{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1992:GZIWXWHKRXZI67Y45Z6WLR3VGN","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":"89e9b740403e2da70f49c0b5167a36940ebbf05bf846107793a3273f276080cc","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"1992-02-03T00:00:00Z","title_canon_sha256":"ed8f3a893fed76c97a599ec0ab7401f5d6912665bd801b44b5658513cc15c04f"},"schema_version":"1.0","source":{"id":"math/9202209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9202209","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"arxiv_version","alias_value":"math/9202209v1","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9202209","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"pith_short_12","alias_value":"GZIWXWHKRXZI","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"GZIWXWHKRXZI67Y4","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"GZIWXWHK","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:9657ef87e0afe892e8d23ef34f38b7f75d0b07a71ae3ab70e2884348b4f4f1e2","target":"graph","created_at":"2026-05-18T01:05:52Z","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":"Circle maps with a flat spot are studied which are differentiable, even on the boundary of the flat spot. Estimates on the Lebesgue measure and the Hausdorff dimension of the non-wandering set are obtained. Also, a sharp transition is found from degenerate geometry similar to what was found earlier for non-differentiable maps with a flat spot to bounded geometry as in critical maps without a flat spot.","authors_text":"Folkert Tangerman, Grzegorz Swiatek, Jacek Graczyk, J. J. P. Veerman","cross_cats":[],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"1992-02-03T00:00:00Z","title":"Scalings in circle maps III"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9202209","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":"sha256:565db3de2fe5c6e362857f1cb329a5bf2fc3731f80b2dc2bdffd28f79c025547","target":"record","created_at":"2026-05-18T01:05:52Z","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":"89e9b740403e2da70f49c0b5167a36940ebbf05bf846107793a3273f276080cc","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"1992-02-03T00:00:00Z","title_canon_sha256":"ed8f3a893fed76c97a599ec0ab7401f5d6912665bd801b44b5658513cc15c04f"},"schema_version":"1.0","source":{"id":"math/9202209","kind":"arxiv","version":1}},"canonical_sha256":"36516bd8ea8df28f7f1cee7d65c775337c9d79c136f2d385b101833eebcaef1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36516bd8ea8df28f7f1cee7d65c775337c9d79c136f2d385b101833eebcaef1e","first_computed_at":"2026-05-18T01:05:52.987603Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:52.987603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UJGVNepoY1crZgFg2yWjl8H98BefKqlLBQpV12U3mzFt5yzPoPvzvFxdJzUfoR7dI5mxJENw+RF68L2WxnyQBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:52.988110Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9202209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:565db3de2fe5c6e362857f1cb329a5bf2fc3731f80b2dc2bdffd28f79c025547","sha256:9657ef87e0afe892e8d23ef34f38b7f75d0b07a71ae3ab70e2884348b4f4f1e2"],"state_sha256":"f0f674b84d8e4f86f4cdfefefc7246bf197db29bc50e567f4ce69ff65c122ec1"}