{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GSGTGG44XLTVU5F2YO76HETDG6","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":"60471b5525928c07ca56c83c04d990abad2570f37782f8891bd905e869c26103","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-20T19:08:52Z","title_canon_sha256":"d7a37cd8a9bead576c8df83a210f9efb0289d34b1b5c38d423273ef9d7b65e3e"},"schema_version":"1.0","source":{"id":"1908.07571","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07571","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07571v1","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07571","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_12","alias_value":"GSGTGG44XLTV","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_16","alias_value":"GSGTGG44XLTVU5F2","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_8","alias_value":"GSGTGG44","created_at":"2026-07-04T23:58:59Z"}],"graph_snapshots":[{"event_id":"sha256:ad0e9e109ddc853c9d951f8137857f62c87616b028ad25b34ffcc2c54876bac1","target":"graph","created_at":"2026-07-04T23:58:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.07571/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that every sufficiently large iterate of a Thurston map which is not doubly covered by a torus endomorphism and which does not have a Levy cycle is isotopic to the subdivision map of a finite subdivision rule. We determine which Thurston maps doubly covered by a torus endomorphism have iterates that are isotopic to subdivision maps of finite subdivision rules. We give conditions under which no iterate of a given Thurston map is isotopic to the subdivision map of a finite subdivision rule.","authors_text":"Kevin M. Pilgrim, Walter Parry, William Floyd","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-20T19:08:52Z","title":"Expansion properties for finite subdivision rules II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07571","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:c279e6d47029b5b47041c22576ac6462a5152a2e32a07c9871c663edcdc9e982","target":"record","created_at":"2026-07-04T23:58:59Z","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":"60471b5525928c07ca56c83c04d990abad2570f37782f8891bd905e869c26103","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-20T19:08:52Z","title_canon_sha256":"d7a37cd8a9bead576c8df83a210f9efb0289d34b1b5c38d423273ef9d7b65e3e"},"schema_version":"1.0","source":{"id":"1908.07571","kind":"arxiv","version":1}},"canonical_sha256":"348d331b9cbae75a74bac3bfe3926337bbed4d48e66b4a15e3addca50ec63108","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"348d331b9cbae75a74bac3bfe3926337bbed4d48e66b4a15e3addca50ec63108","first_computed_at":"2026-07-04T23:58:59.234873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:58:59.234873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nodD2ibGZlEOkQq+FxvHUA68E1IKZ3qDSyatvmORD99Edn6TSlQ4iJ+kOlUDMtW6Xn0Ujjr1I4CvgXA3ggrmDA==","signature_status":"signed_v1","signed_at":"2026-07-04T23:58:59.235240Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.07571","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c279e6d47029b5b47041c22576ac6462a5152a2e32a07c9871c663edcdc9e982","sha256:ad0e9e109ddc853c9d951f8137857f62c87616b028ad25b34ffcc2c54876bac1"],"state_sha256":"327bb507775498842efbdb630c5664ea1229bc64196e7f72d2f0d877e71ca358"}