{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZOPRNSYGOPJMDCJMPFEE7LR54J","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":"1e3c5790acd5a1c16135def99a57bb7b2b4253265b3f25ae31ddf3c6fd43265c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-13T15:24:25Z","title_canon_sha256":"a152cb3cfa6aa68853724b9c178ea33b8ac408fa9c0b162067247355d18297f7"},"schema_version":"1.0","source":{"id":"1201.2861","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.2861","created_at":"2026-05-18T01:22:52Z"},{"alias_kind":"arxiv_version","alias_value":"1201.2861v1","created_at":"2026-05-18T01:22:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.2861","created_at":"2026-05-18T01:22:52Z"},{"alias_kind":"pith_short_12","alias_value":"ZOPRNSYGOPJM","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZOPRNSYGOPJMDCJM","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZOPRNSYG","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:30404ebb7610b101b7aa37182079f3e0f5d2dc876a660509da9b740bf2a92983","target":"graph","created_at":"2026-05-18T01:22:52Z","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":"We introduce {\\it twist unimodal maps} of the interval and describe their structure. Sufficient conditions for the growth of over-rotation interval in families of maps are given.","authors_text":"A. Blokh, K. Snider","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-13T15:24:25Z","title":"Over-rotation numbers for unimodal maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2861","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":"sha256:3fbb10748198f2e37505191fa3093e9dbd68c7a5b33571201767dba92334d820","target":"record","created_at":"2026-05-18T01:22:52Z","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":"1e3c5790acd5a1c16135def99a57bb7b2b4253265b3f25ae31ddf3c6fd43265c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-13T15:24:25Z","title_canon_sha256":"a152cb3cfa6aa68853724b9c178ea33b8ac408fa9c0b162067247355d18297f7"},"schema_version":"1.0","source":{"id":"1201.2861","kind":"arxiv","version":1}},"canonical_sha256":"cb9f16cb0673d2c1892c79484fae3de267f3cfb597f674f9451ff359d36af500","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb9f16cb0673d2c1892c79484fae3de267f3cfb597f674f9451ff359d36af500","first_computed_at":"2026-05-18T01:22:52.651182Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:52.651182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XNcDGUfsJCQl4HkQN10Uv5gL0qLqKV3fafCjLETIkpVRYlhg1RD/54O/7Mw4sHI7fhPHK9KK+Un1lJHZaO4CCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:52.651671Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.2861","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fbb10748198f2e37505191fa3093e9dbd68c7a5b33571201767dba92334d820","sha256:30404ebb7610b101b7aa37182079f3e0f5d2dc876a660509da9b740bf2a92983"],"state_sha256":"17a76fc530a420d501a94412e2f78ae59534a36858df972107c59e5625d027c8"}