{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:U5XTPUEZKIMNYKUZVGCRA2P33E","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":"983a4b86f443483d8a655448695c852d6e9d22414a833d1b226700f838f34790","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-11T14:52:56Z","title_canon_sha256":"b1466f048fe552ac70358ece082d50f03c4f486b0ccd3f28335364d4e4ac9acf"},"schema_version":"1.0","source":{"id":"1810.05062","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.05062","created_at":"2026-05-18T00:03:35Z"},{"alias_kind":"arxiv_version","alias_value":"1810.05062v1","created_at":"2026-05-18T00:03:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05062","created_at":"2026-05-18T00:03:35Z"},{"alias_kind":"pith_short_12","alias_value":"U5XTPUEZKIMN","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U5XTPUEZKIMNYKUZ","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U5XTPUEZ","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:5ffe9a9b61eceb302a9b3462a2c6b758f6b903d75389f92aea994c2f3659f5bc","target":"graph","created_at":"2026-05-18T00:03:35Z","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 consider the membrane model on a box $V_N\\subset \\mathbb{Z}^n$ of size $(2N+1)^n$ with zero boundary condition in the subcritical dimensions $n=2$ and $n=3$. We show optimal estimates for the probability that the field is positive in a subset $D_N$ of $V_N$. In particular we obtain for $D_N=V_N$ that the probability to be positive on the entire domain is exponentially small and the rate is of the order of the surface area $N^{n-1}$.","authors_text":"Florian Schweiger, Jean-Dominique Deuschel, Noemi Kurt, Simon Buchholz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-11T14:52:56Z","title":"Probability to be positive for the membrane model in dimensions 2 and 3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05062","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":"sha256:9d4b6d55254792aea688bd2499766a601fcf7dba1e5b0f1a7caf215a5adcd52e","target":"record","created_at":"2026-05-18T00:03:35Z","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":"983a4b86f443483d8a655448695c852d6e9d22414a833d1b226700f838f34790","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-11T14:52:56Z","title_canon_sha256":"b1466f048fe552ac70358ece082d50f03c4f486b0ccd3f28335364d4e4ac9acf"},"schema_version":"1.0","source":{"id":"1810.05062","kind":"arxiv","version":1}},"canonical_sha256":"a76f37d0995218dc2a99a9851069fbd932ab7eb629c36eec43f4644c7e98a97a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a76f37d0995218dc2a99a9851069fbd932ab7eb629c36eec43f4644c7e98a97a","first_computed_at":"2026-05-18T00:03:35.049839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:35.049839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WVFYoNQuXMS0i3rEKxBlFJXOcjmrXgIcjzD3H2C6aDT9PIaSHPRCIZDFrer2lZjmMQZLYIQmkd6nGMCnkHtDDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:35.050382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.05062","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d4b6d55254792aea688bd2499766a601fcf7dba1e5b0f1a7caf215a5adcd52e","sha256:5ffe9a9b61eceb302a9b3462a2c6b758f6b903d75389f92aea994c2f3659f5bc"],"state_sha256":"64a8aa1bc992f9d911aa03115090497675a86dce5beca82d7f5cd133fdd24a9d"}