{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XE2FYESIYWLZV566DLMHWUDHHO","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":"a95b58b3a851bbb8be3eae1b476e322e2a0b756a0d59bf0abcd8621bbe151154","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-16T06:17:47Z","title_canon_sha256":"1c86ca2f365c4c26c98e0cb2ed8326bffd43da9a73e3b323b94c0a9559b5750d"},"schema_version":"1.0","source":{"id":"1511.04835","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.04835","created_at":"2026-05-18T01:26:51Z"},{"alias_kind":"arxiv_version","alias_value":"1511.04835v1","created_at":"2026-05-18T01:26:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04835","created_at":"2026-05-18T01:26:51Z"},{"alias_kind":"pith_short_12","alias_value":"XE2FYESIYWLZ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XE2FYESIYWLZV566","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XE2FYESI","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:82286eaa9f088de5f43904963e13496c455d99bf2fc9c81bcdb417342e16c696","target":"graph","created_at":"2026-05-18T01:26:51Z","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":"In this paper we study existence of Normally Hyperbolic Invariant Laminations (NHIL) for a nearly integrable system given by the product of the pendulum and the rotator perturbed with a small coupling between the two. This example was introduced by Arnold. Using a {\\it separatrix map}, introduced in a low dimensional case by Zaslavskii-Filonenko and studied in a multidimensional case by Treschev and Piftankin, for an open class of trigonometric perturbations we prove that NHIL do exist. Moreover, using a second order expansion for the separatrix map from [GKZ], we prove that the system restric","authors_text":"Jianlu Zhang, Ke Zhang, Vadim Kaloshin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-16T06:17:47Z","title":"Normally Hyperbolic Invariant Laminations and diffusive behaviour for the generalized Arnold example away from resonances"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04835","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":"sha256:94e49a5cf6994bbd86d3b51a7d79bdd1c12c6dd7d5db3b5875827ca39a64f10c","target":"record","created_at":"2026-05-18T01:26:51Z","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":"a95b58b3a851bbb8be3eae1b476e322e2a0b756a0d59bf0abcd8621bbe151154","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-16T06:17:47Z","title_canon_sha256":"1c86ca2f365c4c26c98e0cb2ed8326bffd43da9a73e3b323b94c0a9559b5750d"},"schema_version":"1.0","source":{"id":"1511.04835","kind":"arxiv","version":1}},"canonical_sha256":"b9345c1248c5979af7de1ad87b50673bb5c2859931e37f6bf51a4096ab3dd83f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9345c1248c5979af7de1ad87b50673bb5c2859931e37f6bf51a4096ab3dd83f","first_computed_at":"2026-05-18T01:26:51.486932Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:51.486932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pBY9fcYRxrtHl2NoAfYReyr1jxw/cR1ZEd0jQJlvANzZxigGQ9sWFZjR8Tbjn1rCfCHv6goUJY8QOpr3Lt6OBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:51.487549Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.04835","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94e49a5cf6994bbd86d3b51a7d79bdd1c12c6dd7d5db3b5875827ca39a64f10c","sha256:82286eaa9f088de5f43904963e13496c455d99bf2fc9c81bcdb417342e16c696"],"state_sha256":"3414e1600aba65bbd1a1f5c48bcdc8495154e0aa82a5f93f1bd9aa9386fff33a"}