{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:N76NL3AJRTCYM53XTERTOQEYHD","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":"5ccd06d261cf7e2b0191362c853849f94a2bf355ff1c823091788134f75c109a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-08T10:59:16Z","title_canon_sha256":"d1f2e2c818050abe9c61a7c7b34f1744126a8d94da545224469b6d545a054192"},"schema_version":"1.0","source":{"id":"1709.02645","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.02645","created_at":"2026-05-17T23:56:04Z"},{"alias_kind":"arxiv_version","alias_value":"1709.02645v6","created_at":"2026-05-17T23:56:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.02645","created_at":"2026-05-17T23:56:04Z"},{"alias_kind":"pith_short_12","alias_value":"N76NL3AJRTCY","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"N76NL3AJRTCYM53X","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"N76NL3AJ","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:4119d34c7cc95a4a537f3f1309ea644472f16ca04800f59df6d01577ee57d95f","target":"graph","created_at":"2026-05-17T23:56:04Z","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":"A classical scenario for tipping is that a dynamical system experiences a slow parameter drift across a fold tipping point, caused by a run-away positive feedback loop. We study what happens if one turns around after one has crossed the threshold. We derive a simple criterion that relates how far the parameter exceeds the tipping threshold maximally and how long the parameter stays above the threshold to avoid tipping in an inverse-square law to observable properties of the dynamical system near the fold.\n  For the case when the dynamical system is subject to stochastic forcing we give an appr","authors_text":"Jan Sieber, Ozkan Karabacak, Paul Ritchie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-08T10:59:16Z","title":"Inverse-square law between time and amplitude for crossing tipping thresholds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02645","kind":"arxiv","version":6},"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":"sha256:746a1f17c45e41cd6b9a000eb46a3921904181a018225847fc75b95cf153ab82","target":"record","created_at":"2026-05-17T23:56:04Z","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":"5ccd06d261cf7e2b0191362c853849f94a2bf355ff1c823091788134f75c109a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-08T10:59:16Z","title_canon_sha256":"d1f2e2c818050abe9c61a7c7b34f1744126a8d94da545224469b6d545a054192"},"schema_version":"1.0","source":{"id":"1709.02645","kind":"arxiv","version":6}},"canonical_sha256":"6ffcd5ec098cc5867777992337409838ccff7a91e7da5b292d8549cc127d9682","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ffcd5ec098cc5867777992337409838ccff7a91e7da5b292d8549cc127d9682","first_computed_at":"2026-05-17T23:56:04.127044Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:04.127044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mOjZPUWmZ2rdAYUYSORxdaVUEr6WfbdZNm/nbunYDnLX80amLpU6G5RN9t0yxxGNM0rDwTgnsu8AVQxJU6a6DQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:04.127672Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.02645","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:746a1f17c45e41cd6b9a000eb46a3921904181a018225847fc75b95cf153ab82","sha256:4119d34c7cc95a4a537f3f1309ea644472f16ca04800f59df6d01577ee57d95f"],"state_sha256":"556c60e0839d6e28c4a15ee9b9ba36077bfeff084addf48934f41d36017f0818"}