{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QJ3JASU7LBUKDZY5HL2KI3AKRY","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":"ef42deaf50a3b3df499a180a939ebc42a54d178691bd97e2d5ad3a4d98d9634b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-08T22:14:49Z","title_canon_sha256":"3664dd301029fae73c58822dd8a242d95b58e6e79471c0455fce96c64fc75440"},"schema_version":"1.0","source":{"id":"1202.1847","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.1847","created_at":"2026-05-18T00:26:40Z"},{"alias_kind":"arxiv_version","alias_value":"1202.1847v1","created_at":"2026-05-18T00:26:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1847","created_at":"2026-05-18T00:26:40Z"},{"alias_kind":"pith_short_12","alias_value":"QJ3JASU7LBUK","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QJ3JASU7LBUKDZY5","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QJ3JASU7","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:e87f08b57336ed587eb10ad509ad1647a7e92f9c4e3cf3fbb41c9b28c985e32c","target":"graph","created_at":"2026-05-18T00:26:40Z","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":"Let (B_t : t > 0) be a planar Brownian motion and define gauge functions $\\phi_\\alpha(s)=log(1/s)^{-\\alpha}$ for $\\alpha>0$. If $\\alpha<1$ we show that almost surely there exists a point x in the plane such that $H^{\\phi_\\alpha}({t > 0 : B_t=x})>0$, but if $\\alpha>1$ almost surely $H^{\\phi_\\alpha} ({t > 0 : B_t=x})=0$ simultaneously for all $x\\in R^2$. This resolves a longstanding open problem posed by S.,J. Taylor in 1986.","authors_text":"Peter M\\\"orters, Valentina Cammarota","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-08T22:14:49Z","title":"On the most visited sites of planar Brownian motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1847","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:ab9a5c282ac8b19660a3bb54135665fe2c054c871ad2a8f8ffc3a913217ffaf0","target":"record","created_at":"2026-05-18T00:26:40Z","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":"ef42deaf50a3b3df499a180a939ebc42a54d178691bd97e2d5ad3a4d98d9634b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-08T22:14:49Z","title_canon_sha256":"3664dd301029fae73c58822dd8a242d95b58e6e79471c0455fce96c64fc75440"},"schema_version":"1.0","source":{"id":"1202.1847","kind":"arxiv","version":1}},"canonical_sha256":"8276904a9f5868a1e71d3af4a46c0a8e33750b7705e3aef97f09aa17ff11b01d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8276904a9f5868a1e71d3af4a46c0a8e33750b7705e3aef97f09aa17ff11b01d","first_computed_at":"2026-05-18T00:26:40.557925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:40.557925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EeCzY6SYYiwyTsKm16fXddndKDV4dU0eEhNAt8yJpKXCZtC9mZk+s3i0qBPrK0TmHD5zFwS4FQ0YrdFaw/QTBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:40.558512Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.1847","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab9a5c282ac8b19660a3bb54135665fe2c054c871ad2a8f8ffc3a913217ffaf0","sha256:e87f08b57336ed587eb10ad509ad1647a7e92f9c4e3cf3fbb41c9b28c985e32c"],"state_sha256":"2e810e23db9b9bd5884a45b0a399bd2475161423517837941e1de51b4d809f27"}