{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:TUNA7MY5H4ZGVMIJI4AKDGZ36D","short_pith_number":"pith:TUNA7MY5","schema_version":"1.0","canonical_sha256":"9d1a0fb31d3f326ab1094700a19b3bf0d869edf0d382b7bed4137266985a5d73","source":{"kind":"arxiv","id":"1409.4808","version":2},"attestation_state":"computed","paper":{"title":"An Equidistribution Result For Dynamical Systems on the Berkovich Projective Line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Kenneth Jacobs","submitted_at":"2014-09-16T21:23:34Z","abstract_excerpt":"Let $K$ be a complete, algebraically closed, non-Archimedean valued field, and let $\\phi\\in K(z)$ with $\\textrm{deg}(\\phi) \\geq 2$. In this paper we consider the family of functions $\\textrm{ordRes}_{\\phi^n}(x)$, which measure the resultant of $\\phi^n$ at points $x$ in $\\textbf{P}^1_{\\textrm{K}}$, the Berkovich projective line, and show that they converge locally uniformly to the diagonal values of the Arakelov-Green's function $g_{\\mu_{\\phi}}(x,x)$ attached to the canonical measure of $\\phi$. Following this, we are able to prove an equidistribution result for Rumely's crucial measures $\\nu_{\\"},"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":"1409.4808","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-09-16T21:23:34Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"54be5c00333ac5243e5d0245cbd3d6bd64eeee67e232175fb57e57eab5dd651e","abstract_canon_sha256":"3bb66fe33e8889d22a59a7bcfd2a408488e91f4fec6b153e33f84bae849ee839"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:27.126403Z","signature_b64":"OtEk80SoFZqWs3/8eIst7SlLqTCHgcnmAxom5wxtAuYz/0MTRc26rlzusktRn1mPKbRlafxYQcgMNY5Iw/arAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d1a0fb31d3f326ab1094700a19b3bf0d869edf0d382b7bed4137266985a5d73","last_reissued_at":"2026-05-18T00:45:27.125807Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:27.125807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Equidistribution Result For Dynamical Systems on the Berkovich Projective Line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Kenneth Jacobs","submitted_at":"2014-09-16T21:23:34Z","abstract_excerpt":"Let $K$ be a complete, algebraically closed, non-Archimedean valued field, and let $\\phi\\in K(z)$ with $\\textrm{deg}(\\phi) \\geq 2$. In this paper we consider the family of functions $\\textrm{ordRes}_{\\phi^n}(x)$, which measure the resultant of $\\phi^n$ at points $x$ in $\\textbf{P}^1_{\\textrm{K}}$, the Berkovich projective line, and show that they converge locally uniformly to the diagonal values of the Arakelov-Green's function $g_{\\mu_{\\phi}}(x,x)$ attached to the canonical measure of $\\phi$. Following this, we are able to prove an equidistribution result for Rumely's crucial measures $\\nu_{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4808","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":""},"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":"1409.4808","created_at":"2026-05-18T00:45:27.125884+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.4808v2","created_at":"2026-05-18T00:45:27.125884+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4808","created_at":"2026-05-18T00:45:27.125884+00:00"},{"alias_kind":"pith_short_12","alias_value":"TUNA7MY5H4ZG","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"TUNA7MY5H4ZGVMIJ","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"TUNA7MY5","created_at":"2026-05-18T12:28:52.271510+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/TUNA7MY5H4ZGVMIJI4AKDGZ36D","json":"https://pith.science/pith/TUNA7MY5H4ZGVMIJI4AKDGZ36D.json","graph_json":"https://pith.science/api/pith-number/TUNA7MY5H4ZGVMIJI4AKDGZ36D/graph.json","events_json":"https://pith.science/api/pith-number/TUNA7MY5H4ZGVMIJI4AKDGZ36D/events.json","paper":"https://pith.science/paper/TUNA7MY5"},"agent_actions":{"view_html":"https://pith.science/pith/TUNA7MY5H4ZGVMIJI4AKDGZ36D","download_json":"https://pith.science/pith/TUNA7MY5H4ZGVMIJI4AKDGZ36D.json","view_paper":"https://pith.science/paper/TUNA7MY5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.4808&json=true","fetch_graph":"https://pith.science/api/pith-number/TUNA7MY5H4ZGVMIJI4AKDGZ36D/graph.json","fetch_events":"https://pith.science/api/pith-number/TUNA7MY5H4ZGVMIJI4AKDGZ36D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TUNA7MY5H4ZGVMIJI4AKDGZ36D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TUNA7MY5H4ZGVMIJI4AKDGZ36D/action/storage_attestation","attest_author":"https://pith.science/pith/TUNA7MY5H4ZGVMIJI4AKDGZ36D/action/author_attestation","sign_citation":"https://pith.science/pith/TUNA7MY5H4ZGVMIJI4AKDGZ36D/action/citation_signature","submit_replication":"https://pith.science/pith/TUNA7MY5H4ZGVMIJI4AKDGZ36D/action/replication_record"}},"created_at":"2026-05-18T00:45:27.125884+00:00","updated_at":"2026-05-18T00:45:27.125884+00:00"}