{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6R3SY6CPIF5N2O4P4XJXQ5UT2R","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":"a018366c91967b2a8cf02b88510780c5228c3890e527871b985a57e2b43adb35","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-04-06T00:38:15Z","title_canon_sha256":"416943b8e4d28941acba52092befb84f02970055d06a588c15370c9a1c31ac17"},"schema_version":"1.0","source":{"id":"1104.0980","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0980","created_at":"2026-05-18T02:02:37Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0980v1","created_at":"2026-05-18T02:02:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0980","created_at":"2026-05-18T02:02:37Z"},{"alias_kind":"pith_short_12","alias_value":"6R3SY6CPIF5N","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6R3SY6CPIF5N2O4P","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6R3SY6CP","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:643ce9daf218feb07a177f48db56d65e1db4869dfaed613867f758fa74ab0d61","target":"graph","created_at":"2026-05-18T02:02:37Z","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 diffeomorphisms $f$ with heteroclinic cycles associated to saddles $P$ and $Q$ of different indices. We say that a cycle of this type can be stabilized if there are diffeomorphisms close to $f$ with a robust cycle associated to hyperbolic sets containing the continuations of $P$ and $Q$. We focus on the case where the indices of these two saddles differ by one. We prove that, excluding one particular case (so-called twisted cycles that additionally satisfy some geometrical restrictions), all such cycles can be stabilized.","authors_text":"Christian Bonatti, Lorenzo J. Diaz, Shin Kiriki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-04-06T00:38:15Z","title":"Stabilization of heterodimensional cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0980","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":"sha256:6ff216d717590740bc4fd7263ad08bf33202afbd6de3c4b02c6f0cb1a703c0e1","target":"record","created_at":"2026-05-18T02:02:37Z","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":"a018366c91967b2a8cf02b88510780c5228c3890e527871b985a57e2b43adb35","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-04-06T00:38:15Z","title_canon_sha256":"416943b8e4d28941acba52092befb84f02970055d06a588c15370c9a1c31ac17"},"schema_version":"1.0","source":{"id":"1104.0980","kind":"arxiv","version":1}},"canonical_sha256":"f4772c784f417add3b8fe5d3787693d45e1e8090a758db251504735324237e4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4772c784f417add3b8fe5d3787693d45e1e8090a758db251504735324237e4e","first_computed_at":"2026-05-18T02:02:37.471394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:02:37.471394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gr+RLtI028Pfizp6Tstr04hwcqhylNUqQ6qv2GvlJY0xDjp26HaoiaTn8H+01VXKCOm7TsMEf2sTQdRmQtFdBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:02:37.472268Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0980","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ff216d717590740bc4fd7263ad08bf33202afbd6de3c4b02c6f0cb1a703c0e1","sha256:643ce9daf218feb07a177f48db56d65e1db4869dfaed613867f758fa74ab0d61"],"state_sha256":"900f664e40caa27a96b26ef25d2f02505651bc8d1615f79fd3f7efbf96335fe3"}