{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DGZZTUZ5LY4YZX7O6OBUH7X25F","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":"4a071a1753d934917449fe0043938f6cf4a284e42c09bee01fdba7ab8ec6739d","cross_cats_sorted":["eess.SP","math.DS","physics.data-an","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2018-04-25T08:16:59Z","title_canon_sha256":"7567c1900c953b0744a80ebd21e6d6f2753ca006275d7602945e9e894b074a7f"},"schema_version":"1.0","source":{"id":"1804.09415","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09415","created_at":"2026-05-17T23:55:20Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09415v1","created_at":"2026-05-17T23:55:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09415","created_at":"2026-05-17T23:55:20Z"},{"alias_kind":"pith_short_12","alias_value":"DGZZTUZ5LY4Y","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DGZZTUZ5LY4YZX7O","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DGZZTUZ5","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:391db1051b74ba5c934088c747a45d8a3e36700b41ec35af1530fce3bd358e3e","target":"graph","created_at":"2026-05-17T23:55:20Z","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 study the maximum mean discrepancy (MMD) in the context of critical transitions modelled by fast-slow stochastic dynamical systems. We establish a new link between the dynamical theory of critical transitions with the statistical aspects of the MMD. In particular, we show that a formal approximation of the MMD near fast subsystem bifurcation points can be computed to leading-order. In particular, this leading order approximation shows that the MMD depends intricately on the fast-slow systems parameters and one can only expect to extract warning signs under rather stringent conditions. Howev","authors_text":"Boumediene Hamzi, Christian Kuehn, Sameh Mohamed","cross_cats":["eess.SP","math.DS","physics.data-an","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2018-04-25T08:16:59Z","title":"A Note on Kernel Methods for Multiscale Systems with Critical Transitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09415","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:e60c487edb62d738f2534f44c70a4fc49bb300a940280e70e8ffb6190e2fcb29","target":"record","created_at":"2026-05-17T23:55:20Z","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":"4a071a1753d934917449fe0043938f6cf4a284e42c09bee01fdba7ab8ec6739d","cross_cats_sorted":["eess.SP","math.DS","physics.data-an","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2018-04-25T08:16:59Z","title_canon_sha256":"7567c1900c953b0744a80ebd21e6d6f2753ca006275d7602945e9e894b074a7f"},"schema_version":"1.0","source":{"id":"1804.09415","kind":"arxiv","version":1}},"canonical_sha256":"19b399d33d5e398cdfeef38343fefae94f09d3465ed7ab1e11b3a3058f02cd8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19b399d33d5e398cdfeef38343fefae94f09d3465ed7ab1e11b3a3058f02cd8d","first_computed_at":"2026-05-17T23:55:20.913170Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:20.913170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4pjYWs6mPVhV0AHNymqzp6vnIxCy7+GktQOVAMPk7XqHxf65DqvSqrYIDQQWZueKObd4cH/qU8VjqNyi1hIlCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:20.913633Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.09415","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e60c487edb62d738f2534f44c70a4fc49bb300a940280e70e8ffb6190e2fcb29","sha256:391db1051b74ba5c934088c747a45d8a3e36700b41ec35af1530fce3bd358e3e"],"state_sha256":"05dd9955a868e1ef89b04d7289713d714cb2cb9f451458e85e8a052c416020eb"}