{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZXHDGK4BGSUWNICGCBSDIAILKZ","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":"a0fd9d5533b8c028e9f0fde080aa01434c526e330bd2572800082af246c126c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-02-05T20:20:30Z","title_canon_sha256":"2818a1a6385b5fe49f02ad43fe0f36ecaeac82647dca38e93a1bf65d31fa06df"},"schema_version":"1.0","source":{"id":"1902.02645","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.02645","created_at":"2026-05-17T23:54:32Z"},{"alias_kind":"arxiv_version","alias_value":"1902.02645v1","created_at":"2026-05-17T23:54:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.02645","created_at":"2026-05-17T23:54:32Z"},{"alias_kind":"pith_short_12","alias_value":"ZXHDGK4BGSUW","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZXHDGK4BGSUWNICG","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZXHDGK4B","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:7b5640f9aaafa7302a4953e43ddd6516bb4ddb894fd6f9c74b982018a2396ad3","target":"graph","created_at":"2026-05-17T23:54:32Z","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 find a constructive bound for the word length of a generating set for the centralizer of an element of the Mapping Class Group. As a consequence, we show that it is algorithmically decidable whether two postcritically finite branched coverings of the sphere are Thurston equivalent.","authors_text":"Kasra Rafi, Michael Yampolsky, Nikita Selinger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-02-05T20:20:30Z","title":"Centralizers in Mapping Class Group and decidability of Thurston Equivalence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02645","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:d42b6a6a60dbadc3271c7d8b1c27b6041d75434aa8b19ea6246d06792f70583b","target":"record","created_at":"2026-05-17T23:54:32Z","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":"a0fd9d5533b8c028e9f0fde080aa01434c526e330bd2572800082af246c126c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-02-05T20:20:30Z","title_canon_sha256":"2818a1a6385b5fe49f02ad43fe0f36ecaeac82647dca38e93a1bf65d31fa06df"},"schema_version":"1.0","source":{"id":"1902.02645","kind":"arxiv","version":1}},"canonical_sha256":"cdce332b8134a966a046106434010b5656b4ecfcc3db9e518e4d099a0b6f6036","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cdce332b8134a966a046106434010b5656b4ecfcc3db9e518e4d099a0b6f6036","first_computed_at":"2026-05-17T23:54:32.577306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:32.577306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0veM+ILIp5zRzRwqkbcJGypnKU83nWscBXRVKjwM8nM87ubB4Yncy7iR/5RuB4MvW85X5darbJEgT2ND0d7yAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:32.577749Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.02645","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d42b6a6a60dbadc3271c7d8b1c27b6041d75434aa8b19ea6246d06792f70583b","sha256:7b5640f9aaafa7302a4953e43ddd6516bb4ddb894fd6f9c74b982018a2396ad3"],"state_sha256":"e53c3faf70adfb07055f1b229aeb0616a5a08e6572280d8b42b75cca79705e63"}