{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:IUJRBGZJKV3HHIS6JURNKNMDLJ","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":"73f49bc7d8358e2cb1d5862fe28fa9a76264d46181435e0d2a33047c7dcd5fee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-07-10T09:18:50Z","title_canon_sha256":"adb3d56af3e1613c2ac73810076f15d6ff948269cbbcd521c3b37d3ef4b89e3e"},"schema_version":"1.0","source":{"id":"2307.04434","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.04434","created_at":"2026-07-05T06:29:13Z"},{"alias_kind":"arxiv_version","alias_value":"2307.04434v1","created_at":"2026-07-05T06:29:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.04434","created_at":"2026-07-05T06:29:13Z"},{"alias_kind":"pith_short_12","alias_value":"IUJRBGZJKV3H","created_at":"2026-07-05T06:29:13Z"},{"alias_kind":"pith_short_16","alias_value":"IUJRBGZJKV3HHIS6","created_at":"2026-07-05T06:29:13Z"},{"alias_kind":"pith_short_8","alias_value":"IUJRBGZJ","created_at":"2026-07-05T06:29:13Z"}],"graph_snapshots":[{"event_id":"sha256:0e06337aed7aa77a067063cd40668a90f260bdc14f572ce9aa6c144d75540594","target":"graph","created_at":"2026-07-05T06:29:13Z","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/2307.04434/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the critical level-set of Gaussian free field (GFF) on the metric graph $\\widetilde{\\mathbb{Z}}^d,d>6$. We prove that the one-arm probability (i.e. the probability of the event that the origin is connected to the boundary of the box $B(N)$) is proportional to $N^{-2}$, where $B(N)$ is centered at the origin and has side length $2\\lfloor N \\rfloor$. Our proof is hugely inspired by Kozma and Nachmias [29] which proves the analogous result of the critical bond percolation for $d\\geq 11$, and by Werner [51] which conjectures the similarity between the GFF level-set and the ","authors_text":"Jian Ding, Zhenhao Cai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-07-10T09:18:50Z","title":"One-arm exponent of critical level-set for metric graph Gaussian free field in high dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.04434","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":"sha256:274d0853804fc5c151453fd0c333b92c17379306e69f5c4bdd9319d28413558a","target":"record","created_at":"2026-07-05T06:29:13Z","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":"73f49bc7d8358e2cb1d5862fe28fa9a76264d46181435e0d2a33047c7dcd5fee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-07-10T09:18:50Z","title_canon_sha256":"adb3d56af3e1613c2ac73810076f15d6ff948269cbbcd521c3b37d3ef4b89e3e"},"schema_version":"1.0","source":{"id":"2307.04434","kind":"arxiv","version":1}},"canonical_sha256":"4513109b29557673a25e4d22d535835a6544200f2760593d7bea4a25e1a0390a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4513109b29557673a25e4d22d535835a6544200f2760593d7bea4a25e1a0390a","first_computed_at":"2026-07-05T06:29:13.295045Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:29:13.295045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WfGqRcm2F+Wip2SOW8lwuRlQhYfmLWji+3omFAU69yu2gwezlPx4sC85OzTMYKeTTZit5fwsY0Hsz8af53kVCA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:29:13.295654Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.04434","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:274d0853804fc5c151453fd0c333b92c17379306e69f5c4bdd9319d28413558a","sha256:0e06337aed7aa77a067063cd40668a90f260bdc14f572ce9aa6c144d75540594"],"state_sha256":"bde142a9de8026608af9578258d745f36729fcf02df1fcf6878320986643486b"}