{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:EATF4UR3IMNBYSCH37XNZJJO7X","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":"5a372fc986ecbdc30be8a2bda51e5d7c3684f428bf07ff1c46a0863de2b292b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-06-11T09:31:10Z","title_canon_sha256":"6636fe52999c6e772e1e51a682cfbee44d242af994bb46a631a17de1189fe197"},"schema_version":"1.0","source":{"id":"2106.06264","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.06264","created_at":"2026-07-05T05:12:48Z"},{"alias_kind":"arxiv_version","alias_value":"2106.06264v3","created_at":"2026-07-05T05:12:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.06264","created_at":"2026-07-05T05:12:48Z"},{"alias_kind":"pith_short_12","alias_value":"EATF4UR3IMNB","created_at":"2026-07-05T05:12:48Z"},{"alias_kind":"pith_short_16","alias_value":"EATF4UR3IMNBYSCH","created_at":"2026-07-05T05:12:48Z"},{"alias_kind":"pith_short_8","alias_value":"EATF4UR3","created_at":"2026-07-05T05:12:48Z"}],"graph_snapshots":[{"event_id":"sha256:d94c21f3c3872063ead7a9cee3a34d672d050fb5c70523da40df6b68bfac19be","target":"graph","created_at":"2026-07-05T05:12:48Z","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/2106.06264/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The present work is devoted to the study of the large time behaviour of a critical Brownian diffusion in two dimensions, whose drift is divergence-free, ergodic and given by the curl of the 2-dimensional Gaussian Free Field. We prove the conjecture, made in [B. T\\'oth, B. Valk\\'o, J. Stat. Phys., 2012], according to which the diffusion coefficient $D(t)$ diverges as $\\sqrt{\\log t}$ for $t\\to\\infty$. Starting from the fundamental work by Alder and Wainwright [B. Alder, T. Wainright, Phys. Rev. Lett. 1967], logarithmically superdiffusive behaviour has been predicted to occur for a wide variety o","authors_text":"Fabio Toninelli, Giuseppe Cannizzaro, Levi Haunschmid-Sibitz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-06-11T09:31:10Z","title":"$\\sqrt{\\log t}$-superdiffusivity for a Brownian particle in the curl of the 2d GFF"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.06264","kind":"arxiv","version":3},"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:fd78b7e9ae18ec0b1d8da885ab078d04896f2973ae57a3f586542402352bb5de","target":"record","created_at":"2026-07-05T05:12:48Z","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":"5a372fc986ecbdc30be8a2bda51e5d7c3684f428bf07ff1c46a0863de2b292b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-06-11T09:31:10Z","title_canon_sha256":"6636fe52999c6e772e1e51a682cfbee44d242af994bb46a631a17de1189fe197"},"schema_version":"1.0","source":{"id":"2106.06264","kind":"arxiv","version":3}},"canonical_sha256":"20265e523b431a1c4847dfeedca52efdc6f7dadc63d7e61d1d8c0f7cf96cf662","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20265e523b431a1c4847dfeedca52efdc6f7dadc63d7e61d1d8c0f7cf96cf662","first_computed_at":"2026-07-05T05:12:48.601205Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:12:48.601205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uYfhUF0QKDI7FBfFBHVd5TLhyANx9BKmFPNgjUMJtTAdVkLSrpeJSwRvnLbHM04aUH/f5PcS3aeU7CnL11TTDg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:12:48.601704Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.06264","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd78b7e9ae18ec0b1d8da885ab078d04896f2973ae57a3f586542402352bb5de","sha256:d94c21f3c3872063ead7a9cee3a34d672d050fb5c70523da40df6b68bfac19be"],"state_sha256":"88115071fdc69cc33b34c4b0be2de451e013fa399b5386749f34e474279a4171"}