{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ECIQYJQTS4LJ62Q2LAQTPVVXNL","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":"8a4fce6ddf2a1ced798f2f3d84bef4ba724f7fd4dda8b6714550633c0e365bb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-06-10T19:33:51Z","title_canon_sha256":"6d1e741eaf8343a03557faaf7920930918a36f3cfa3875cad30d603c3733ce32"},"schema_version":"1.0","source":{"id":"1006.2123","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.2123","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"1006.2123v4","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.2123","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"ECIQYJQTS4LJ","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"ECIQYJQTS4LJ62Q2","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"ECIQYJQT","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:73a961b0856f2f33cdb2e2838d81742a81da599ba898bf986955d1bc5c670d35","target":"graph","created_at":"2026-05-18T02:38:18Z","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 study line patterns in a free group by considering the topology of the decomposition space, a quotient of the boundary at infinity of the free group related to the line pattern. We show that the group of quasi-isometries preserving a line pattern in a free group acts by isometries on a related space if and only if there are no cut pairs in the decomposition space.","authors_text":"Christopher H. Cashen, Natasa Macura","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-06-10T19:33:51Z","title":"Line Patterns in Free Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.2123","kind":"arxiv","version":4},"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:ad9b27adc605581c0e156b7249d633108c3e4e3d6303c76cffe52500f3a52dcd","target":"record","created_at":"2026-05-18T02:38:18Z","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":"8a4fce6ddf2a1ced798f2f3d84bef4ba724f7fd4dda8b6714550633c0e365bb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-06-10T19:33:51Z","title_canon_sha256":"6d1e741eaf8343a03557faaf7920930918a36f3cfa3875cad30d603c3733ce32"},"schema_version":"1.0","source":{"id":"1006.2123","kind":"arxiv","version":4}},"canonical_sha256":"20910c261397169f6a1a582137d6b76ae4b303ebd82faaa6508978b8098565c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20910c261397169f6a1a582137d6b76ae4b303ebd82faaa6508978b8098565c5","first_computed_at":"2026-05-18T02:38:18.474986Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:18.474986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QVvoxQ83R6djV8nhQIcc2hstoiDRnYCk9l/z44TzZ+p7OTSC2nhlXFODbPqrraTEUKMXdu8gv1bEZw06M++TAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:18.475684Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.2123","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad9b27adc605581c0e156b7249d633108c3e4e3d6303c76cffe52500f3a52dcd","sha256:73a961b0856f2f33cdb2e2838d81742a81da599ba898bf986955d1bc5c670d35"],"state_sha256":"1b6bd3269fcc57b97280f8128b95108e907afe152d04755443711b8312845d5f"}