{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:3LLKFN6X2PS6ZR5GJ5CVKBLQCS","short_pith_number":"pith:3LLKFN6X","schema_version":"1.0","canonical_sha256":"dad6a2b7d7d3e5ecc7a64f4555057014b4914e092c44b5dd8f5ad2f9c170acd2","source":{"kind":"arxiv","id":"1511.00224","version":2},"attestation_state":"computed","paper":{"title":"Linearity of regression for weak records, revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jacek Weso{\\l}owski, Rafa{\\l} Karczewski","submitted_at":"2015-11-01T10:13:55Z","abstract_excerpt":"Since many years characterization of distribution by linearity of regression of non-adjacent weak records E(W_{i+s}|W_i) = \\beta_1 W_i+\\beta_0 for discrete observations has been known to be a difficult question. Lopez- Blazquez (2004) proposed an interesting idea of reducing it to the adjacent case and claimed to have the characterization problem completely solved. We will explain that, unfortunately, there is a major aw in the proof given in that paper. This aw is related to fact that in some situations the operator responsible for reduction of the non-adjacent case to the adjacent one is not"},"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":"1511.00224","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-01T10:13:55Z","cross_cats_sorted":[],"title_canon_sha256":"cd8fe9e71e35f6e885f087563dfeefd8b52e1a68748ec4d03b7c046e805e7443","abstract_canon_sha256":"85f9d77ae0d34a1be6f3a69ac8dcd9dae087d1c511bbe3f2632cfc0320916036"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:18.024809Z","signature_b64":"O0pEC6g3My8qxSq4I1wUGF2eCNIYQfwdke7IUcBp+sUrShakTvljfqEavw7NwWAGzN7RRfM2nRJQWFfSf5IcAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dad6a2b7d7d3e5ecc7a64f4555057014b4914e092c44b5dd8f5ad2f9c170acd2","last_reissued_at":"2026-05-18T01:11:18.024268Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:18.024268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linearity of regression for weak records, revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jacek Weso{\\l}owski, Rafa{\\l} Karczewski","submitted_at":"2015-11-01T10:13:55Z","abstract_excerpt":"Since many years characterization of distribution by linearity of regression of non-adjacent weak records E(W_{i+s}|W_i) = \\beta_1 W_i+\\beta_0 for discrete observations has been known to be a difficult question. Lopez- Blazquez (2004) proposed an interesting idea of reducing it to the adjacent case and claimed to have the characterization problem completely solved. We will explain that, unfortunately, there is a major aw in the proof given in that paper. This aw is related to fact that in some situations the operator responsible for reduction of the non-adjacent case to the adjacent one is not"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00224","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":"1511.00224","created_at":"2026-05-18T01:11:18.024350+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.00224v2","created_at":"2026-05-18T01:11:18.024350+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00224","created_at":"2026-05-18T01:11:18.024350+00:00"},{"alias_kind":"pith_short_12","alias_value":"3LLKFN6X2PS6","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"3LLKFN6X2PS6ZR5G","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"3LLKFN6X","created_at":"2026-05-18T12:29:02.477457+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/3LLKFN6X2PS6ZR5GJ5CVKBLQCS","json":"https://pith.science/pith/3LLKFN6X2PS6ZR5GJ5CVKBLQCS.json","graph_json":"https://pith.science/api/pith-number/3LLKFN6X2PS6ZR5GJ5CVKBLQCS/graph.json","events_json":"https://pith.science/api/pith-number/3LLKFN6X2PS6ZR5GJ5CVKBLQCS/events.json","paper":"https://pith.science/paper/3LLKFN6X"},"agent_actions":{"view_html":"https://pith.science/pith/3LLKFN6X2PS6ZR5GJ5CVKBLQCS","download_json":"https://pith.science/pith/3LLKFN6X2PS6ZR5GJ5CVKBLQCS.json","view_paper":"https://pith.science/paper/3LLKFN6X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.00224&json=true","fetch_graph":"https://pith.science/api/pith-number/3LLKFN6X2PS6ZR5GJ5CVKBLQCS/graph.json","fetch_events":"https://pith.science/api/pith-number/3LLKFN6X2PS6ZR5GJ5CVKBLQCS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3LLKFN6X2PS6ZR5GJ5CVKBLQCS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3LLKFN6X2PS6ZR5GJ5CVKBLQCS/action/storage_attestation","attest_author":"https://pith.science/pith/3LLKFN6X2PS6ZR5GJ5CVKBLQCS/action/author_attestation","sign_citation":"https://pith.science/pith/3LLKFN6X2PS6ZR5GJ5CVKBLQCS/action/citation_signature","submit_replication":"https://pith.science/pith/3LLKFN6X2PS6ZR5GJ5CVKBLQCS/action/replication_record"}},"created_at":"2026-05-18T01:11:18.024350+00:00","updated_at":"2026-05-18T01:11:18.024350+00:00"}