{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:SZU3YSK4PZNRR7C5OCIVIUILBS","short_pith_number":"pith:SZU3YSK4","schema_version":"1.0","canonical_sha256":"9669bc495c7e5b18fc5d709154510b0c885770ef7c2a7dede380b2eb1b484fbb","source":{"kind":"arxiv","id":"2010.14320","version":2},"attestation_state":"computed","paper":{"title":"Dynamics of zeroes under repeated differentiation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.CA","math.MP"],"primary_cat":"math.PR","authors_text":"Jeremy Hoskins, Zakhar Kabluchko","submitted_at":"2020-10-27T14:30:24Z","abstract_excerpt":"Consider a random polynomial $P_n$ of degree $n$ whose roots are independent random variables sampled according to some probability distribution $\\mu_0$ on the complex plane $\\mathbb C$. It is natural to conjecture that, for a fixed $t\\in [0,1)$ and as $n\\to\\infty$, the zeroes of the $[tn]$-th derivative of $P_n$ are distributed according to some measure $\\mu_t$ on $\\mathbb C$. Assuming either that $\\mu_0$ is concentrated on the real line or that it is rotationally invariant, Steinerberger [Proc. AMS, 2019] and O'Rourke and Steinerberger [arXiv:1910.12161] derived nonlocal transport equations "},"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":"2010.14320","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-10-27T14:30:24Z","cross_cats_sorted":["math-ph","math.AP","math.CA","math.MP"],"title_canon_sha256":"f330e002b6199ec6fb02780a66b5e71c4f11d097ea531faee09304d4555ed2b0","abstract_canon_sha256":"58fe86229707097a5377eddffd8794383f59edcd9cffdd08981b34e2bae43339"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:08:43.081263Z","signature_b64":"CBtgn3D7Ak0hWOwlbb6JGnQanIYHgomEFSJjjhDWfOeXtux/sWFNF0SCf4a9n/N4twv1Opqu8P2kICqAScBlCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9669bc495c7e5b18fc5d709154510b0c885770ef7c2a7dede380b2eb1b484fbb","last_reissued_at":"2026-07-05T03:08:43.080902Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:08:43.080902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamics of zeroes under repeated differentiation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.CA","math.MP"],"primary_cat":"math.PR","authors_text":"Jeremy Hoskins, Zakhar Kabluchko","submitted_at":"2020-10-27T14:30:24Z","abstract_excerpt":"Consider a random polynomial $P_n$ of degree $n$ whose roots are independent random variables sampled according to some probability distribution $\\mu_0$ on the complex plane $\\mathbb C$. It is natural to conjecture that, for a fixed $t\\in [0,1)$ and as $n\\to\\infty$, the zeroes of the $[tn]$-th derivative of $P_n$ are distributed according to some measure $\\mu_t$ on $\\mathbb C$. Assuming either that $\\mu_0$ is concentrated on the real line or that it is rotationally invariant, Steinerberger [Proc. AMS, 2019] and O'Rourke and Steinerberger [arXiv:1910.12161] derived nonlocal transport equations "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.14320","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/2010.14320/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":"2010.14320","created_at":"2026-07-05T03:08:43.080956+00:00"},{"alias_kind":"arxiv_version","alias_value":"2010.14320v2","created_at":"2026-07-05T03:08:43.080956+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.14320","created_at":"2026-07-05T03:08:43.080956+00:00"},{"alias_kind":"pith_short_12","alias_value":"SZU3YSK4PZNR","created_at":"2026-07-05T03:08:43.080956+00:00"},{"alias_kind":"pith_short_16","alias_value":"SZU3YSK4PZNRR7C5","created_at":"2026-07-05T03:08:43.080956+00:00"},{"alias_kind":"pith_short_8","alias_value":"SZU3YSK4","created_at":"2026-07-05T03:08:43.080956+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SZU3YSK4PZNRR7C5OCIVIUILBS","json":"https://pith.science/pith/SZU3YSK4PZNRR7C5OCIVIUILBS.json","graph_json":"https://pith.science/api/pith-number/SZU3YSK4PZNRR7C5OCIVIUILBS/graph.json","events_json":"https://pith.science/api/pith-number/SZU3YSK4PZNRR7C5OCIVIUILBS/events.json","paper":"https://pith.science/paper/SZU3YSK4"},"agent_actions":{"view_html":"https://pith.science/pith/SZU3YSK4PZNRR7C5OCIVIUILBS","download_json":"https://pith.science/pith/SZU3YSK4PZNRR7C5OCIVIUILBS.json","view_paper":"https://pith.science/paper/SZU3YSK4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2010.14320&json=true","fetch_graph":"https://pith.science/api/pith-number/SZU3YSK4PZNRR7C5OCIVIUILBS/graph.json","fetch_events":"https://pith.science/api/pith-number/SZU3YSK4PZNRR7C5OCIVIUILBS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SZU3YSK4PZNRR7C5OCIVIUILBS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SZU3YSK4PZNRR7C5OCIVIUILBS/action/storage_attestation","attest_author":"https://pith.science/pith/SZU3YSK4PZNRR7C5OCIVIUILBS/action/author_attestation","sign_citation":"https://pith.science/pith/SZU3YSK4PZNRR7C5OCIVIUILBS/action/citation_signature","submit_replication":"https://pith.science/pith/SZU3YSK4PZNRR7C5OCIVIUILBS/action/replication_record"}},"created_at":"2026-07-05T03:08:43.080956+00:00","updated_at":"2026-07-05T03:08:43.080956+00:00"}