{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:S3JNPIU5A5UFVE52Q4X7KYHP5U","short_pith_number":"pith:S3JNPIU5","schema_version":"1.0","canonical_sha256":"96d2d7a29d07685a93ba872ff560efed06637cb5ffd1b182532b4ea406e2f61c","source":{"kind":"arxiv","id":"1610.06835","version":4},"attestation_state":"computed","paper":{"title":"On sequences of expected maxima and expected ranges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Nickos Papadatos","submitted_at":"2016-10-21T16:07:44Z","abstract_excerpt":"We investigate conditions in order to decide whether a given sequence of real numbers represents expected maxima or expected ranges. The main result provides a novel necessary and sufficient condition, relating an expected maxima sequence to a translation of a Bernstein function through its L\\'{e}vy-Khintchine representation.\n  Key words and phrases: expected maxima; expected ranges; Bernstein functions, L\\'{e}vy-Khintchine representation, order statistics."},"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":"1610.06835","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-10-21T16:07:44Z","cross_cats_sorted":[],"title_canon_sha256":"4588d9e1ef79c381b84cf0c8fc60f7173ad9298a086c4e7f87865cf3c3f6a9de","abstract_canon_sha256":"b7051c41c27da0a608a90c3963d9a39ecda0d7a5fe3d97cc581b4bafba3ac98f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:38.061521Z","signature_b64":"kIU2BcVPnb/Egj0NHmFHdz+BfvFs7UznYa3oMdF+db5ry4PRtWJ1TiUhotPMuvVXpZltO1N0L5FFEKpTQl6bDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96d2d7a29d07685a93ba872ff560efed06637cb5ffd1b182532b4ea406e2f61c","last_reissued_at":"2026-05-18T00:13:38.060849Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:38.060849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On sequences of expected maxima and expected ranges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Nickos Papadatos","submitted_at":"2016-10-21T16:07:44Z","abstract_excerpt":"We investigate conditions in order to decide whether a given sequence of real numbers represents expected maxima or expected ranges. The main result provides a novel necessary and sufficient condition, relating an expected maxima sequence to a translation of a Bernstein function through its L\\'{e}vy-Khintchine representation.\n  Key words and phrases: expected maxima; expected ranges; Bernstein functions, L\\'{e}vy-Khintchine representation, order statistics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06835","kind":"arxiv","version":4},"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":"1610.06835","created_at":"2026-05-18T00:13:38.060948+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.06835v4","created_at":"2026-05-18T00:13:38.060948+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06835","created_at":"2026-05-18T00:13:38.060948+00:00"},{"alias_kind":"pith_short_12","alias_value":"S3JNPIU5A5UF","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_16","alias_value":"S3JNPIU5A5UFVE52","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_8","alias_value":"S3JNPIU5","created_at":"2026-05-18T12:30:41.710351+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/S3JNPIU5A5UFVE52Q4X7KYHP5U","json":"https://pith.science/pith/S3JNPIU5A5UFVE52Q4X7KYHP5U.json","graph_json":"https://pith.science/api/pith-number/S3JNPIU5A5UFVE52Q4X7KYHP5U/graph.json","events_json":"https://pith.science/api/pith-number/S3JNPIU5A5UFVE52Q4X7KYHP5U/events.json","paper":"https://pith.science/paper/S3JNPIU5"},"agent_actions":{"view_html":"https://pith.science/pith/S3JNPIU5A5UFVE52Q4X7KYHP5U","download_json":"https://pith.science/pith/S3JNPIU5A5UFVE52Q4X7KYHP5U.json","view_paper":"https://pith.science/paper/S3JNPIU5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.06835&json=true","fetch_graph":"https://pith.science/api/pith-number/S3JNPIU5A5UFVE52Q4X7KYHP5U/graph.json","fetch_events":"https://pith.science/api/pith-number/S3JNPIU5A5UFVE52Q4X7KYHP5U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S3JNPIU5A5UFVE52Q4X7KYHP5U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S3JNPIU5A5UFVE52Q4X7KYHP5U/action/storage_attestation","attest_author":"https://pith.science/pith/S3JNPIU5A5UFVE52Q4X7KYHP5U/action/author_attestation","sign_citation":"https://pith.science/pith/S3JNPIU5A5UFVE52Q4X7KYHP5U/action/citation_signature","submit_replication":"https://pith.science/pith/S3JNPIU5A5UFVE52Q4X7KYHP5U/action/replication_record"}},"created_at":"2026-05-18T00:13:38.060948+00:00","updated_at":"2026-05-18T00:13:38.060948+00:00"}