{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:CMCG6CBE5PPSP3W3VVCUNRDTFD","short_pith_number":"pith:CMCG6CBE","schema_version":"1.0","canonical_sha256":"13046f0824ebdf27eedbad4546c47328ff1398921737b0d00478a118f494660d","source":{"kind":"arxiv","id":"1801.05663","version":4},"attestation_state":"computed","paper":{"title":"The scaling limit of the membrane model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alessandra Cipriani, Biltu Dan, Rajat Subhra Hazra","submitted_at":"2018-01-17T13:57:35Z","abstract_excerpt":"On the integer lattice we consider the discrete membrane model, a random interface in which the field has Laplacian interaction. We prove that, under appropriate rescaling, the discrete membrane model converges to the continuum membrane model in $d\\ge 2$. Namely, it is shown that the scaling limit in $d=2,\\,3$ is a H\\\"older continuous random field, while in $d\\ge 4$ the membrane model converges to a random distribution. As a by-product of the proof in $d=2,\\,3$, we obtain the scaling limit of the maximum. This work complements the analogous results of Caravenna and Deuschel (2009) in $d=1$."},"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":"1801.05663","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-17T13:57:35Z","cross_cats_sorted":[],"title_canon_sha256":"722435317fd6751c201f5eeb9f36eaefbc386caddd630d395b7f541d8b9edacc","abstract_canon_sha256":"fc091b5fa6b9255ff2a158381ae07d188bfa52fae56c78e39a4dbaa7edc1c617"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:18.645714Z","signature_b64":"LwL6WW3qiIwWXvLo6HdAJYcHLS0MzOiP5B2JedIfc5ftPoH431uC8itAF4KAx1bHRy2ThTCl6uHZqnC1YuRIBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13046f0824ebdf27eedbad4546c47328ff1398921737b0d00478a118f494660d","last_reissued_at":"2026-05-17T23:52:18.645018Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:18.645018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The scaling limit of the membrane model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alessandra Cipriani, Biltu Dan, Rajat Subhra Hazra","submitted_at":"2018-01-17T13:57:35Z","abstract_excerpt":"On the integer lattice we consider the discrete membrane model, a random interface in which the field has Laplacian interaction. We prove that, under appropriate rescaling, the discrete membrane model converges to the continuum membrane model in $d\\ge 2$. Namely, it is shown that the scaling limit in $d=2,\\,3$ is a H\\\"older continuous random field, while in $d\\ge 4$ the membrane model converges to a random distribution. As a by-product of the proof in $d=2,\\,3$, we obtain the scaling limit of the maximum. This work complements the analogous results of Caravenna and Deuschel (2009) in $d=1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05663","kind":"arxiv","version":4},"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":"1801.05663","created_at":"2026-05-17T23:52:18.645135+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.05663v4","created_at":"2026-05-17T23:52:18.645135+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.05663","created_at":"2026-05-17T23:52:18.645135+00:00"},{"alias_kind":"pith_short_12","alias_value":"CMCG6CBE5PPS","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"CMCG6CBE5PPSP3W3","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"CMCG6CBE","created_at":"2026-05-18T12:32:16.446611+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/CMCG6CBE5PPSP3W3VVCUNRDTFD","json":"https://pith.science/pith/CMCG6CBE5PPSP3W3VVCUNRDTFD.json","graph_json":"https://pith.science/api/pith-number/CMCG6CBE5PPSP3W3VVCUNRDTFD/graph.json","events_json":"https://pith.science/api/pith-number/CMCG6CBE5PPSP3W3VVCUNRDTFD/events.json","paper":"https://pith.science/paper/CMCG6CBE"},"agent_actions":{"view_html":"https://pith.science/pith/CMCG6CBE5PPSP3W3VVCUNRDTFD","download_json":"https://pith.science/pith/CMCG6CBE5PPSP3W3VVCUNRDTFD.json","view_paper":"https://pith.science/paper/CMCG6CBE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.05663&json=true","fetch_graph":"https://pith.science/api/pith-number/CMCG6CBE5PPSP3W3VVCUNRDTFD/graph.json","fetch_events":"https://pith.science/api/pith-number/CMCG6CBE5PPSP3W3VVCUNRDTFD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CMCG6CBE5PPSP3W3VVCUNRDTFD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CMCG6CBE5PPSP3W3VVCUNRDTFD/action/storage_attestation","attest_author":"https://pith.science/pith/CMCG6CBE5PPSP3W3VVCUNRDTFD/action/author_attestation","sign_citation":"https://pith.science/pith/CMCG6CBE5PPSP3W3VVCUNRDTFD/action/citation_signature","submit_replication":"https://pith.science/pith/CMCG6CBE5PPSP3W3VVCUNRDTFD/action/replication_record"}},"created_at":"2026-05-17T23:52:18.645135+00:00","updated_at":"2026-05-17T23:52:18.645135+00:00"}