{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:KOKMLBSVKKZTVHOQ7RHD66NPBN","short_pith_number":"pith:KOKMLBSV","schema_version":"1.0","canonical_sha256":"5394c5865552b33a9dd0fc4e3f79af0b4a6d37af2953bb8f451267ab2a532e16","source":{"kind":"arxiv","id":"2302.00547","version":3},"attestation_state":"computed","paper":{"title":"Upper bounds on the fluctuations for a class of degenerate convex $\\nabla \\phi$-interface models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Paul Dario","submitted_at":"2023-02-01T16:11:29Z","abstract_excerpt":"We derive upper bounds on the fluctuations of a class of random surfaces of the $\\nabla \\phi$-type with convex interaction potentials. The Brascamp-Lieb concentration inequality provides an upper bound on these fluctuations for uniformly convex potentials. We extend these results to twice continuously differentiable convex potentials whose second derivative grows asymptotically like a polynomial and may vanish on an (arbitrarily large) interval. Specifically, we prove that, when the underlying graph is the $d$-dimensional torus of side length $L$, the variance of the height is smaller than $C "},"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":"2302.00547","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-02-01T16:11:29Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"fab88beba3706b7c5f0456aff3448204be87c8806f0361c7ddaf1756839b3097","abstract_canon_sha256":"eff32d3d76b2c45e736573cd2949722eb281fb2db1a692e27e54f71c7b70edca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:35:59.444427Z","signature_b64":"/L8NrtFvb9naIkJUuT2NH8BWdrnYU/BUMBFSqK6H0+onAAWhHNLbZtzJ88Guk/nlUNHkSgMpe/EnCoNXXEmMDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5394c5865552b33a9dd0fc4e3f79af0b4a6d37af2953bb8f451267ab2a532e16","last_reissued_at":"2026-07-05T07:35:59.444028Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:35:59.444028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Upper bounds on the fluctuations for a class of degenerate convex $\\nabla \\phi$-interface models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Paul Dario","submitted_at":"2023-02-01T16:11:29Z","abstract_excerpt":"We derive upper bounds on the fluctuations of a class of random surfaces of the $\\nabla \\phi$-type with convex interaction potentials. The Brascamp-Lieb concentration inequality provides an upper bound on these fluctuations for uniformly convex potentials. We extend these results to twice continuously differentiable convex potentials whose second derivative grows asymptotically like a polynomial and may vanish on an (arbitrarily large) interval. Specifically, we prove that, when the underlying graph is the $d$-dimensional torus of side length $L$, the variance of the height is smaller than $C "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.00547","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.00547/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2302.00547","created_at":"2026-07-05T07:35:59.444085+00:00"},{"alias_kind":"arxiv_version","alias_value":"2302.00547v3","created_at":"2026-07-05T07:35:59.444085+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.00547","created_at":"2026-07-05T07:35:59.444085+00:00"},{"alias_kind":"pith_short_12","alias_value":"KOKMLBSVKKZT","created_at":"2026-07-05T07:35:59.444085+00:00"},{"alias_kind":"pith_short_16","alias_value":"KOKMLBSVKKZTVHOQ","created_at":"2026-07-05T07:35:59.444085+00:00"},{"alias_kind":"pith_short_8","alias_value":"KOKMLBSV","created_at":"2026-07-05T07:35:59.444085+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.08964","citing_title":"Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models","ref_index":29,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KOKMLBSVKKZTVHOQ7RHD66NPBN","json":"https://pith.science/pith/KOKMLBSVKKZTVHOQ7RHD66NPBN.json","graph_json":"https://pith.science/api/pith-number/KOKMLBSVKKZTVHOQ7RHD66NPBN/graph.json","events_json":"https://pith.science/api/pith-number/KOKMLBSVKKZTVHOQ7RHD66NPBN/events.json","paper":"https://pith.science/paper/KOKMLBSV"},"agent_actions":{"view_html":"https://pith.science/pith/KOKMLBSVKKZTVHOQ7RHD66NPBN","download_json":"https://pith.science/pith/KOKMLBSVKKZTVHOQ7RHD66NPBN.json","view_paper":"https://pith.science/paper/KOKMLBSV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2302.00547&json=true","fetch_graph":"https://pith.science/api/pith-number/KOKMLBSVKKZTVHOQ7RHD66NPBN/graph.json","fetch_events":"https://pith.science/api/pith-number/KOKMLBSVKKZTVHOQ7RHD66NPBN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KOKMLBSVKKZTVHOQ7RHD66NPBN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KOKMLBSVKKZTVHOQ7RHD66NPBN/action/storage_attestation","attest_author":"https://pith.science/pith/KOKMLBSVKKZTVHOQ7RHD66NPBN/action/author_attestation","sign_citation":"https://pith.science/pith/KOKMLBSVKKZTVHOQ7RHD66NPBN/action/citation_signature","submit_replication":"https://pith.science/pith/KOKMLBSVKKZTVHOQ7RHD66NPBN/action/replication_record"}},"created_at":"2026-07-05T07:35:59.444085+00:00","updated_at":"2026-07-05T07:35:59.444085+00:00"}