZ7YCAR3HUBY72BK3JSLF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The free group does not have the finite cover property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.GT"],"primary_cat":"math.LO","authors_text":"Rizos Sklinos","submitted_at":"2013-12-02T20:40:44Z","abstract_excerpt":"We prove that the first order theory of nonabelian free groups eliminates the \"there exists infinitely many\" quantifier (in eq). Equivalently, since the theory of nonabelian free groups is stable, it does not have the finite cover property. We also extend our results to torsion-free hyperbolic groups under some conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0586","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:42:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ndXX6op/xATSA2elFY8tHZtn8kLCt7g0sTUJ5A44nc5MZ7QqCEgdEh+Ns2pHoB6pN3Ty2D6LYNHrA2+8Yq6RBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:09:23.149162Z"},"content_sha256":"68aea93376a889b484d76d9f8d3513e1c754e468a1c7aa01b7ce620db0a783dd","schema_version":"1.0","event_id":"sha256:68aea93376a889b484d76d9f8d3513e1c754e468a1c7aa01b7ce620db0a783dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UI66OSZ7YCAR3HUBY72BK3JSLF/bundle.json","state_url":"https://pith.science/pith/UI66OSZ7YCAR3HUBY72BK3JSLF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UI66OSZ7YCAR3HUBY72BK3JSLF/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":"2026-06-25T08:09:23Z","links":{"resolver":"https://pith.science/pith/UI66OSZ7YCAR3HUBY72BK3JSLF","bundle":"https://pith.science/pith/UI66OSZ7YCAR3HUBY72BK3JSLF/bundle.json","state":"https://pith.science/pith/UI66OSZ7YCAR3HUBY72BK3JSLF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UI66OSZ7YCAR3HUBY72BK3JSLF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UI66OSZ7YCAR3HUBY72BK3JSLF","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":"2d85af9e6bce9b65a8dd9619646f13e0711d2478a7de757a7ebca1d9a55e627f","cross_cats_sorted":["math.GR","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-12-02T20:40:44Z","title_canon_sha256":"9c1e9c780d711154b44faae60f7a246b58346585d5c8943334dcc499502b09e7"},"schema_version":"1.0","source":{"id":"1312.0586","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0586","created_at":"2026-05-18T00:42:52Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0586v2","created_at":"2026-05-18T00:42:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0586","created_at":"2026-05-18T00:42:52Z"},{"alias_kind":"pith_short_12","alias_value":"UI66OSZ7YCAR","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UI66OSZ7YCAR3HUB","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UI66OSZ7","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:68aea93376a889b484d76d9f8d3513e1c754e468a1c7aa01b7ce620db0a783dd","target":"graph","created_at":"2026-05-18T00:42:52Z","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 prove that the first order theory of nonabelian free groups eliminates the \"there exists infinitely many\" quantifier (in eq). Equivalently, since the theory of nonabelian free groups is stable, it does not have the finite cover property. We also extend our results to torsion-free hyperbolic groups under some conditions.","authors_text":"Rizos Sklinos","cross_cats":["math.GR","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-12-02T20:40:44Z","title":"The free group does not have the finite cover property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0586","kind":"arxiv","version":2},"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":"sha256:232c3c82d57934a4fba0c355f7a90aaaac341585db8c585f9e6991a032d52429","target":"record","created_at":"2026-05-18T00:42:52Z","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":"2d85af9e6bce9b65a8dd9619646f13e0711d2478a7de757a7ebca1d9a55e627f","cross_cats_sorted":["math.GR","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-12-02T20:40:44Z","title_canon_sha256":"9c1e9c780d711154b44faae60f7a246b58346585d5c8943334dcc499502b09e7"},"schema_version":"1.0","source":{"id":"1312.0586","kind":"arxiv","version":2}},"canonical_sha256":"a23de74b3fc0811d9e81c7f4156d325943ba3c70bc46940f1381db9294b0afe7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a23de74b3fc0811d9e81c7f4156d325943ba3c70bc46940f1381db9294b0afe7","first_computed_at":"2026-05-18T00:42:52.093333Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:52.093333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j9Wq577d2K3lAS9C+3lZrX6OKjaQXY6Of39McmjFtC6zg8FywIoT1t46RbOyGLbxqDdQB4sJOvokJJpswbqUCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:52.093914Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.0586","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:232c3c82d57934a4fba0c355f7a90aaaac341585db8c585f9e6991a032d52429","sha256:68aea93376a889b484d76d9f8d3513e1c754e468a1c7aa01b7ce620db0a783dd"],"state_sha256":"f6e90caa67b59b47c9e229b6ce3bab8c02c346a596fc378f90ff2dba66e694b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tF4TuYYTdaxcWWYVBGfLywmaGnbKVpXDS5+4Y5uEey5+11NskwOC9+cVlMVA7ejG5PDEvxO2LeJjAOnke4YLCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T08:09:23.150996Z","bundle_sha256":"554f399b40cc55e8b23efb38ae1842be5df9388d63457531e1659db8daa0ae10"}}