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This is a random field $\\varphi\\in\\mathbb Z^{\\Lambda_n}$ with law proportional to $e^{\\frac12\\beta(\\varphi,\\Delta_n\\varphi)}\\prod_{x\\in\\Lambda_n}\\#(d\\varphi_x)$, where $\\Delta_n$ is the hierarchical Laplacian, $\\beta$ is the inverse temperature and $\\#$ is the counting measure on $\\mathbb Z$. Denoting $\\beta_c:=2\\pi^2/\\log b$ and $m_n:=\\beta^{-1/2}[(2\\log b)^{1/2}n-\\frac32(2\\log b)^{-1/2}\\log n]$, for $0<\\beta<\\beta_c$ we prove"},"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":"2309.09389","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-09-17T22:21:05Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0131f1524059fe9286dc890c0a228d4dcba548bec87e0a846e933b833cee6a63","abstract_canon_sha256":"74efa4492d1fd41b36247e6c4679fb20510ad477ca05a223dbb4a497ddf3aeaf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:14:56.793848Z","signature_b64":"Z6qFL6btoS5uDQEn8DRU1TduItuNyzZZorE0l4qU7oGOeymVpmBGVIP1uiQEhkhIZX7VnF5v1wNroKKwpXovAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b59ccf35611c9dfb3694e6ba852b07666355f447411b109527ae5e5558ba8b0b","last_reissued_at":"2026-07-05T07:14:56.793379Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:14:56.793379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A limit law for the maximum of subcritical DG-model on a hierarchical lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Haiyu Huang, Marek Biskup","submitted_at":"2023-09-17T22:21:05Z","abstract_excerpt":"We study the extremal properties of the \"integer-valued Gaussian\" a.k.a.\\ DG-model on the hierarchical lattice $\\Lambda_n:=\\{1,\\dots,b\\}^n$ (with $b\\ge2$) of depth $n$. This is a random field $\\varphi\\in\\mathbb Z^{\\Lambda_n}$ with law proportional to $e^{\\frac12\\beta(\\varphi,\\Delta_n\\varphi)}\\prod_{x\\in\\Lambda_n}\\#(d\\varphi_x)$, where $\\Delta_n$ is the hierarchical Laplacian, $\\beta$ is the inverse temperature and $\\#$ is the counting measure on $\\mathbb Z$. Denoting $\\beta_c:=2\\pi^2/\\log b$ and $m_n:=\\beta^{-1/2}[(2\\log b)^{1/2}n-\\frac32(2\\log b)^{-1/2}\\log n]$, for $0<\\beta<\\beta_c$ we prove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.09389","kind":"arxiv","version":2},"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/2309.09389/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":"2309.09389","created_at":"2026-07-05T07:14:56.793438+00:00"},{"alias_kind":"arxiv_version","alias_value":"2309.09389v2","created_at":"2026-07-05T07:14:56.793438+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.09389","created_at":"2026-07-05T07:14:56.793438+00:00"},{"alias_kind":"pith_short_12","alias_value":"WWOM6NLBDSO7","created_at":"2026-07-05T07:14:56.793438+00:00"},{"alias_kind":"pith_short_16","alias_value":"WWOM6NLBDSO7WNUU","created_at":"2026-07-05T07:14:56.793438+00:00"},{"alias_kind":"pith_short_8","alias_value":"WWOM6NLB","created_at":"2026-07-05T07:14:56.793438+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.09592","citing_title":"Extremal process of the local time of simple random walk on a regular tree","ref_index":16,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WWOM6NLBDSO7WNUU425IKKYHMZ","json":"https://pith.science/pith/WWOM6NLBDSO7WNUU425IKKYHMZ.json","graph_json":"https://pith.science/api/pith-number/WWOM6NLBDSO7WNUU425IKKYHMZ/graph.json","events_json":"https://pith.science/api/pith-number/WWOM6NLBDSO7WNUU425IKKYHMZ/events.json","paper":"https://pith.science/paper/WWOM6NLB"},"agent_actions":{"view_html":"https://pith.science/pith/WWOM6NLBDSO7WNUU425IKKYHMZ","download_json":"https://pith.science/pith/WWOM6NLBDSO7WNUU425IKKYHMZ.json","view_paper":"https://pith.science/paper/WWOM6NLB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2309.09389&json=true","fetch_graph":"https://pith.science/api/pith-number/WWOM6NLBDSO7WNUU425IKKYHMZ/graph.json","fetch_events":"https://pith.science/api/pith-number/WWOM6NLBDSO7WNUU425IKKYHMZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WWOM6NLBDSO7WNUU425IKKYHMZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WWOM6NLBDSO7WNUU425IKKYHMZ/action/storage_attestation","attest_author":"https://pith.science/pith/WWOM6NLBDSO7WNUU425IKKYHMZ/action/author_attestation","sign_citation":"https://pith.science/pith/WWOM6NLBDSO7WNUU425IKKYHMZ/action/citation_signature","submit_replication":"https://pith.science/pith/WWOM6NLBDSO7WNUU425IKKYHMZ/action/replication_record"}},"created_at":"2026-07-05T07:14:56.793438+00:00","updated_at":"2026-07-05T07:14:56.793438+00:00"}