{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:KDFLKD7RLYQYKPICFXGMMPYGDY","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":"3bea4c0932a9210ce701f7e25dc407480eb174aab4bc5cb7f8110eb54e0d7687","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2007-10-19T05:52:11Z","title_canon_sha256":"8da582f835ce4c42aa64d6afd5cc5fc81f90cc2800447c93095b6d0a11c218b1"},"schema_version":"1.0","source":{"id":"0710.3633","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.3633","created_at":"2026-05-18T03:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"0710.3633v3","created_at":"2026-05-18T03:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.3633","created_at":"2026-05-18T03:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"KDFLKD7RLYQY","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"KDFLKD7RLYQYKPIC","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"KDFLKD7R","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:8772ae506a896c96de2746ae97b4a20c5f7a7ba8a50bd83426a3f18b584f494a","target":"graph","created_at":"2026-05-18T03:46:04Z","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 describe an explicit relationship between strand diagrams and piecewise-linear functions for elements of Thompson's group F. Using this correspondence, we investigate the dynamics of elements of F, and we show that conjugacy of one-bump functions can be described by a Mather-type invariant.","authors_text":"Francesco Matucci, James Belk","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2007-10-19T05:52:11Z","title":"Dynamics in Thompson's Group F"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.3633","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:c9122cf0302ad6ef596c060604771bac2bf1d8119aa4e06f960a9409b62a9037","target":"record","created_at":"2026-05-18T03:46:04Z","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":"3bea4c0932a9210ce701f7e25dc407480eb174aab4bc5cb7f8110eb54e0d7687","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2007-10-19T05:52:11Z","title_canon_sha256":"8da582f835ce4c42aa64d6afd5cc5fc81f90cc2800447c93095b6d0a11c218b1"},"schema_version":"1.0","source":{"id":"0710.3633","kind":"arxiv","version":3}},"canonical_sha256":"50cab50ff15e21853d022dccc63f061e16677fd5e80b6ad788be2c359ddec2cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50cab50ff15e21853d022dccc63f061e16677fd5e80b6ad788be2c359ddec2cd","first_computed_at":"2026-05-18T03:46:04.314251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:04.314251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aZmYkhzlTsngV8LjZnc/5LD7ifcM7DilIGIQCigO7ER9GLuhQNPLpdeQ95623RQTdvf1x7bJv0bLuFDwWRPxDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:04.315233Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.3633","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9122cf0302ad6ef596c060604771bac2bf1d8119aa4e06f960a9409b62a9037","sha256:8772ae506a896c96de2746ae97b4a20c5f7a7ba8a50bd83426a3f18b584f494a"],"state_sha256":"c73f2d2387cb5e7e3702a678213eb2f4e3ffbee0d1be1c81f7c367994f1822dc"}