{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SAIJPGNOHXDKTH77NPR2F4MCN2","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":"572b8b81334593653d68b4c4d0085a5bdc25f42890ff29d1daa38759e38da62c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-04T20:40:51Z","title_canon_sha256":"cdc851fbf5750b2dca24f7aab965a3c29eb1f5b6e07e75cc8cd70d6f3e730cc8"},"schema_version":"1.0","source":{"id":"1406.1206","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.1206","created_at":"2026-05-18T01:27:36Z"},{"alias_kind":"arxiv_version","alias_value":"1406.1206v2","created_at":"2026-05-18T01:27:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1206","created_at":"2026-05-18T01:27:36Z"},{"alias_kind":"pith_short_12","alias_value":"SAIJPGNOHXDK","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SAIJPGNOHXDKTH77","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SAIJPGNO","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:d27cfb6663591a73af70c94dc9307b0ca9233061b57efc3f3dd342f87175237f","target":"graph","created_at":"2026-05-18T01:27:36Z","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 obtain sharp asymptotics for the probability that the (2+1)-dimensional discrete SOS interface at low temperature is positive in a large region. For a square region $\\Lambda$, both under the infinite volume measure and under the measure with zero boundary conditions around $\\Lambda$, this probability turns out to behave like $\\exp(-\\tau_\\beta(0) L \\log L )$, with $\\tau_\\beta(0)$ the surface tension at zero tilt, also called step free energy, and $L$ the box side. This behavior is qualitatively different from the one found for continuous height massless gradient interface models.","authors_text":"Fabio Lucio Toninelli, Fabio Martinelli, Pietro Caputo","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-04T20:40:51Z","title":"On the probability of staying above a wall for the (2+1)-dimensional SOS model at low temperature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1206","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":"sha256:0e87caff983b5a1ac6e2a0f42ecacad0196222b971f72e0d9cb0983995821e14","target":"record","created_at":"2026-05-18T01:27:36Z","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":"572b8b81334593653d68b4c4d0085a5bdc25f42890ff29d1daa38759e38da62c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-04T20:40:51Z","title_canon_sha256":"cdc851fbf5750b2dca24f7aab965a3c29eb1f5b6e07e75cc8cd70d6f3e730cc8"},"schema_version":"1.0","source":{"id":"1406.1206","kind":"arxiv","version":2}},"canonical_sha256":"90109799ae3dc6a99fff6be3a2f1826e821ac93de63c8464ff9814abafd6ad77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90109799ae3dc6a99fff6be3a2f1826e821ac93de63c8464ff9814abafd6ad77","first_computed_at":"2026-05-18T01:27:36.855561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:36.855561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UYI0+rQ/AuTdj3nS02eGbnn+0IWcG8hZoR5UWxtOIxkeuEeWSd5VyHECiNStLR8MaUDXCMtIaCOIHLM8Rx2+Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:36.856133Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.1206","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e87caff983b5a1ac6e2a0f42ecacad0196222b971f72e0d9cb0983995821e14","sha256:d27cfb6663591a73af70c94dc9307b0ca9233061b57efc3f3dd342f87175237f"],"state_sha256":"5f61489918dc361f10e58dea540579471fc7f3781b646b63941f642e3e26313a"}