{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:CYL5NM3CBQTEPF7BW5SE2CRI4C","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":"0f950cec935f9e3c5c57a16bcfb58dcc6beb877573f9aba0d09dbaca21b215a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-06-04T15:11:49Z","title_canon_sha256":"91760b685815d7e323cb66b8df74edf8a4457cdd58d981df041f7f8b9133843e"},"schema_version":"1.0","source":{"id":"2406.02397","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.02397","created_at":"2026-07-05T08:43:10Z"},{"alias_kind":"arxiv_version","alias_value":"2406.02397v2","created_at":"2026-07-05T08:43:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.02397","created_at":"2026-07-05T08:43:10Z"},{"alias_kind":"pith_short_12","alias_value":"CYL5NM3CBQTE","created_at":"2026-07-05T08:43:10Z"},{"alias_kind":"pith_short_16","alias_value":"CYL5NM3CBQTEPF7B","created_at":"2026-07-05T08:43:10Z"},{"alias_kind":"pith_short_8","alias_value":"CYL5NM3C","created_at":"2026-07-05T08:43:10Z"}],"graph_snapshots":[{"event_id":"sha256:0ec6ad21779ed7b2fb4c68bf9759b8bf0daee46ac1ef61b16ef736dd74a3d430","target":"graph","created_at":"2026-07-05T08:43:10Z","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/2406.02397/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For the critical level-set of the Gaussian free field on the metric graph of $\\mathbb Z^d$, we consider the one-arm probability $\\theta_d(N)$, i.e., the probability that the boundary of a box of side length $2N$ is connected to the center. We prove that $\\theta_d(N)$ is $O(N^{-\\frac{d}{2}+1})$ for $3\\le d\\le 5$, and is $N^{-2+o(1)}$ for $d=6$. Our upper bounds match the lower bounds in a previous work by Ding and Wirth up to a constant factor for $3\\le d\\le 5$, and match the exponent therein for $d=6$. Combined with our previous result that $\\theta_d(N) \\asymp N^{-2}$ for $d>6$, this seems to ","authors_text":"Jian Ding, Zhenhao Cai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-06-04T15:11:49Z","title":"One-arm Probabilities for Metric Graph Gaussian Free Fields below and at the Critical Dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.02397","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:d5303936b18696d5876602b174ffa986ccc2b694b89215e66b6e636f76770038","target":"record","created_at":"2026-07-05T08:43:10Z","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":"0f950cec935f9e3c5c57a16bcfb58dcc6beb877573f9aba0d09dbaca21b215a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-06-04T15:11:49Z","title_canon_sha256":"91760b685815d7e323cb66b8df74edf8a4457cdd58d981df041f7f8b9133843e"},"schema_version":"1.0","source":{"id":"2406.02397","kind":"arxiv","version":2}},"canonical_sha256":"1617d6b3620c264797e1b7644d0a28e0a04001bbfadcc5527fe3b38f4049e419","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1617d6b3620c264797e1b7644d0a28e0a04001bbfadcc5527fe3b38f4049e419","first_computed_at":"2026-07-05T08:43:10.387672Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:43:10.387672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LcCbmkZ5KNAk1UchSbfTfI2w5M6lQh1dRXO+/f27M9TV/E2Hg7Vy0yreNNBJ8tRl+4p8uNBeBJWMeenPkAiyAA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:43:10.388099Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.02397","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5303936b18696d5876602b174ffa986ccc2b694b89215e66b6e636f76770038","sha256:0ec6ad21779ed7b2fb4c68bf9759b8bf0daee46ac1ef61b16ef736dd74a3d430"],"state_sha256":"1bb009338c596503f37ea49e9f28c1017607cc3b1fc84e2ef4253e4b8784319d"}