{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:2ERA7F3EQFATVCTUUZGKAHEGRO","short_pith_number":"pith:2ERA7F3E","canonical_record":{"source":{"id":"1808.07218","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-22T04:52:02Z","cross_cats_sorted":[],"title_canon_sha256":"b09747878c88695b713fa2a506b558a83202c1e86a8829572c3d460a2207fbbc","abstract_canon_sha256":"2d36631f1ed90a6d57937348ff98ec1ed7aa860d7e3ebe8226fb559b65f33b22"},"schema_version":"1.0"},"canonical_sha256":"d1220f976481413a8a74a64ca01c868b9879e71f2e4c630baa3d6e428d49ec60","source":{"kind":"arxiv","id":"1808.07218","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.07218","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"1808.07218v1","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.07218","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"2ERA7F3EQFAT","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"2ERA7F3EQFATVCTU","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"2ERA7F3E","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:2ERA7F3EQFATVCTUUZGKAHEGRO","target":"record","payload":{"canonical_record":{"source":{"id":"1808.07218","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-22T04:52:02Z","cross_cats_sorted":[],"title_canon_sha256":"b09747878c88695b713fa2a506b558a83202c1e86a8829572c3d460a2207fbbc","abstract_canon_sha256":"2d36631f1ed90a6d57937348ff98ec1ed7aa860d7e3ebe8226fb559b65f33b22"},"schema_version":"1.0"},"canonical_sha256":"d1220f976481413a8a74a64ca01c868b9879e71f2e4c630baa3d6e428d49ec60","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:29.565648Z","signature_b64":"343rMcxkFSPIb0mlJtQn3IrxurTPIFqxdMcXC6XhX6iFNIYYgNnFsgwKtCgqDYvxXEL/UHxsdZIJvuHVqlKFCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1220f976481413a8a74a64ca01c868b9879e71f2e4c630baa3d6e428d49ec60","last_reissued_at":"2026-05-18T00:07:29.565094Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:29.565094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.07218","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:07:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eImhZ+sP3Dg+ZtN3cXBUUNYXqkYpWPj1XoRNnvVhLCO8dgUk2Xg2CZd0WEjvAXCCU5nE2lc82Zjq4Nv7jZtjDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:53:18.469461Z"},"content_sha256":"3c1d6129f08ed3f3fc2167df1bf9957e5bad25137d74aa05ba0c426fb292cabf","schema_version":"1.0","event_id":"sha256:3c1d6129f08ed3f3fc2167df1bf9957e5bad25137d74aa05ba0c426fb292cabf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:2ERA7F3EQFATVCTUUZGKAHEGRO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast growth of the number of periodic points arising from heterodimensional connections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dmitry Turaev, Katsutoshi Shinohara, Masayuki Asaoka","submitted_at":"2018-08-22T04:52:02Z","abstract_excerpt":"We consider C^r-diffeomorphisms of a compact smooth manifold having a pair of robust heterodimensional cycles where r is a positive integer or infinity. We prove that if certain conditions about the signatures of non-linearities and Schwarzian derivatives of the transition maps are satisfied, then by giving C^r arbitrarily small perturbation, we can produce a periodic point at which the first return map in the center direction is C^r-flat. As a consequence, we will prove that C^r-generic diffeomorphisms in the neighborhood of the initial diffeomorphism exhibit super-exponential growth of numbe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07218","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:07:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+rKIU1RWVmC6+rm0zM9gDtav45AQbLsiZs//Y+6IJdGuHqxdVsiRCrZu8gBt5SQypzujPkWOz6IxhxtS806tAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:53:18.470201Z"},"content_sha256":"d9b0e958da74baeb00b6e2e47e06a764bef5c41c1a7d20c0fe36a870c6ad1778","schema_version":"1.0","event_id":"sha256:d9b0e958da74baeb00b6e2e47e06a764bef5c41c1a7d20c0fe36a870c6ad1778"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2ERA7F3EQFATVCTUUZGKAHEGRO/bundle.json","state_url":"https://pith.science/pith/2ERA7F3EQFATVCTUUZGKAHEGRO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2ERA7F3EQFATVCTUUZGKAHEGRO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T16:53:18Z","links":{"resolver":"https://pith.science/pith/2ERA7F3EQFATVCTUUZGKAHEGRO","bundle":"https://pith.science/pith/2ERA7F3EQFATVCTUUZGKAHEGRO/bundle.json","state":"https://pith.science/pith/2ERA7F3EQFATVCTUUZGKAHEGRO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2ERA7F3EQFATVCTUUZGKAHEGRO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2ERA7F3EQFATVCTUUZGKAHEGRO","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":"2d36631f1ed90a6d57937348ff98ec1ed7aa860d7e3ebe8226fb559b65f33b22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-22T04:52:02Z","title_canon_sha256":"b09747878c88695b713fa2a506b558a83202c1e86a8829572c3d460a2207fbbc"},"schema_version":"1.0","source":{"id":"1808.07218","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.07218","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"1808.07218v1","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.07218","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"2ERA7F3EQFAT","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"2ERA7F3EQFATVCTU","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"2ERA7F3E","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:d9b0e958da74baeb00b6e2e47e06a764bef5c41c1a7d20c0fe36a870c6ad1778","target":"graph","created_at":"2026-05-18T00:07:29Z","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 C^r-diffeomorphisms of a compact smooth manifold having a pair of robust heterodimensional cycles where r is a positive integer or infinity. We prove that if certain conditions about the signatures of non-linearities and Schwarzian derivatives of the transition maps are satisfied, then by giving C^r arbitrarily small perturbation, we can produce a periodic point at which the first return map in the center direction is C^r-flat. As a consequence, we will prove that C^r-generic diffeomorphisms in the neighborhood of the initial diffeomorphism exhibit super-exponential growth of numbe","authors_text":"Dmitry Turaev, Katsutoshi Shinohara, Masayuki Asaoka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-22T04:52:02Z","title":"Fast growth of the number of periodic points arising from heterodimensional connections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07218","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":"sha256:3c1d6129f08ed3f3fc2167df1bf9957e5bad25137d74aa05ba0c426fb292cabf","target":"record","created_at":"2026-05-18T00:07:29Z","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":"2d36631f1ed90a6d57937348ff98ec1ed7aa860d7e3ebe8226fb559b65f33b22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-22T04:52:02Z","title_canon_sha256":"b09747878c88695b713fa2a506b558a83202c1e86a8829572c3d460a2207fbbc"},"schema_version":"1.0","source":{"id":"1808.07218","kind":"arxiv","version":1}},"canonical_sha256":"d1220f976481413a8a74a64ca01c868b9879e71f2e4c630baa3d6e428d49ec60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1220f976481413a8a74a64ca01c868b9879e71f2e4c630baa3d6e428d49ec60","first_computed_at":"2026-05-18T00:07:29.565094Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:29.565094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"343rMcxkFSPIb0mlJtQn3IrxurTPIFqxdMcXC6XhX6iFNIYYgNnFsgwKtCgqDYvxXEL/UHxsdZIJvuHVqlKFCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:29.565648Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.07218","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c1d6129f08ed3f3fc2167df1bf9957e5bad25137d74aa05ba0c426fb292cabf","sha256:d9b0e958da74baeb00b6e2e47e06a764bef5c41c1a7d20c0fe36a870c6ad1778"],"state_sha256":"c03ccb7d9b82c97920e649fcbd326aadd2f9d9f0935ca2bc5a6adbb030a81bbf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eB07fhEFhug5DeRXOeLkqTTRL/47mBGb35dbTtNXGnu7cdneYpU44avvQrBGEGaxpPW0mPVIiQsNqwNMk/mBCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T16:53:18.474021Z","bundle_sha256":"ef6836505011d4d6cb4e780c1c7e446f6e093fad35562fe882b2a201757c4e6d"}}