{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RZDTSCGTISFLB2UMMOM7SOWS4Z","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":"c7bf9f0dab26f443393ad4fd1db472d061b5e260317dd08ef968c0b56cf57764","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-15T14:52:45Z","title_canon_sha256":"cb89c64d47a75f624c01609b050f203c00ce343af56dcc7f509f620b66416b4b"},"schema_version":"1.0","source":{"id":"1810.06428","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.06428","created_at":"2026-05-17T23:39:41Z"},{"alias_kind":"arxiv_version","alias_value":"1810.06428v2","created_at":"2026-05-17T23:39:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.06428","created_at":"2026-05-17T23:39:41Z"},{"alias_kind":"pith_short_12","alias_value":"RZDTSCGTISFL","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RZDTSCGTISFLB2UM","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RZDTSCGT","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:784c6857ff930ca441fb1eccef8c338e4acccc4a00736e814ef8c6c974fdf570","target":"graph","created_at":"2026-05-17T23:39:41Z","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 study the $\\nabla \\phi$ model with uniformly convex Hamiltonian $\\mathcal{H} (\\phi) := \\sum V(\\nabla \\phi)$ and prove a quantitative rate of convergence for the finite-volume surface tension as well as a quantitative rate estimate for the $L^2$-norm for the field subject to affine boundary condition. One of our motivations is to develop a new toolbox for studying this problem that does not rely on the Helffer-Sj\\\"ostrand representation. Instead, we make use of the variational formulation of the partition function, the notion of displacement convexity from the theory of optimal transport, an","authors_text":"Paul Dario","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-15T14:52:45Z","title":"Quantitative homogenization of the disordered $\\nabla \\phi$ model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06428","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:ced3c19534015301d4f9942051d59d881a41cad886a8b1fed699a05d9edb23e3","target":"record","created_at":"2026-05-17T23:39:41Z","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":"c7bf9f0dab26f443393ad4fd1db472d061b5e260317dd08ef968c0b56cf57764","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-15T14:52:45Z","title_canon_sha256":"cb89c64d47a75f624c01609b050f203c00ce343af56dcc7f509f620b66416b4b"},"schema_version":"1.0","source":{"id":"1810.06428","kind":"arxiv","version":2}},"canonical_sha256":"8e473908d3448ab0ea8c6399f93ad2e6417b48b2e4577afc2fc6e9c835acb6b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e473908d3448ab0ea8c6399f93ad2e6417b48b2e4577afc2fc6e9c835acb6b0","first_computed_at":"2026-05-17T23:39:41.615440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:41.615440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G1CrXsTlmhvk+lkyD9KatWTNNb3Wmzsh9m8EG9w70jcwDZHTSDDLrPad+XIjv+sdUVRbB1PSjhCWE3Q4JGhHCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:41.616141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.06428","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ced3c19534015301d4f9942051d59d881a41cad886a8b1fed699a05d9edb23e3","sha256:784c6857ff930ca441fb1eccef8c338e4acccc4a00736e814ef8c6c974fdf570"],"state_sha256":"ed4e060f528a4cf1d2ea32092f9d661117da66c9596f93c14eb7a32a6886aa28"}