{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NYEILOFZ6RQLP3LLZF7E7SK3PA","merge_version":"pith-open-graph-merge-v1","event_count":7,"valid_event_count":7,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"31927e08fad083fe63d4fff027681801f73208a58265aac2c3c46b8ee1da24a6","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-07T15:55:05Z","title_canon_sha256":"efe69fdc144ddaf8880c056da9a5896f46bd578adb42c64c410d12eb3540d94c"},"schema_version":"1.0","source":{"id":"2607.06428","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.06428","created_at":"2026-07-08T01:19:25Z"},{"alias_kind":"arxiv_version","alias_value":"2607.06428v1","created_at":"2026-07-08T01:19:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06428","created_at":"2026-07-08T01:19:25Z"},{"alias_kind":"pith_short_12","alias_value":"NYEILOFZ6RQL","created_at":"2026-07-08T01:19:25Z"},{"alias_kind":"pith_short_16","alias_value":"NYEILOFZ6RQLP3LL","created_at":"2026-07-08T01:19:25Z"},{"alias_kind":"pith_short_8","alias_value":"NYEILOFZ","created_at":"2026-07-08T01:19:25Z"}],"graph_snapshots":[{"event_id":"sha256:499ab2b781e60791820764ea4b67ac28a2ae9cc1dd0218e8ee5004c62d2a4b88","target":"graph","created_at":"2026-07-08T01:19:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.06428/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct early-warning signals for impending critical transitions in non-Markovian systems. We analyze stochastic forcings such as fractional Brownian motion, fractional Ornstein-Uhlenbeck processes and red noise in fast-slow systems exhibiting such transitions. We show that the effectiveness of indicators such as autocovariance, autocorrelation, and spectral density depends on several properties of the underlying system. In particular, we compare the influence of the Hurst index and the bifurcation type. We prove that the rotatory dynamics associated with a Hopf bifurcation substantially ","authors_text":"Alexandra Blessing, Dennis Rudik, Paolo Bernuzzi","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-07T15:55:05Z","title":"Impact of spinning on the early-warning signs in non-Markovian stochastic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06428","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":"sha256:74d53509a16de9838a1187a07ed11a90522f299dcad47051a0cea89ad7c76d69","target":"record","created_at":"2026-07-08T01:19:25Z","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":"31927e08fad083fe63d4fff027681801f73208a58265aac2c3c46b8ee1da24a6","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-07T15:55:05Z","title_canon_sha256":"efe69fdc144ddaf8880c056da9a5896f46bd578adb42c64c410d12eb3540d94c"},"schema_version":"1.0","source":{"id":"2607.06428","kind":"arxiv","version":1}},"canonical_sha256":"6e0885b8b9f460b7ed6bc97e4fc95b780ba06c8e1a259ec863a4bcdf043cf270","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e0885b8b9f460b7ed6bc97e4fc95b780ba06c8e1a259ec863a4bcdf043cf270","first_computed_at":"2026-07-08T01:19:25.015800Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-08T01:19:25.015800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WzkA8jtKt3pN1oYSbdobO5j9WKFtt/QKcxHaBdt/SMGejsSb0YfCIgOqtYYkP0kq0ddF9eg+UHnOIgnOwBWtCg==","signature_status":"signed_v1","signed_at":"2026-07-08T01:19:25.016233Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.06428","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:240549678536a77ffb590351800bfda9b28674103e1280c8304b59a4a8cf43c7","sha256:24611868b3ac24dd82556d97c89a92f07c8d97ef7a8bdd9eb42f08b536747aac","sha256:5ab513a1220e2084368fd57b63d290c4744b273e769d406bd9e4f133f0118ebd","sha256:b30c1c75d8bc62eaf76245567cba72ee42a4fa8a509b99d06d55f16597ac56a5","sha256:f0019310edca2cdf689fb217e25ecfe4151392b41d71c5d7ad770d9af688ae2b"]}],"invalid_events":[],"applied_event_ids":["sha256:74d53509a16de9838a1187a07ed11a90522f299dcad47051a0cea89ad7c76d69","sha256:499ab2b781e60791820764ea4b67ac28a2ae9cc1dd0218e8ee5004c62d2a4b88"],"state_sha256":"6170a75e2213d34d9f62caa836e00e88e3442a5ec7e4a2d3ead2472846f9854c"}