{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:2C6U3SOF7JAJCY6QF3HZ6BVJQR","short_pith_number":"pith:2C6U3SOF","schema_version":"1.0","canonical_sha256":"d0bd4dc9c5fa409163d02ecf9f06a9844e0bf70acfdb3aac20e8f5f57c3b6faa","source":{"kind":"arxiv","id":"1609.07971","version":2},"attestation_state":"computed","paper":{"title":"Self-averaging sequences which fail to converge","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eric Cator, Henk Don","submitted_at":"2016-09-26T13:53:42Z","abstract_excerpt":"We consider self-averaging sequences in which each term is a weighted average over previous terms. For several sequences of this kind it is known that they do not converge to a limit. These sequences share the property that $n$th term is mainly based on terms around a fixed fraction of $n$. We give a probabilistic interpretation to such sequences and give weak conditions under which it is natural to expect non-convergence. Our methods are illustrated by application to the group Russian roulette problem."},"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":"1609.07971","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-26T13:53:42Z","cross_cats_sorted":[],"title_canon_sha256":"637e44adf9615aeed59d7a48ce59a1ea607696ecb38cc5c7afabb3fd158e6f58","abstract_canon_sha256":"749a345e81d3ae52436075a6f138e4e404db331cc7721f9a6f37925b1a695fbb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:25.993472Z","signature_b64":"pxxnUbSSpEhIkCk4K3AzBBEkg5jTUYqHn4/pUHj2nnWF2t0TSRfhuead8Wrri9VGSwpxmphm13I1+DNdLfamDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0bd4dc9c5fa409163d02ecf9f06a9844e0bf70acfdb3aac20e8f5f57c3b6faa","last_reissued_at":"2026-05-18T01:03:25.992884Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:25.992884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Self-averaging sequences which fail to converge","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eric Cator, Henk Don","submitted_at":"2016-09-26T13:53:42Z","abstract_excerpt":"We consider self-averaging sequences in which each term is a weighted average over previous terms. For several sequences of this kind it is known that they do not converge to a limit. These sequences share the property that $n$th term is mainly based on terms around a fixed fraction of $n$. We give a probabilistic interpretation to such sequences and give weak conditions under which it is natural to expect non-convergence. Our methods are illustrated by application to the group Russian roulette problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07971","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":"1609.07971","created_at":"2026-05-18T01:03:25.992969+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.07971v2","created_at":"2026-05-18T01:03:25.992969+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07971","created_at":"2026-05-18T01:03:25.992969+00:00"},{"alias_kind":"pith_short_12","alias_value":"2C6U3SOF7JAJ","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"2C6U3SOF7JAJCY6Q","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"2C6U3SOF","created_at":"2026-05-18T12:29:52.810259+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/2C6U3SOF7JAJCY6QF3HZ6BVJQR","json":"https://pith.science/pith/2C6U3SOF7JAJCY6QF3HZ6BVJQR.json","graph_json":"https://pith.science/api/pith-number/2C6U3SOF7JAJCY6QF3HZ6BVJQR/graph.json","events_json":"https://pith.science/api/pith-number/2C6U3SOF7JAJCY6QF3HZ6BVJQR/events.json","paper":"https://pith.science/paper/2C6U3SOF"},"agent_actions":{"view_html":"https://pith.science/pith/2C6U3SOF7JAJCY6QF3HZ6BVJQR","download_json":"https://pith.science/pith/2C6U3SOF7JAJCY6QF3HZ6BVJQR.json","view_paper":"https://pith.science/paper/2C6U3SOF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.07971&json=true","fetch_graph":"https://pith.science/api/pith-number/2C6U3SOF7JAJCY6QF3HZ6BVJQR/graph.json","fetch_events":"https://pith.science/api/pith-number/2C6U3SOF7JAJCY6QF3HZ6BVJQR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2C6U3SOF7JAJCY6QF3HZ6BVJQR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2C6U3SOF7JAJCY6QF3HZ6BVJQR/action/storage_attestation","attest_author":"https://pith.science/pith/2C6U3SOF7JAJCY6QF3HZ6BVJQR/action/author_attestation","sign_citation":"https://pith.science/pith/2C6U3SOF7JAJCY6QF3HZ6BVJQR/action/citation_signature","submit_replication":"https://pith.science/pith/2C6U3SOF7JAJCY6QF3HZ6BVJQR/action/replication_record"}},"created_at":"2026-05-18T01:03:25.992969+00:00","updated_at":"2026-05-18T01:03:25.992969+00:00"}