{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:O5SYWROTKJZXSZ4WSGPNL4RPOS","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":"97a2e07b9f19197081ea7ac1e4361a7874282fff4dfa0fb9ca911d75b4743f9f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-12-15T22:49:25Z","title_canon_sha256":"650a0da103515477169cf0b7c139513ae1bf6cd10892f36c28c958ea6415fafb"},"schema_version":"1.0","source":{"id":"1412.4830","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.4830","created_at":"2026-05-18T02:31:10Z"},{"alias_kind":"arxiv_version","alias_value":"1412.4830v1","created_at":"2026-05-18T02:31:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4830","created_at":"2026-05-18T02:31:10Z"},{"alias_kind":"pith_short_12","alias_value":"O5SYWROTKJZX","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O5SYWROTKJZXSZ4W","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O5SYWROT","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:ecc168064e57b7042b5d30249cc9a754a40ca895a2260277afc899da2f02b13b","target":"graph","created_at":"2026-05-18T02:31:10Z","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 consider the class of diffeomorphisms of a manifold that its differential keeps invariant a one-dimensional subbundle $E$. For that type of diffeomorphisms is naturally defined a one-parameter family called $E-$translation. We prove that if a diffeomorphisms in above mentioned class is conjugate to its $E-$translation and the conjugacy is at distance $\\alpha$-H\\\"older to the identity respect to the parameter and $\\alpha>1/2$, then the $E$-direction is hyperbolic.\n  This theorem is also sharp as it is be discussed with some examples. We also deal with the continuously stable case in the Skew","authors_text":"Enrique R. Pujals, Javier Correa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-12-15T22:49:25Z","title":"H\\\"older stability for $C^r$ central translations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4830","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:f46093cb4761e6af3c801e9cc9a3f648b77c0cb228b51c808376c5e3273801d1","target":"record","created_at":"2026-05-18T02:31:10Z","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":"97a2e07b9f19197081ea7ac1e4361a7874282fff4dfa0fb9ca911d75b4743f9f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-12-15T22:49:25Z","title_canon_sha256":"650a0da103515477169cf0b7c139513ae1bf6cd10892f36c28c958ea6415fafb"},"schema_version":"1.0","source":{"id":"1412.4830","kind":"arxiv","version":1}},"canonical_sha256":"77658b45d35273796796919ed5f22f74a292828ae41ce398268dbcb6185941f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77658b45d35273796796919ed5f22f74a292828ae41ce398268dbcb6185941f8","first_computed_at":"2026-05-18T02:31:10.385073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:10.385073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OuI0zaeTklZqbDGfcLJDO5Kt8m/dywcuy8cjYwBtWOn2R3Q9uCVFek3M5QEezaUmJpt/xk06SU2dSwymg/1dDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:10.385577Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.4830","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f46093cb4761e6af3c801e9cc9a3f648b77c0cb228b51c808376c5e3273801d1","sha256:ecc168064e57b7042b5d30249cc9a754a40ca895a2260277afc899da2f02b13b"],"state_sha256":"4dd495d86f452fb86c312eaec950f6b542aa07f4ed55feb3f2dfd944ebd88371"}