{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QELO27LFN5IYQVDXVFT5BZM7DZ","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":"78799a2fed5bb645fac2463670aa90a2f3bd3192dbbaf6bf3596cfc89e64574a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-11-11T16:14:08Z","title_canon_sha256":"89e19f86402c6106978c1ecc6b11f8d190dc0b2aad8ebb770d49eb6a1ea1060d"},"schema_version":"1.0","source":{"id":"1411.2868","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2868","created_at":"2026-05-18T01:02:46Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2868v3","created_at":"2026-05-18T01:02:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2868","created_at":"2026-05-18T01:02:46Z"},{"alias_kind":"pith_short_12","alias_value":"QELO27LFN5IY","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"QELO27LFN5IYQVDX","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"QELO27LF","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:c16bc0ef3578d9bc2064f62e7736e017b184988db91e9de710a121a0c7771d9a","target":"graph","created_at":"2026-05-18T01:02:46Z","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":"Richard J. Thompson invented his group F in the 60s; it is a group full of surprises: it has a finite presentation with 2 generators and 2 relators, and a derived group that is simple; it admits a peculiar infinite presentation and has a local definition which implies that F is dense in the topological group of all orientation preserving homeomorphisms of the unit interval.\n  In this monograph groups G are studied which depend on three parameters I, A, and P and which generalize the local definition of Thompson's group F thus: G consists of all orientation preserving PL-homeomorphisms of the r","authors_text":"Ralph Strebel, Robert Bieri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-11-11T16:14:08Z","title":"On Groups of PL-homeomorphisms of the Real Line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2868","kind":"arxiv","version":3},"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:f9c1b4fabc862b10ff76c35b04f9f4fdd095c99030bd3bbcd2d583ecbd41d413","target":"record","created_at":"2026-05-18T01:02:46Z","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":"78799a2fed5bb645fac2463670aa90a2f3bd3192dbbaf6bf3596cfc89e64574a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-11-11T16:14:08Z","title_canon_sha256":"89e19f86402c6106978c1ecc6b11f8d190dc0b2aad8ebb770d49eb6a1ea1060d"},"schema_version":"1.0","source":{"id":"1411.2868","kind":"arxiv","version":3}},"canonical_sha256":"8116ed7d656f51885477a967d0e59f1e6f2e376008b061740e5a8cc8716b4d6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8116ed7d656f51885477a967d0e59f1e6f2e376008b061740e5a8cc8716b4d6c","first_computed_at":"2026-05-18T01:02:46.033884Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:46.033884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zvOyG4zziX+Tc/SSWg6NaZT/8M8GboBo5SD2CIm2hlogIPTsB7cy6UI63hE2MH/W0nlQYWoD21LPWgQuup8FBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:46.034289Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2868","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9c1b4fabc862b10ff76c35b04f9f4fdd095c99030bd3bbcd2d583ecbd41d413","sha256:c16bc0ef3578d9bc2064f62e7736e017b184988db91e9de710a121a0c7771d9a"],"state_sha256":"9a2d3bddb340241093a2adbb89955d4887ae10b06bbda5a01a7306c1a8486783"}