{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:7MOHFWHO3RT6HQC7HVR6DHZFCJ","short_pith_number":"pith:7MOHFWHO","schema_version":"1.0","canonical_sha256":"fb1c72d8eedc67e3c05f3d63e19f251262d2cd7c14bf63624b7d353fd51ad4bb","source":{"kind":"arxiv","id":"2309.02865","version":2},"attestation_state":"computed","paper":{"title":"What is a $p$-adic Dyson Brownian motion?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT"],"primary_cat":"math.PR","authors_text":"Roger Van Peski","submitted_at":"2023-09-06T09:45:33Z","abstract_excerpt":"We consider the singular numbers of a certain explicit continuous-time Markov jump process on $\\mathrm{GL}_N(\\mathbb{Q}_p)$, which we argue gives the closest $p$-adic analogue of multiplicative Dyson Brownian motion. We do so by explicitly classifying the possible dynamics of singular numbers of processes on $\\mathrm{GL}_N(\\mathbb{Q}_p)$ satisfying natural properties possessed by Brownian motion on $\\mathrm{GL}_N(\\mathbb{C})$. Computing the evolution of singular numbers explicitly, we find that the $N$-tuple of singular numbers in decreasing order evolves as a Poisson jump process on $\\mathbb{"},"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":"2309.02865","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-09-06T09:45:33Z","cross_cats_sorted":["math.CO","math.NT"],"title_canon_sha256":"407cb0e973d31ac504028046951d089803f8201a2a9d6e4bfdc3c9299437f4a6","abstract_canon_sha256":"cad47633fdedabfd0663fa5a54b3c26b3ea6fb824d043444df1e8b5b8f167b4e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:30:48.397801Z","signature_b64":"lKF0jGivwIZGWWM8gitt3Rq6r+rgPxFQ6wImuojToxP4Q3q12ML4670QPiuakfcgEuT0RB+2A/wmWRoOVnYwDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb1c72d8eedc67e3c05f3d63e19f251262d2cd7c14bf63624b7d353fd51ad4bb","last_reissued_at":"2026-07-05T08:30:48.397305Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:30:48.397305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"What is a $p$-adic Dyson Brownian motion?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT"],"primary_cat":"math.PR","authors_text":"Roger Van Peski","submitted_at":"2023-09-06T09:45:33Z","abstract_excerpt":"We consider the singular numbers of a certain explicit continuous-time Markov jump process on $\\mathrm{GL}_N(\\mathbb{Q}_p)$, which we argue gives the closest $p$-adic analogue of multiplicative Dyson Brownian motion. We do so by explicitly classifying the possible dynamics of singular numbers of processes on $\\mathrm{GL}_N(\\mathbb{Q}_p)$ satisfying natural properties possessed by Brownian motion on $\\mathrm{GL}_N(\\mathbb{C})$. Computing the evolution of singular numbers explicitly, we find that the $N$-tuple of singular numbers in decreasing order evolves as a Poisson jump process on $\\mathbb{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.02865","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/2309.02865/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":"2309.02865","created_at":"2026-07-05T08:30:48.397373+00:00"},{"alias_kind":"arxiv_version","alias_value":"2309.02865v2","created_at":"2026-07-05T08:30:48.397373+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.02865","created_at":"2026-07-05T08:30:48.397373+00:00"},{"alias_kind":"pith_short_12","alias_value":"7MOHFWHO3RT6","created_at":"2026-07-05T08:30:48.397373+00:00"},{"alias_kind":"pith_short_16","alias_value":"7MOHFWHO3RT6HQC7","created_at":"2026-07-05T08:30:48.397373+00:00"},{"alias_kind":"pith_short_8","alias_value":"7MOHFWHO","created_at":"2026-07-05T08:30:48.397373+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.20444","citing_title":"Eigenvalue Distribution of $p$-adic Random Matrices Among Algebraic Extensions, with an Analogue for $p$-adic Random Polynomials","ref_index":32,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7MOHFWHO3RT6HQC7HVR6DHZFCJ","json":"https://pith.science/pith/7MOHFWHO3RT6HQC7HVR6DHZFCJ.json","graph_json":"https://pith.science/api/pith-number/7MOHFWHO3RT6HQC7HVR6DHZFCJ/graph.json","events_json":"https://pith.science/api/pith-number/7MOHFWHO3RT6HQC7HVR6DHZFCJ/events.json","paper":"https://pith.science/paper/7MOHFWHO"},"agent_actions":{"view_html":"https://pith.science/pith/7MOHFWHO3RT6HQC7HVR6DHZFCJ","download_json":"https://pith.science/pith/7MOHFWHO3RT6HQC7HVR6DHZFCJ.json","view_paper":"https://pith.science/paper/7MOHFWHO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2309.02865&json=true","fetch_graph":"https://pith.science/api/pith-number/7MOHFWHO3RT6HQC7HVR6DHZFCJ/graph.json","fetch_events":"https://pith.science/api/pith-number/7MOHFWHO3RT6HQC7HVR6DHZFCJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7MOHFWHO3RT6HQC7HVR6DHZFCJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7MOHFWHO3RT6HQC7HVR6DHZFCJ/action/storage_attestation","attest_author":"https://pith.science/pith/7MOHFWHO3RT6HQC7HVR6DHZFCJ/action/author_attestation","sign_citation":"https://pith.science/pith/7MOHFWHO3RT6HQC7HVR6DHZFCJ/action/citation_signature","submit_replication":"https://pith.science/pith/7MOHFWHO3RT6HQC7HVR6DHZFCJ/action/replication_record"}},"created_at":"2026-07-05T08:30:48.397373+00:00","updated_at":"2026-07-05T08:30:48.397373+00:00"}