{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:Q4KVFEOALKMQ3E3SEXUE2KN223","short_pith_number":"pith:Q4KVFEOA","schema_version":"1.0","canonical_sha256":"87155291c05a990d937225e84d29bad6ced34aa2b33299a7b3f326b24bbc2e22","source":{"kind":"arxiv","id":"1709.08611","version":1},"attestation_state":"computed","paper":{"title":"A Characterization of Convex Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Paolo Leonetti","submitted_at":"2017-09-25T17:41:23Z","abstract_excerpt":"Let $D$ be a convex subset of a real vector space. It is shown that a radially lower semicontinuous function $f: D\\to \\mathbf{R}\\cup \\{+\\infty\\}$ is convex if and only if for all $x,y \\in D$ there exists $\\alpha=\\alpha(x,y) \\in (0,1)$ such that $f(\\alpha x+(1-\\alpha)y) \\le \\alpha f(x)+(1-\\alpha)f(y)$."},"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":"1709.08611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-09-25T17:41:23Z","cross_cats_sorted":[],"title_canon_sha256":"cb2f625d9ab46fbd547046ef6f42ff289d3ec69eb18ae9b551fdb1026473592b","abstract_canon_sha256":"c5927dec7905fce20ca7159d9da157e9461a448510be0d819ebcbfdd596e66b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:25.226402Z","signature_b64":"ihiuOt58S4Zvnj5Zs1jxjJ4j8pG3tr0EHD3FC/BMfL1ZfZmFOQZKttDHjnMIOyRJXhJrL3LSU/9XQn6LmezVBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87155291c05a990d937225e84d29bad6ced34aa2b33299a7b3f326b24bbc2e22","last_reissued_at":"2026-05-18T00:34:25.225727Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:25.225727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Characterization of Convex Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Paolo Leonetti","submitted_at":"2017-09-25T17:41:23Z","abstract_excerpt":"Let $D$ be a convex subset of a real vector space. It is shown that a radially lower semicontinuous function $f: D\\to \\mathbf{R}\\cup \\{+\\infty\\}$ is convex if and only if for all $x,y \\in D$ there exists $\\alpha=\\alpha(x,y) \\in (0,1)$ such that $f(\\alpha x+(1-\\alpha)y) \\le \\alpha f(x)+(1-\\alpha)f(y)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08611","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":"1709.08611","created_at":"2026-05-18T00:34:25.225804+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.08611v1","created_at":"2026-05-18T00:34:25.225804+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08611","created_at":"2026-05-18T00:34:25.225804+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q4KVFEOALKMQ","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q4KVFEOALKMQ3E3S","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q4KVFEOA","created_at":"2026-05-18T12:31:37.085036+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/Q4KVFEOALKMQ3E3SEXUE2KN223","json":"https://pith.science/pith/Q4KVFEOALKMQ3E3SEXUE2KN223.json","graph_json":"https://pith.science/api/pith-number/Q4KVFEOALKMQ3E3SEXUE2KN223/graph.json","events_json":"https://pith.science/api/pith-number/Q4KVFEOALKMQ3E3SEXUE2KN223/events.json","paper":"https://pith.science/paper/Q4KVFEOA"},"agent_actions":{"view_html":"https://pith.science/pith/Q4KVFEOALKMQ3E3SEXUE2KN223","download_json":"https://pith.science/pith/Q4KVFEOALKMQ3E3SEXUE2KN223.json","view_paper":"https://pith.science/paper/Q4KVFEOA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.08611&json=true","fetch_graph":"https://pith.science/api/pith-number/Q4KVFEOALKMQ3E3SEXUE2KN223/graph.json","fetch_events":"https://pith.science/api/pith-number/Q4KVFEOALKMQ3E3SEXUE2KN223/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q4KVFEOALKMQ3E3SEXUE2KN223/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q4KVFEOALKMQ3E3SEXUE2KN223/action/storage_attestation","attest_author":"https://pith.science/pith/Q4KVFEOALKMQ3E3SEXUE2KN223/action/author_attestation","sign_citation":"https://pith.science/pith/Q4KVFEOALKMQ3E3SEXUE2KN223/action/citation_signature","submit_replication":"https://pith.science/pith/Q4KVFEOALKMQ3E3SEXUE2KN223/action/replication_record"}},"created_at":"2026-05-18T00:34:25.225804+00:00","updated_at":"2026-05-18T00:34:25.225804+00:00"}