{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:FGHNENCEX3PSBSGCVGVN2FNY3L","short_pith_number":"pith:FGHNENCE","schema_version":"1.0","canonical_sha256":"298ed23444bedf20c8c2a9aadd15b8dacd9f481fa9bd875d097ffdd744837a1a","source":{"kind":"arxiv","id":"2408.13037","version":1},"attestation_state":"computed","paper":{"title":"A phase transition for the cokernels of random band matrices over the p-adic integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Andr\\'as M\\'esz\\'aros","submitted_at":"2024-08-23T12:52:01Z","abstract_excerpt":"Let $\\mathbf{B}_n$ be an $n\\times n$ Haar-uniform band matrix over $\\mathbb{Z}_p$ with band width $w_n$. We prove that $\\text{cok}(\\mathbf{B}_n)$ has Cohen-Lenstra limiting distribution if and only if \\[\\lim_{n\\to\\infty} \\left(w_n-\\log_p(n)\\right)=+\\infty.\\]"},"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":"2408.13037","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-08-23T12:52:01Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"69b0c23c6fa442c05ffe72a4fa2a3adee68335829a6198ab400a3a606a34f154","abstract_canon_sha256":"b0076b578d0b41e482c96025fee1d1bf960e4f841432b2e54469469dc8b91d65"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:58:34.180841Z","signature_b64":"ZIlQfjtlzQ8gJPeCNuJgSApX3munjOqCIUAd3dpyGcOJ1IimbINIkbMGiiS5cUxDAcN/pjGaR/2eV9mFpJF7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"298ed23444bedf20c8c2a9aadd15b8dacd9f481fa9bd875d097ffdd744837a1a","last_reissued_at":"2026-07-05T08:58:34.180404Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:58:34.180404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A phase transition for the cokernels of random band matrices over the p-adic integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Andr\\'as M\\'esz\\'aros","submitted_at":"2024-08-23T12:52:01Z","abstract_excerpt":"Let $\\mathbf{B}_n$ be an $n\\times n$ Haar-uniform band matrix over $\\mathbb{Z}_p$ with band width $w_n$. We prove that $\\text{cok}(\\mathbf{B}_n)$ has Cohen-Lenstra limiting distribution if and only if \\[\\lim_{n\\to\\infty} \\left(w_n-\\log_p(n)\\right)=+\\infty.\\]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.13037","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.13037/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":"2408.13037","created_at":"2026-07-05T08:58:34.180468+00:00"},{"alias_kind":"arxiv_version","alias_value":"2408.13037v1","created_at":"2026-07-05T08:58:34.180468+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.13037","created_at":"2026-07-05T08:58:34.180468+00:00"},{"alias_kind":"pith_short_12","alias_value":"FGHNENCEX3PS","created_at":"2026-07-05T08:58:34.180468+00:00"},{"alias_kind":"pith_short_16","alias_value":"FGHNENCEX3PSBSGC","created_at":"2026-07-05T08:58:34.180468+00:00"},{"alias_kind":"pith_short_8","alias_value":"FGHNENCE","created_at":"2026-07-05T08:58:34.180468+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.17895","citing_title":"Persistence diagrams of random triangular matrices over finite fields","ref_index":31,"is_internal_anchor":false},{"citing_arxiv_id":"2606.06993","citing_title":"A mod $p$ determinant criterion for Cohen--Lenstra convergence of random $p$-adic matrices with prescribed zero patterns","ref_index":8,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FGHNENCEX3PSBSGCVGVN2FNY3L","json":"https://pith.science/pith/FGHNENCEX3PSBSGCVGVN2FNY3L.json","graph_json":"https://pith.science/api/pith-number/FGHNENCEX3PSBSGCVGVN2FNY3L/graph.json","events_json":"https://pith.science/api/pith-number/FGHNENCEX3PSBSGCVGVN2FNY3L/events.json","paper":"https://pith.science/paper/FGHNENCE"},"agent_actions":{"view_html":"https://pith.science/pith/FGHNENCEX3PSBSGCVGVN2FNY3L","download_json":"https://pith.science/pith/FGHNENCEX3PSBSGCVGVN2FNY3L.json","view_paper":"https://pith.science/paper/FGHNENCE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2408.13037&json=true","fetch_graph":"https://pith.science/api/pith-number/FGHNENCEX3PSBSGCVGVN2FNY3L/graph.json","fetch_events":"https://pith.science/api/pith-number/FGHNENCEX3PSBSGCVGVN2FNY3L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FGHNENCEX3PSBSGCVGVN2FNY3L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FGHNENCEX3PSBSGCVGVN2FNY3L/action/storage_attestation","attest_author":"https://pith.science/pith/FGHNENCEX3PSBSGCVGVN2FNY3L/action/author_attestation","sign_citation":"https://pith.science/pith/FGHNENCEX3PSBSGCVGVN2FNY3L/action/citation_signature","submit_replication":"https://pith.science/pith/FGHNENCEX3PSBSGCVGVN2FNY3L/action/replication_record"}},"created_at":"2026-07-05T08:58:34.180468+00:00","updated_at":"2026-07-05T08:58:34.180468+00:00"}