{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:VX4V4N2SIS343I67VVC2U3454C","short_pith_number":"pith:VX4V4N2S","schema_version":"1.0","canonical_sha256":"adf95e375244b7cda3dfad45aa6f9de0a4cf2c087a0f12199ba524b38fdaf8f1","source":{"kind":"arxiv","id":"1301.0887","version":1},"attestation_state":"computed","paper":{"title":"Convergence in a multidimensional randomized Keynesian beauty contest","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrew R. Wade, Michael Grinfeld, Stanislav Volkov","submitted_at":"2013-01-05T10:22:34Z","abstract_excerpt":"We study the asymptotics of a Markovian system of $N \\geq 3$ particles in $[0,1]^d$ in which, at each step in discrete time, the particle farthest from the current centre of mass is removed and replaced by an independent $U [0,1]^d$ random particle. We show that the limiting configuration contains $N-1$ coincident particles at a random location $\\xi_N \\in [0,1]^d$. A key tool in the analysis is a Lyapunov function based on the squared radius of gyration (sum of squared distances) of the points. For d=1 we give additional results on the distribution of the limit $\\xi_N$, showing, among other th"},"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":"1301.0887","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-05T10:22:34Z","cross_cats_sorted":[],"title_canon_sha256":"589b7ecdb8fb976a5c342ba9cba42133f43cb85ba6a71f79d541d85481cfbbcf","abstract_canon_sha256":"89980f90c121eb74d7143a0c82c8acf485172db12170c56fd7c982c3f22fbc28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:01.786393Z","signature_b64":"Zih/PuqA5PQtMePdPINMRjZk7ZJKf5GXkESapcow2pjB7tvwbKG+epbRHm2Go0+er4zclWxZ8fPJZAExXXoiBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adf95e375244b7cda3dfad45aa6f9de0a4cf2c087a0f12199ba524b38fdaf8f1","last_reissued_at":"2026-05-18T02:18:01.785704Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:01.785704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence in a multidimensional randomized Keynesian beauty contest","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrew R. Wade, Michael Grinfeld, Stanislav Volkov","submitted_at":"2013-01-05T10:22:34Z","abstract_excerpt":"We study the asymptotics of a Markovian system of $N \\geq 3$ particles in $[0,1]^d$ in which, at each step in discrete time, the particle farthest from the current centre of mass is removed and replaced by an independent $U [0,1]^d$ random particle. We show that the limiting configuration contains $N-1$ coincident particles at a random location $\\xi_N \\in [0,1]^d$. A key tool in the analysis is a Lyapunov function based on the squared radius of gyration (sum of squared distances) of the points. For d=1 we give additional results on the distribution of the limit $\\xi_N$, showing, among other th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0887","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":""},"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":"1301.0887","created_at":"2026-05-18T02:18:01.785806+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.0887v1","created_at":"2026-05-18T02:18:01.785806+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0887","created_at":"2026-05-18T02:18:01.785806+00:00"},{"alias_kind":"pith_short_12","alias_value":"VX4V4N2SIS34","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"VX4V4N2SIS343I67","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"VX4V4N2S","created_at":"2026-05-18T12:28:04.890932+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/VX4V4N2SIS343I67VVC2U3454C","json":"https://pith.science/pith/VX4V4N2SIS343I67VVC2U3454C.json","graph_json":"https://pith.science/api/pith-number/VX4V4N2SIS343I67VVC2U3454C/graph.json","events_json":"https://pith.science/api/pith-number/VX4V4N2SIS343I67VVC2U3454C/events.json","paper":"https://pith.science/paper/VX4V4N2S"},"agent_actions":{"view_html":"https://pith.science/pith/VX4V4N2SIS343I67VVC2U3454C","download_json":"https://pith.science/pith/VX4V4N2SIS343I67VVC2U3454C.json","view_paper":"https://pith.science/paper/VX4V4N2S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.0887&json=true","fetch_graph":"https://pith.science/api/pith-number/VX4V4N2SIS343I67VVC2U3454C/graph.json","fetch_events":"https://pith.science/api/pith-number/VX4V4N2SIS343I67VVC2U3454C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VX4V4N2SIS343I67VVC2U3454C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VX4V4N2SIS343I67VVC2U3454C/action/storage_attestation","attest_author":"https://pith.science/pith/VX4V4N2SIS343I67VVC2U3454C/action/author_attestation","sign_citation":"https://pith.science/pith/VX4V4N2SIS343I67VVC2U3454C/action/citation_signature","submit_replication":"https://pith.science/pith/VX4V4N2SIS343I67VVC2U3454C/action/replication_record"}},"created_at":"2026-05-18T02:18:01.785806+00:00","updated_at":"2026-05-18T02:18:01.785806+00:00"}