{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:T2PAYCE5E7TWKPIOEPXVBWBJHG","short_pith_number":"pith:T2PAYCE5","canonical_record":{"source":{"id":"1907.11601","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-07-26T14:45:54Z","cross_cats_sorted":[],"title_canon_sha256":"bd62814d8b77f3792b6e07055a8d2b50f05905f48222f601af8021ce8e42ed45","abstract_canon_sha256":"4033f35f383acce34b1b266c79cb5096950c178e20f3e3c8e1f64b58075f5bdd"},"schema_version":"1.0"},"canonical_sha256":"9e9e0c089d27e7653d0e23ef50d8293989170f10b96aa9e12201fd603b773e11","source":{"kind":"arxiv","id":"1907.11601","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.11601","created_at":"2026-05-17T23:39:28Z"},{"alias_kind":"arxiv_version","alias_value":"1907.11601v1","created_at":"2026-05-17T23:39:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.11601","created_at":"2026-05-17T23:39:28Z"},{"alias_kind":"pith_short_12","alias_value":"T2PAYCE5E7TW","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"T2PAYCE5E7TWKPIO","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"T2PAYCE5","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:T2PAYCE5E7TWKPIOEPXVBWBJHG","target":"record","payload":{"canonical_record":{"source":{"id":"1907.11601","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-07-26T14:45:54Z","cross_cats_sorted":[],"title_canon_sha256":"bd62814d8b77f3792b6e07055a8d2b50f05905f48222f601af8021ce8e42ed45","abstract_canon_sha256":"4033f35f383acce34b1b266c79cb5096950c178e20f3e3c8e1f64b58075f5bdd"},"schema_version":"1.0"},"canonical_sha256":"9e9e0c089d27e7653d0e23ef50d8293989170f10b96aa9e12201fd603b773e11","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:28.574707Z","signature_b64":"sBRab4GmsZL3lzKz1du50cZU10s1mKuZdsCJ/95864p1uLBc2XKzsoqZvsi6kFyYSiECEFFk36oDsjpa8qT7Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e9e0c089d27e7653d0e23ef50d8293989170f10b96aa9e12201fd603b773e11","last_reissued_at":"2026-05-17T23:39:28.574137Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:28.574137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.11601","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":"2026-05-17T23:39:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lsDEgQv3AQrGSLs8ufbj2UTQgzuo+LT4enceAktfgeprXXMnRu9C1txfiCKYh2Z/s0lUUQ1otrGoyEt0hQrIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:12:09.663985Z"},"content_sha256":"90cf4ce7b6a2b324d303bd1fe6d7e93d63b90a5ee979557384a070981977b075","schema_version":"1.0","event_id":"sha256:90cf4ce7b6a2b324d303bd1fe6d7e93d63b90a5ee979557384a070981977b075"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:T2PAYCE5E7TWKPIOEPXVBWBJHG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rate-induced Tipping in Discrete-time Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Claire Kiers","submitted_at":"2019-07-26T14:45:54Z","abstract_excerpt":"We develop a definition of rate-induced tipping (R-tipping) in discrete-time dynamical systems (maps) and prove results giving conditions under which R-tipping will or will not happen. Specifically, we study (possibly non-invertible) maps with a time-varying parameter subject to a parameter shift. We show that each stable path has a unique associated solution (a local pullback attractor) which stays near the path for all negative time. When the parameter changes slowly, this local pullback attractor stays near the path for all time, but if the parameter changes quickly, the local pullback attr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11601","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":"2026-05-17T23:39:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fLd+4tLbnSxlwG+NREfqqcUfJpFSc86Vzw5cLujFoxAuc1Hl8hMUSUZDI5TKjsJqPmup2zbN+AjKmPBI4nljCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:12:09.664342Z"},"content_sha256":"974ae9b250b656f2c8ee944045a542a9eb6b58482385778aadad21d86d3677e7","schema_version":"1.0","event_id":"sha256:974ae9b250b656f2c8ee944045a542a9eb6b58482385778aadad21d86d3677e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T2PAYCE5E7TWKPIOEPXVBWBJHG/bundle.json","state_url":"https://pith.science/pith/T2PAYCE5E7TWKPIOEPXVBWBJHG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T2PAYCE5E7TWKPIOEPXVBWBJHG/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":"2026-06-30T23:12:09Z","links":{"resolver":"https://pith.science/pith/T2PAYCE5E7TWKPIOEPXVBWBJHG","bundle":"https://pith.science/pith/T2PAYCE5E7TWKPIOEPXVBWBJHG/bundle.json","state":"https://pith.science/pith/T2PAYCE5E7TWKPIOEPXVBWBJHG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T2PAYCE5E7TWKPIOEPXVBWBJHG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:T2PAYCE5E7TWKPIOEPXVBWBJHG","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":"4033f35f383acce34b1b266c79cb5096950c178e20f3e3c8e1f64b58075f5bdd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-07-26T14:45:54Z","title_canon_sha256":"bd62814d8b77f3792b6e07055a8d2b50f05905f48222f601af8021ce8e42ed45"},"schema_version":"1.0","source":{"id":"1907.11601","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.11601","created_at":"2026-05-17T23:39:28Z"},{"alias_kind":"arxiv_version","alias_value":"1907.11601v1","created_at":"2026-05-17T23:39:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.11601","created_at":"2026-05-17T23:39:28Z"},{"alias_kind":"pith_short_12","alias_value":"T2PAYCE5E7TW","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"T2PAYCE5E7TWKPIO","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"T2PAYCE5","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:974ae9b250b656f2c8ee944045a542a9eb6b58482385778aadad21d86d3677e7","target":"graph","created_at":"2026-05-17T23:39:28Z","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 develop a definition of rate-induced tipping (R-tipping) in discrete-time dynamical systems (maps) and prove results giving conditions under which R-tipping will or will not happen. Specifically, we study (possibly non-invertible) maps with a time-varying parameter subject to a parameter shift. We show that each stable path has a unique associated solution (a local pullback attractor) which stays near the path for all negative time. When the parameter changes slowly, this local pullback attractor stays near the path for all time, but if the parameter changes quickly, the local pullback attr","authors_text":"Claire Kiers","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-07-26T14:45:54Z","title":"Rate-induced Tipping in Discrete-time Dynamical Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11601","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":"sha256:90cf4ce7b6a2b324d303bd1fe6d7e93d63b90a5ee979557384a070981977b075","target":"record","created_at":"2026-05-17T23:39:28Z","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":"4033f35f383acce34b1b266c79cb5096950c178e20f3e3c8e1f64b58075f5bdd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-07-26T14:45:54Z","title_canon_sha256":"bd62814d8b77f3792b6e07055a8d2b50f05905f48222f601af8021ce8e42ed45"},"schema_version":"1.0","source":{"id":"1907.11601","kind":"arxiv","version":1}},"canonical_sha256":"9e9e0c089d27e7653d0e23ef50d8293989170f10b96aa9e12201fd603b773e11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e9e0c089d27e7653d0e23ef50d8293989170f10b96aa9e12201fd603b773e11","first_computed_at":"2026-05-17T23:39:28.574137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:28.574137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sBRab4GmsZL3lzKz1du50cZU10s1mKuZdsCJ/95864p1uLBc2XKzsoqZvsi6kFyYSiECEFFk36oDsjpa8qT7Bw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:28.574707Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.11601","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90cf4ce7b6a2b324d303bd1fe6d7e93d63b90a5ee979557384a070981977b075","sha256:974ae9b250b656f2c8ee944045a542a9eb6b58482385778aadad21d86d3677e7"],"state_sha256":"9de29fe14efe10ab2d17adaa3f7d9e84cd7601f2efcea1d18b50a0e299b271b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nSpk7Z8i5srjndNznLWP+v8qxvsqLBNAYbKQiVRKHM144DRF1SkkWiOLviKHHmmVeOAvdY7PDc/e8SFjL3jnBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T23:12:09.666260Z","bundle_sha256":"12d6263bde610fd58c64b3e7247b58f682505ef7050555425f471c69d4789c5f"}}