{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KO746JRFPMBEWHYPWRDYZFKUIK","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":"fc26a9cc04869e148b8b39b78c7d910f8e62815261870066d77808760e28b2c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-22T02:52:30Z","title_canon_sha256":"5d5df05d3ff96bf892481e27c997ea7d1082cba488dd6a5adbb94a7bfaa5800d"},"schema_version":"1.0","source":{"id":"1612.07422","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07422","created_at":"2026-05-18T00:47:19Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07422v1","created_at":"2026-05-18T00:47:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07422","created_at":"2026-05-18T00:47:19Z"},{"alias_kind":"pith_short_12","alias_value":"KO746JRFPMBE","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KO746JRFPMBEWHYP","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KO746JRF","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:69a77b775da1875538bbb8399e2ad6458e37b334c9313b822c1afd51da96bc1e","target":"graph","created_at":"2026-05-18T00:47:19Z","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":"Let $f$ be an exact area-preserving monotone twist diffeomorphism of the infinite cylinder and $P_{\\omega,f}(\\xi)$ be the associated Peierls barrier. In this paper, we give the H\\\"{o}lder regularity of $P_{\\omega,f}(\\xi)$ with respect to the parameter $f$. In fact, we prove that if the rotation symbol $\\omega\\in (\\mathbb{R}\\setminus\\mathbb{Q})\\bigcup(\\mathbb{Q}+)\\bigcup(\\mathbb{Q}-)$, then $P_{\\omega,f}(\\xi)$ is $1/3$-H\\\"{o}lder continuous in $f$, i.e. $$|P_{\\omega,f'}(\\xi)-P_{\\omega,f}(\\xi)|\\leq C\\|f'-f\\|_{C^1}^{1/3} ,~~\\forall \\xi\\in\\mathbb{R}$$ where $C$ is a constant. Similar results also ","authors_text":"Chong-Qing Cheng, Qinbo Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-22T02:52:30Z","title":"Regular dependence of the Peierls barriers on perturbations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07422","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":"sha256:741610d71efa4849e91096d0e0b45425b4a124cecc5734cf8e5fac7a834967eb","target":"record","created_at":"2026-05-18T00:47:19Z","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":"fc26a9cc04869e148b8b39b78c7d910f8e62815261870066d77808760e28b2c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-22T02:52:30Z","title_canon_sha256":"5d5df05d3ff96bf892481e27c997ea7d1082cba488dd6a5adbb94a7bfaa5800d"},"schema_version":"1.0","source":{"id":"1612.07422","kind":"arxiv","version":1}},"canonical_sha256":"53bfcf26257b024b1f0fb4478c955442ab7b7257ddc4f11af24a6a88e76b0db6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53bfcf26257b024b1f0fb4478c955442ab7b7257ddc4f11af24a6a88e76b0db6","first_computed_at":"2026-05-18T00:47:19.988244Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:19.988244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G3ZsJ1T0kjFlQmitkLN9dDdWnPcMBIUuHs91W7aF51sgOER3MqPwiVGa652r9QiwpUeS3xCkbi706fAKSN3TAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:19.988894Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.07422","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:741610d71efa4849e91096d0e0b45425b4a124cecc5734cf8e5fac7a834967eb","sha256:69a77b775da1875538bbb8399e2ad6458e37b334c9313b822c1afd51da96bc1e"],"state_sha256":"62ddb2d2d809b8f15f4e88dad77aa5b0193e965bdde740ecf806c001f6403411"}