{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3IC5TPJPX6LQZ72YGCN4TLZTZT","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":"ebd46cdee0ff397c70ed6222c72aa01f4a10458b776ca26275c65d44a1ea331f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-17T19:06:54Z","title_canon_sha256":"115509931e981eb50c2036ee1c61436dba31d86816636b99a605e638e261f20e"},"schema_version":"1.0","source":{"id":"1504.04606","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04606","created_at":"2026-05-18T01:08:32Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04606v3","created_at":"2026-05-18T01:08:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04606","created_at":"2026-05-18T01:08:32Z"},{"alias_kind":"pith_short_12","alias_value":"3IC5TPJPX6LQ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3IC5TPJPX6LQZ72Y","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3IC5TPJP","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:1000d985f29913499c3e514693b10fb5b2a907d8fe412a4acd1ea6998f4d9eb0","target":"graph","created_at":"2026-05-18T01:08:32Z","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 study the level lines of GFF starting from interior points. We show that the level line of GFF starting from an interior point turns out to be a sequence of level loops. The sequence of level loops satisfies \"target-independent\" property. All sequences of level loops starting from interior points give a tree-structure of the plane. We also introduce the continuum exploration process of GFF starting from interior. The continuum exploration process of whole-plane GFF satisfies \"reversibility\".","authors_text":"Hao Wu, Menglu Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-17T19:06:54Z","title":"Level Lines of Gaussian Free Field II: Whole-Plane GFF"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04606","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":"sha256:9628e3cb841a47ba4d05d084cd5e793b3902c24d7d3d8661c52054350a913373","target":"record","created_at":"2026-05-18T01:08:32Z","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":"ebd46cdee0ff397c70ed6222c72aa01f4a10458b776ca26275c65d44a1ea331f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-17T19:06:54Z","title_canon_sha256":"115509931e981eb50c2036ee1c61436dba31d86816636b99a605e638e261f20e"},"schema_version":"1.0","source":{"id":"1504.04606","kind":"arxiv","version":3}},"canonical_sha256":"da05d9bd2fbf970cff58309bc9af33ccd565260fa374b2f3ac3092c8082373a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da05d9bd2fbf970cff58309bc9af33ccd565260fa374b2f3ac3092c8082373a2","first_computed_at":"2026-05-18T01:08:32.613943Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:32.613943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LZWQPL79bfTRkdk1RCWSZ2I3jeVmXb7vSBwcQPFEuRUcz6Gx/KYkp1RZn31tQd2+u62E0QJtsqy/BOSiulVJCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:32.614680Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.04606","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9628e3cb841a47ba4d05d084cd5e793b3902c24d7d3d8661c52054350a913373","sha256:1000d985f29913499c3e514693b10fb5b2a907d8fe412a4acd1ea6998f4d9eb0"],"state_sha256":"c9d83589a5b35a69a1410fb5fc2042e56a1f56f70207a461c5d3610992c13ed6"}