{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XYW2ANSKW3Y6HO2YEAZIC4QDTT","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":"f18272909a638d7bc124353519e2a0f485a12d413d614c4a802474e889337354","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-03T13:10:38Z","title_canon_sha256":"21b7248950ba1b4ac4261ac44c81c1058890cd5dd2acb86cce8632fc70a35352"},"schema_version":"1.0","source":{"id":"1301.0616","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0616","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0616v1","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0616","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"pith_short_12","alias_value":"XYW2ANSKW3Y6","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XYW2ANSKW3Y6HO2Y","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XYW2ANSK","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:f9f7b2fdb59d57cbe02d33c5cfe0104fdbcd3fa813234906d2ec50664d981a77","target":"graph","created_at":"2026-05-18T02:38:17Z","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 show that the abstract commensurator of Thompson's group F is composed of four building blocks: two isomorphism types of simple groups, the multiplicative group of the positive rationals and a cyclic group of order two. The main result establishes the simplicity of a certain group of piecewise linear homeomorphisms of the real line.","authors_text":"Claas E. R\\\"over, Jos\\'e Burillo, Sean Cleary","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-03T13:10:38Z","title":"Addendum to \"Commensurations and Subgroups of Finite Index of Thompson's Group F\""},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0616","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":"sha256:8138c45430a67a16536e61bab2e3e78cc201691aa8d41626d4c7b1d15592cc2a","target":"record","created_at":"2026-05-18T02:38:17Z","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":"f18272909a638d7bc124353519e2a0f485a12d413d614c4a802474e889337354","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-03T13:10:38Z","title_canon_sha256":"21b7248950ba1b4ac4261ac44c81c1058890cd5dd2acb86cce8632fc70a35352"},"schema_version":"1.0","source":{"id":"1301.0616","kind":"arxiv","version":1}},"canonical_sha256":"be2da0364ab6f1e3bb5820328172039cc19c76fc266225e8bad2caadbe980510","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be2da0364ab6f1e3bb5820328172039cc19c76fc266225e8bad2caadbe980510","first_computed_at":"2026-05-18T02:38:17.430171Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:17.430171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k6rW77vPFLG1vnMBYKBQLmrM1Hacvk/AbPnriBSmi34qSmR1EPppqY/NMYJZlUfRJASNhScyPgxEykrqhET0BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:17.430751Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.0616","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8138c45430a67a16536e61bab2e3e78cc201691aa8d41626d4c7b1d15592cc2a","sha256:f9f7b2fdb59d57cbe02d33c5cfe0104fdbcd3fa813234906d2ec50664d981a77"],"state_sha256":"a07c0787fe1fa3ffeacddf68c35014d20303148f1b1f0b835a03700562e4e24c"}