{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QXKNUDLE4HHMMSFMETXQASF6FY","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":"a127752becf6417aa6aff116eb95ee03c0304691a4930d12dee66ec1d49e487f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-27T12:22:37Z","title_canon_sha256":"9118b737c8a0e1006e66c111727b119b5d7de4c67836d344aba3aa9cd48bb8bf"},"schema_version":"1.0","source":{"id":"1605.08605","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08605","created_at":"2026-05-18T01:11:04Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08605v2","created_at":"2026-05-18T01:11:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08605","created_at":"2026-05-18T01:11:04Z"},{"alias_kind":"pith_short_12","alias_value":"QXKNUDLE4HHM","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"QXKNUDLE4HHMMSFM","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"QXKNUDLE","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:5d553e51a9483f32d6311977d825c406e64543c9f08d4a037c0c68734d46e4ac","target":"graph","created_at":"2026-05-18T01:11:04Z","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 prove  a Russo-Seymour-Welsch percolation theorem  for nodal domains and nodal lines  associated to a natural  infinite dimensional space of  real analytic functions on  the real plane. More precisely, let  $U$  be  a   smooth  connected  bounded  open  set   in  $\\mathbb R^2$  and  $\\gamma,  \\gamma'$  two disjoint  arcs  of  positive length  in  the  boundary of $U$. We prove that there exists a positive constant  $c$, such that for any  positive scale $s$, with probability at  least    $c$    there    exists    a    connected    component    of  $\\{x\\in  \\bar U,  \\, f(sx)  \\textgreater{} ","authors_text":"Damien Gayet (IF), Vincent Beffara (IF)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-27T12:22:37Z","title":"Percolation of random nodal lines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08605","kind":"arxiv","version":2},"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":"sha256:5d5e92bffc0125f38932ba42d11696042423ed8b38c05854f27341464cefb845","target":"record","created_at":"2026-05-18T01:11:04Z","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":"a127752becf6417aa6aff116eb95ee03c0304691a4930d12dee66ec1d49e487f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-27T12:22:37Z","title_canon_sha256":"9118b737c8a0e1006e66c111727b119b5d7de4c67836d344aba3aa9cd48bb8bf"},"schema_version":"1.0","source":{"id":"1605.08605","kind":"arxiv","version":2}},"canonical_sha256":"85d4da0d64e1cec648ac24ef0048be2e15a2561fee4f85d3281fbf17e1ac0e98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85d4da0d64e1cec648ac24ef0048be2e15a2561fee4f85d3281fbf17e1ac0e98","first_computed_at":"2026-05-18T01:11:04.671034Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:04.671034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dgoC2HdkGqmpyO7ZF/u3V2qp+kUIgJIrnTcQqMswC2L8tXF9f/r6f0ZvXlVR/JRqIISvnlI49wSeVipIE9jFDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:04.671413Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.08605","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d5e92bffc0125f38932ba42d11696042423ed8b38c05854f27341464cefb845","sha256:5d553e51a9483f32d6311977d825c406e64543c9f08d4a037c0c68734d46e4ac"],"state_sha256":"224a8a6c026a1d1dea48c6ce12d04452add319f599c3dc9eaccb30232fdab966"}