{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:KSSUCOCKZGJBOSPIGJKCHUAKWD","short_pith_number":"pith:KSSUCOCK","schema_version":"1.0","canonical_sha256":"54a541384ac9921749e8325423d00ab0e8ea9523b9103044ed37b3b883b83821","source":{"kind":"arxiv","id":"math/0611882","version":2},"attestation_state":"computed","paper":{"title":"The limiting move-to-front search-cost in law of large numbers asymptotic regimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Javiera Barrera, Joaqu\\'in Fontbona","submitted_at":"2006-11-28T19:12:31Z","abstract_excerpt":"We explicitly compute the limiting transient distribution of the search-cost in the move-to-front Markov chain when the number of objects tends to infinity, for general families of deterministic or random request rates. Our techniques are based on a \"law of large numbers for random partitions,\" a scaling limit that allows us to exactly compute limiting expectation of empirical functionals of the request probabilities of objects. In particular, we show that the limiting search-cost can be split at an explicit deterministic threshold into one random variable in equilibrium, and a second one rela"},"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":"math/0611882","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2006-11-28T19:12:31Z","cross_cats_sorted":[],"title_canon_sha256":"db97e6249c349a1891f8f7baa13aa581905d908102127a765c046d4a8890cf7b","abstract_canon_sha256":"d0eb4860ebdad4a3d410e9b17061771b81ca88f318e34291588fb2c50c614efe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:08.486575Z","signature_b64":"siTqy5Ks/cRwSdG29EQc7w05EPSb8SJ0MgO85iiUTPVYea5PswrzdgCC1uFnHJI0CtyqjIIgYRGHShoIaox3DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54a541384ac9921749e8325423d00ab0e8ea9523b9103044ed37b3b883b83821","last_reissued_at":"2026-05-18T04:40:08.486053Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:08.486053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The limiting move-to-front search-cost in law of large numbers asymptotic regimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Javiera Barrera, Joaqu\\'in Fontbona","submitted_at":"2006-11-28T19:12:31Z","abstract_excerpt":"We explicitly compute the limiting transient distribution of the search-cost in the move-to-front Markov chain when the number of objects tends to infinity, for general families of deterministic or random request rates. Our techniques are based on a \"law of large numbers for random partitions,\" a scaling limit that allows us to exactly compute limiting expectation of empirical functionals of the request probabilities of objects. In particular, we show that the limiting search-cost can be split at an explicit deterministic threshold into one random variable in equilibrium, and a second one rela"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611882","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":"math/0611882","created_at":"2026-05-18T04:40:08.486134+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0611882v2","created_at":"2026-05-18T04:40:08.486134+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611882","created_at":"2026-05-18T04:40:08.486134+00:00"},{"alias_kind":"pith_short_12","alias_value":"KSSUCOCKZGJB","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"KSSUCOCKZGJBOSPI","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"KSSUCOCK","created_at":"2026-05-18T12:25:54.717736+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/KSSUCOCKZGJBOSPIGJKCHUAKWD","json":"https://pith.science/pith/KSSUCOCKZGJBOSPIGJKCHUAKWD.json","graph_json":"https://pith.science/api/pith-number/KSSUCOCKZGJBOSPIGJKCHUAKWD/graph.json","events_json":"https://pith.science/api/pith-number/KSSUCOCKZGJBOSPIGJKCHUAKWD/events.json","paper":"https://pith.science/paper/KSSUCOCK"},"agent_actions":{"view_html":"https://pith.science/pith/KSSUCOCKZGJBOSPIGJKCHUAKWD","download_json":"https://pith.science/pith/KSSUCOCKZGJBOSPIGJKCHUAKWD.json","view_paper":"https://pith.science/paper/KSSUCOCK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0611882&json=true","fetch_graph":"https://pith.science/api/pith-number/KSSUCOCKZGJBOSPIGJKCHUAKWD/graph.json","fetch_events":"https://pith.science/api/pith-number/KSSUCOCKZGJBOSPIGJKCHUAKWD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KSSUCOCKZGJBOSPIGJKCHUAKWD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KSSUCOCKZGJBOSPIGJKCHUAKWD/action/storage_attestation","attest_author":"https://pith.science/pith/KSSUCOCKZGJBOSPIGJKCHUAKWD/action/author_attestation","sign_citation":"https://pith.science/pith/KSSUCOCKZGJBOSPIGJKCHUAKWD/action/citation_signature","submit_replication":"https://pith.science/pith/KSSUCOCKZGJBOSPIGJKCHUAKWD/action/replication_record"}},"created_at":"2026-05-18T04:40:08.486134+00:00","updated_at":"2026-05-18T04:40:08.486134+00:00"}