{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:NYEILOFZ6RQLP3LLZF7E7SK3PA","short_pith_number":"pith:NYEILOFZ","canonical_record":{"source":{"id":"2607.06428","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-07T15:55:05Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"efe69fdc144ddaf8880c056da9a5896f46bd578adb42c64c410d12eb3540d94c","abstract_canon_sha256":"31927e08fad083fe63d4fff027681801f73208a58265aac2c3c46b8ee1da24a6"},"schema_version":"1.0"},"canonical_sha256":"6e0885b8b9f460b7ed6bc97e4fc95b780ba06c8e1a259ec863a4bcdf043cf270","source":{"kind":"arxiv","id":"2607.06428","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:NYEILOFZ6RQLP3LLZF7E7SK3PA","target":"record","payload":{"canonical_record":{"source":{"id":"2607.06428","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-07T15:55:05Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"efe69fdc144ddaf8880c056da9a5896f46bd578adb42c64c410d12eb3540d94c","abstract_canon_sha256":"31927e08fad083fe63d4fff027681801f73208a58265aac2c3c46b8ee1da24a6"},"schema_version":"1.0"},"canonical_sha256":"6e0885b8b9f460b7ed6bc97e4fc95b780ba06c8e1a259ec863a4bcdf043cf270","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-08T01:19:25.016233Z","signature_b64":"WzkA8jtKt3pN1oYSbdobO5j9WKFtt/QKcxHaBdt/SMGejsSb0YfCIgOqtYYkP0kq0ddF9eg+UHnOIgnOwBWtCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e0885b8b9f460b7ed6bc97e4fc95b780ba06c8e1a259ec863a4bcdf043cf270","last_reissued_at":"2026-07-08T01:19:25.015800Z","signature_status":"signed_v1","first_computed_at":"2026-07-08T01:19:25.015800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.06428","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":"2026-07-08T01:19:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4RYZXSjYxRWBlYXadFEjQc7voRWP/YGDxlujq43/5uR8NppoPFLaK8ywlLtBXv5kxZGfN2gG+Ysz0DfBREHjDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T07:42:19.585722Z"},"content_sha256":"74d53509a16de9838a1187a07ed11a90522f299dcad47051a0cea89ad7c76d69","schema_version":"1.0","event_id":"sha256:74d53509a16de9838a1187a07ed11a90522f299dcad47051a0cea89ad7c76d69"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:NYEILOFZ6RQLP3LLZF7E7SK3PA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Impact of spinning on the early-warning signs in non-Markovian stochastic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Alexandra Blessing, Dennis Rudik, Paolo Bernuzzi","submitted_at":"2026-07-07T15:55:05Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06428","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.06428/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-08T01:19:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SkEzp/V97rNaO5ICy7kPO4+FpDfKN8vxfczNEMxwx3MXEnEt5lVPFCAX0cyWz7kJDZEeB0znLVo9J+6d2jPRCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T07:42:19.586797Z"},"content_sha256":"499ab2b781e60791820764ea4b67ac28a2ae9cc1dd0218e8ee5004c62d2a4b88","schema_version":"1.0","event_id":"sha256:499ab2b781e60791820764ea4b67ac28a2ae9cc1dd0218e8ee5004c62d2a4b88"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:NYEILOFZ6RQLP3LLZF7E7SK3PA","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1098/rsos.250573.eprint:https://royalsocietypublishing.org/rsos/article-pdf/doi/10.1098/rsos.250573/2823160/rsos.250573.pdf.url:https://doi.org/10.1098/rsos.250573.49) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"A. Morr, D. Kreher, and N. Boers. “Red noise in continuous-time stochastic modelling.” In:R. Soc. Open Sci.12.8 (Aug. 2025), p. 250573.issn: 2054-5703.doi:10.1098/rsos. 250573. eprint:https://royalsocietypublishing.org/rsos/article- pdf/doi","arxiv_id":"2607.06428","detector":"doi_compliance","evidence":{"ref_index":38,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"A. Morr, D. Kreher, and N. Boers. “Red noise in continuous-time stochastic modelling.” In:R. Soc. Open Sci.12.8 (Aug. 2025), p. 250573.issn: 2054-5703.doi:10.1098/rsos. 250573. eprint:https://royalsocietypublishing.org/rsos/article- pdf/doi","reconstructed_doi":"10.1098/rsos.250573.eprint:https://royalsocietypublishing.org/rsos/article-pdf/doi/10.1098/rsos.250573/2823160/rsos.250573.pdf.url:https://doi.org/10.1098/rsos.250573.49"},"severity":"advisory","ref_index":38,"audited_at":"2026-07-09T07:27:44.143559Z","event_type":"pith.integrity.v1","detected_doi":"10.1098/rsos.250573.eprint:https://royalsocietypublishing.org/rsos/article-pdf/doi/10.1098/rsos.250573/2823160/rsos.250573.pdf.url:https://doi.org/10.1098/rsos.250573.49","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"80cac640a9cdca64bb89ae5aab7a0b3ed203760e3681907d5fa69f361daa54b4","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":7783,"payload_sha256":"24124128ab5927ee1ee13ba7d3943bfb800aa7fc1f1d3a979735e67963443007","signature_b64":"WnOkB3hOtw0vpdFN14TK+95ZCQwSX6pMSI8Bt9lcdObF/y5zOZse6mvF6pO3z/3GmKL6R+aK2smLc6XAS+e4BQ==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-09T07:32:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/OKn3BAvGmzp6LAd4rrMA35cmRoxr6Ojcw74k+jPxPHUqHt2nJhEneuwwwblUOtU6hkGKtQIga9bduo77FALDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T07:42:19.594025Z"},"content_sha256":"240549678536a77ffb590351800bfda9b28674103e1280c8304b59a4a8cf43c7","schema_version":"1.0","event_id":"sha256:240549678536a77ffb590351800bfda9b28674103e1280c8304b59a4a8cf43c7"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:NYEILOFZ6RQLP3LLZF7E7SK3PA","target":"integrity","payload":{"note":"Identifier '10.1088/1748-9326/acbc8d.url:https://doi.org/10.1088/1748-9326/acbc8d' is syntactically valid but the DOI registry (doi.org) returned 404, and Crossref / OpenAlex / internal corpus also have no record. The cited work could not be located through any authoritative source.","snippet":"J. J. Clarke et al. “Seeking more robust early warning signals for climate tipping points: the ratio of spectra method (ROSA).” In:Environ. Res. Lett.18.3 (Feb. 2023), p. 035006. doi:10.1088/1748-9326/acbc8d.url:https://doi.org/10.1088/1748","arxiv_id":"2607.06428","detector":"doi_compliance","evidence":{"doi":"10.1088/1748-9326/acbc8d.url:https://doi.org/10.1088/1748-9326/acbc8d","arxiv_id":null,"ref_index":16,"raw_excerpt":"J. J. Clarke et al. “Seeking more robust early warning signals for climate tipping points: the ratio of spectra method (ROSA).” In:Environ. Res. Lett.18.3 (Feb. 2023), p. 035006. doi:10.1088/1748-9326/acbc8d.url:https://doi.org/10.1088/1748-9326/acbc8d","verdict_class":"cross_source","checked_sources":["crossref_by_doi","openalex_by_doi","doi_org_head"]},"severity":"critical","ref_index":16,"audited_at":"2026-07-09T07:27:44.143559Z","event_type":"pith.integrity.v1","detected_doi":"10.1088/1748-9326/acbc8d.url:https://doi.org/10.1088/1748-9326/acbc8d","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"unresolvable_identifier","evidence_hash":"7efbf8c39d31dac24c87737abcebc8639e84eb82962201ad44212b035f762b99","paper_version":1,"verdict_class":"cross_source","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":7782,"payload_sha256":"67bf25eb92c7445e9a64c4b1e32a0d68f145f89356604c0968cbeff672fe80a3","signature_b64":"hWrGbM25EjmkesnrETOJMg5zgsvtqrz6hGDNsqzPUUGMaDVF0PXCEuCSJODp8K+icb4Hh7d4to1vLPPO4e22Aw==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-09T07:32:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4/DgC9JJrmlk066/uQEjzASIehVjEQUzBHpWD7z2aXJtzD1JekQKo0V51wZuENU4TZ3Dz5EVvPKFHHEsIkzbDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T07:42:19.594794Z"},"content_sha256":"f0019310edca2cdf689fb217e25ecfe4151392b41d71c5d7ad770d9af688ae2b","schema_version":"1.0","event_id":"sha256:f0019310edca2cdf689fb217e25ecfe4151392b41d71c5d7ad770d9af688ae2b"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:NYEILOFZ6RQLP3LLZF7E7SK3PA","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1214/ejp.v8-125.url:https://doi.org/10.1214/EJP.v8-125) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"P. Cheridito, H. Kawaguchi, and M. Maejima. “Fractional Ornstein-Uhlenbeck processes.” In:Electron. J. Probab.8.none (2003), pp. 1–14.doi:10.1214/EJP.v8-125.url:https: //doi.org/10.1214/EJP.v8-125","arxiv_id":"2607.06428","detector":"doi_compliance","evidence":{"ref_index":14,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"P. Cheridito, H. Kawaguchi, and M. Maejima. “Fractional Ornstein-Uhlenbeck processes.” In:Electron. J. Probab.8.none (2003), pp. 1–14.doi:10.1214/EJP.v8-125.url:https: //doi.org/10.1214/EJP.v8-125","reconstructed_doi":"10.1214/ejp.v8-125.url:https://doi.org/10.1214/EJP.v8-125"},"severity":"advisory","ref_index":14,"audited_at":"2026-07-09T07:27:44.143559Z","event_type":"pith.integrity.v1","detected_doi":"10.1214/ejp.v8-125.url:https://doi.org/10.1214/EJP.v8-125","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"4c6be51dd8c37fbb98a3697554e8e91830042e5492381174d13f328bd833fc66","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":7781,"payload_sha256":"af16e2ae2befdf1138477278b4d834b4df1b60fc92a7a6f3c023fe2689067780","signature_b64":"u2N0m2I9b0e5kaIC0iJYB0QH0wXoH5njwiRtv05wdlEhDBGDgGFy2WX5plI0GUxfqb1Nn6q2PYXfc8kkKCb9Bg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-09T07:32:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cYU+zB7eSNhMDElP+fSLOwQoyGq19DiSBlpFcjlW4HJ+T4V24oLwjLBF5h80GqS3oqPGLERpXs4rFauYEqF4Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T07:42:19.595550Z"},"content_sha256":"b30c1c75d8bc62eaf76245567cba72ee42a4fa8a509b99d06d55f16597ac56a5","schema_version":"1.0","event_id":"sha256:b30c1c75d8bc62eaf76245567cba72ee42a4fa8a509b99d06d55f16597ac56a5"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:NYEILOFZ6RQLP3LLZF7E7SK3PA","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1016/j.chaos.2024.115409.url:https://www.sciencedirect.com/science/article/pii/S0960077924009615) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"Z. Chen et al. “Effective detection of early warning signal with power spectrum in climate change system.” In:Chaos Solit. Fractals187 (2024), p. 115409.issn: 0960-0779.doi: https://doi.org/10.1016/j.chaos.2024.115409.url:https://www.scienc","arxiv_id":"2607.06428","detector":"doi_compliance","evidence":{"ref_index":13,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"Z. Chen et al. “Effective detection of early warning signal with power spectrum in climate change system.” In:Chaos Solit. Fractals187 (2024), p. 115409.issn: 0960-0779.doi: https://doi.org/10.1016/j.chaos.2024.115409.url:https://www.scienc","reconstructed_doi":"10.1016/j.chaos.2024.115409.url:https://www.sciencedirect.com/science/article/pii/S0960077924009615"},"severity":"advisory","ref_index":13,"audited_at":"2026-07-09T07:27:44.143559Z","event_type":"pith.integrity.v1","detected_doi":"10.1016/j.chaos.2024.115409.url:https://www.sciencedirect.com/science/article/pii/S0960077924009615","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"089d55abc8d3b2f8afea17109d8a2889057696d0366e53b57fed75bb90288f7c","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":7780,"payload_sha256":"486486e411692c3f6ec78cdef44aa350402c0a02653b39c0e0eab2f8ef7d7609","signature_b64":"FkYru9dWV7no3kAn2Y/J62rlSIBPy8+xyfY9DGTkKfUxyaMGNwAcDU9LO9xalWqzr25BCx1ts9waULbXG0bnBg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-09T07:32:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WQqzRJ6LTgNIfLRpvom3gotrXMH+ZRVbLkwbQqmvKS5BgNjjn++HK/DVsIC30lhHZPzUXJffa9NfzJ82YDttBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T07:42:19.596341Z"},"content_sha256":"5ab513a1220e2084368fd57b63d290c4744b273e769d406bd9e4f133f0118ebd","schema_version":"1.0","event_id":"sha256:5ab513a1220e2084368fd57b63d290c4744b273e769d406bd9e4f133f0118ebd"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:NYEILOFZ6RQLP3LLZF7E7SK3PA","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1175/1520-0485(1994)024<1911:ASBMOS>) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"P. Cessi. “A Simple Box Model of Stochastically Forced Thermohaline Flow.” In:J. Phys. Oceanogr.24.9 (1994), pp. 1911–1920.doi:10.1175/1520-0485(1994)024<1911:ASBMOS> 2.0.CO;2.url:https://journals.ametsoc.org/view/journals/phoc/24/9/1520- 0","arxiv_id":"2607.06428","detector":"doi_compliance","evidence":{"ref_index":12,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"P. Cessi. “A Simple Box Model of Stochastically Forced Thermohaline Flow.” In:J. Phys. Oceanogr.24.9 (1994), pp. 1911–1920.doi:10.1175/1520-0485(1994)024<1911:ASBMOS> 2.0.CO;2.url:https://journals.ametsoc.org/view/journals/phoc/24/9/1520- 0","reconstructed_doi":"10.1175/1520-0485(1994)024<1911:ASBMOS>"},"severity":"advisory","ref_index":12,"audited_at":"2026-07-09T07:27:44.143559Z","event_type":"pith.integrity.v1","detected_doi":"10.1175/1520-0485(1994)024<1911:ASBMOS>","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"716cd296ff90a48e7122e1d754ecd959483a595d54bc6b928b40594388453635","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":7779,"payload_sha256":"4923b8d5fed1f9d1fe9bbd9c601a8a137805c0b277a0980254115bcad49f3960","signature_b64":"PVrTA40vt4+0ojdpgu18cvbLV+Whv/PQyExQUf2Zzmv8vkVtbABPg0PgVnTr+G94bL7O+4siy7vcBTJbHxolBQ==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-09T07:32:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EATYazyCptFjH3rmZ9poFNmePqHtKWBm+70jdAxNgrpkP/4WV/rnf93GgrU/gwSTmgVKXjhc7RkWSwtdhqTqDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T07:42:19.597057Z"},"content_sha256":"24611868b3ac24dd82556d97c89a92f07c8d97ef7a8bdd9eb42f08b536747aac","schema_version":"1.0","event_id":"sha256:24611868b3ac24dd82556d97c89a92f07c8d97ef7a8bdd9eb42f08b536747aac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NYEILOFZ6RQLP3LLZF7E7SK3PA/bundle.json","state_url":"https://pith.science/pith/NYEILOFZ6RQLP3LLZF7E7SK3PA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NYEILOFZ6RQLP3LLZF7E7SK3PA/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":"2026-08-12T07:42:19Z","links":{"resolver":"https://pith.science/pith/NYEILOFZ6RQLP3LLZF7E7SK3PA","bundle":"https://pith.science/pith/NYEILOFZ6RQLP3LLZF7E7SK3PA/bundle.json","state":"https://pith.science/pith/NYEILOFZ6RQLP3LLZF7E7SK3PA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NYEILOFZ6RQLP3LLZF7E7SK3PA/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lga+GUVdOySvXEQA0v4YYfH+Xm2p6B0D4Wc+LGTjiPIT1htOShC7ozykBaxtaw+7wQiuwoq53KNuGKpOTmz2CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T07:42:19.603042Z","bundle_sha256":"ed432cce9284bd8d23038e62b89e0ba24c97c7f3e80c2dbb437dd3fc102def7a"}}