{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ADMBF5FFYHSXMSY4VMNWXTD7OB","short_pith_number":"pith:ADMBF5FF","schema_version":"1.0","canonical_sha256":"00d812f4a5c1e5764b1cab1b6bcc7f704ee76053abb49b45df040eab2c1f2b2c","source":{"kind":"arxiv","id":"1405.5241","version":1},"attestation_state":"computed","paper":{"title":"Harmonic pinnacles in the Discrete Gaussian model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Allan Sly, Eyal Lubetzky, Fabio Martinelli","submitted_at":"2014-05-20T20:55:12Z","abstract_excerpt":"The 2D Discrete Gaussian model gives each height function $\\eta : \\mathbb{Z}^2\\to\\mathbb{Z}$ a probability proportional to $\\exp(-\\beta \\mathcal{H}(\\eta))$, where $\\beta$ is the inverse-temperature and $\\mathcal{H}(\\eta) = \\sum_{x\\sim y}(\\eta_x-\\eta_y)^2$ sums over nearest-neighbor bonds. We consider the model at large fixed $\\beta$, where it is flat unlike its continuous analog (the Gaussian Free Field).\n  We first establish that the maximum height in an $L\\times L$ box with 0 boundary conditions concentrates on two integers $M,M+1$ with $M\\sim \\sqrt{(1/2\\pi\\beta)\\log L\\log\\log L}$. The key i"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1405.5241","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-20T20:55:12Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"15f7978026de0de47e93263df6ae0503153c0114b1c557eac63ab90d2ce59916","abstract_canon_sha256":"461b23efab4cb48c4a737925d080f517f424918e548c277e0807230c315a5317"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:24.716595Z","signature_b64":"b2PC+WWL8d+Cctg6DZxx8tTWO4T3GzjJdKUa0JoryFwHlOgQwp8ZTyeACk3UQoBTapYujLyTtgvSlICxpDShDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00d812f4a5c1e5764b1cab1b6bcc7f704ee76053abb49b45df040eab2c1f2b2c","last_reissued_at":"2026-05-18T02:51:24.716014Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:24.716014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Harmonic pinnacles in the Discrete Gaussian model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Allan Sly, Eyal Lubetzky, Fabio Martinelli","submitted_at":"2014-05-20T20:55:12Z","abstract_excerpt":"The 2D Discrete Gaussian model gives each height function $\\eta : \\mathbb{Z}^2\\to\\mathbb{Z}$ a probability proportional to $\\exp(-\\beta \\mathcal{H}(\\eta))$, where $\\beta$ is the inverse-temperature and $\\mathcal{H}(\\eta) = \\sum_{x\\sim y}(\\eta_x-\\eta_y)^2$ sums over nearest-neighbor bonds. We consider the model at large fixed $\\beta$, where it is flat unlike its continuous analog (the Gaussian Free Field).\n  We first establish that the maximum height in an $L\\times L$ box with 0 boundary conditions concentrates on two integers $M,M+1$ with $M\\sim \\sqrt{(1/2\\pi\\beta)\\log L\\log\\log L}$. The key i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5241","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1405.5241","created_at":"2026-05-18T02:51:24.716124+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.5241v1","created_at":"2026-05-18T02:51:24.716124+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5241","created_at":"2026-05-18T02:51:24.716124+00:00"},{"alias_kind":"pith_short_12","alias_value":"ADMBF5FFYHSX","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"ADMBF5FFYHSXMSY4","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"ADMBF5FF","created_at":"2026-05-18T12:28:19.803747+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ADMBF5FFYHSXMSY4VMNWXTD7OB","json":"https://pith.science/pith/ADMBF5FFYHSXMSY4VMNWXTD7OB.json","graph_json":"https://pith.science/api/pith-number/ADMBF5FFYHSXMSY4VMNWXTD7OB/graph.json","events_json":"https://pith.science/api/pith-number/ADMBF5FFYHSXMSY4VMNWXTD7OB/events.json","paper":"https://pith.science/paper/ADMBF5FF"},"agent_actions":{"view_html":"https://pith.science/pith/ADMBF5FFYHSXMSY4VMNWXTD7OB","download_json":"https://pith.science/pith/ADMBF5FFYHSXMSY4VMNWXTD7OB.json","view_paper":"https://pith.science/paper/ADMBF5FF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.5241&json=true","fetch_graph":"https://pith.science/api/pith-number/ADMBF5FFYHSXMSY4VMNWXTD7OB/graph.json","fetch_events":"https://pith.science/api/pith-number/ADMBF5FFYHSXMSY4VMNWXTD7OB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ADMBF5FFYHSXMSY4VMNWXTD7OB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ADMBF5FFYHSXMSY4VMNWXTD7OB/action/storage_attestation","attest_author":"https://pith.science/pith/ADMBF5FFYHSXMSY4VMNWXTD7OB/action/author_attestation","sign_citation":"https://pith.science/pith/ADMBF5FFYHSXMSY4VMNWXTD7OB/action/citation_signature","submit_replication":"https://pith.science/pith/ADMBF5FFYHSXMSY4VMNWXTD7OB/action/replication_record"}},"created_at":"2026-05-18T02:51:24.716124+00:00","updated_at":"2026-05-18T02:51:24.716124+00:00"}