{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:HILTVUIYJCKZRSQSCSSMALGIUB","short_pith_number":"pith:HILTVUIY","schema_version":"1.0","canonical_sha256":"3a173ad118489598ca1214a4c02cc8a0676c4f18179c0496c1cdcd7ecd7b5729","source":{"kind":"arxiv","id":"1502.03897","version":2},"attestation_state":"computed","paper":{"title":"Linear Perturbations of Quasiconvex Functions and Convexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Khanh Pham Duy, Marc Lassonde","submitted_at":"2015-02-13T06:43:03Z","abstract_excerpt":"Let $E$ be a real vector space with dual space $E^*$ and let $C\\subset E$ be a convex subset with more than one point. Let $f : C\\to\\mathbb{R}$ be a function satisfying a mild stability property at 'flat' points of the (relative) boundary of $C$. We show that $f$ is convex if and only if for some linear form $c^*$ on $E$ not constant on $C$, the function $f+\\lambda c^*$ is quasiconvex for all $\\lambda\\in\\mathbb{R}$."},"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":"1502.03897","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-13T06:43:03Z","cross_cats_sorted":[],"title_canon_sha256":"7097397bb770e6a7ceb02afb10d591b89d86e7a65c813cbb67b28a11bca7627e","abstract_canon_sha256":"812b29d6836d8842736dc1aaab98d96b50274191b6ab8d6dcd2b179affd572f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:31.173016Z","signature_b64":"hMZwYAct9OByfSyaoeOTn5fKF0aHr+Oe4+r+3WUIePldUQj+6Qw+VG4AhZrCmfN7a/yclVUX7hWANpmOitDeAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a173ad118489598ca1214a4c02cc8a0676c4f18179c0496c1cdcd7ecd7b5729","last_reissued_at":"2026-05-18T02:18:31.172557Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:31.172557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear Perturbations of Quasiconvex Functions and Convexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Khanh Pham Duy, Marc Lassonde","submitted_at":"2015-02-13T06:43:03Z","abstract_excerpt":"Let $E$ be a real vector space with dual space $E^*$ and let $C\\subset E$ be a convex subset with more than one point. Let $f : C\\to\\mathbb{R}$ be a function satisfying a mild stability property at 'flat' points of the (relative) boundary of $C$. We show that $f$ is convex if and only if for some linear form $c^*$ on $E$ not constant on $C$, the function $f+\\lambda c^*$ is quasiconvex for all $\\lambda\\in\\mathbb{R}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03897","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":"1502.03897","created_at":"2026-05-18T02:18:31.172644+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.03897v2","created_at":"2026-05-18T02:18:31.172644+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.03897","created_at":"2026-05-18T02:18:31.172644+00:00"},{"alias_kind":"pith_short_12","alias_value":"HILTVUIYJCKZ","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"HILTVUIYJCKZRSQS","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"HILTVUIY","created_at":"2026-05-18T12:29:25.134429+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/HILTVUIYJCKZRSQSCSSMALGIUB","json":"https://pith.science/pith/HILTVUIYJCKZRSQSCSSMALGIUB.json","graph_json":"https://pith.science/api/pith-number/HILTVUIYJCKZRSQSCSSMALGIUB/graph.json","events_json":"https://pith.science/api/pith-number/HILTVUIYJCKZRSQSCSSMALGIUB/events.json","paper":"https://pith.science/paper/HILTVUIY"},"agent_actions":{"view_html":"https://pith.science/pith/HILTVUIYJCKZRSQSCSSMALGIUB","download_json":"https://pith.science/pith/HILTVUIYJCKZRSQSCSSMALGIUB.json","view_paper":"https://pith.science/paper/HILTVUIY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.03897&json=true","fetch_graph":"https://pith.science/api/pith-number/HILTVUIYJCKZRSQSCSSMALGIUB/graph.json","fetch_events":"https://pith.science/api/pith-number/HILTVUIYJCKZRSQSCSSMALGIUB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HILTVUIYJCKZRSQSCSSMALGIUB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HILTVUIYJCKZRSQSCSSMALGIUB/action/storage_attestation","attest_author":"https://pith.science/pith/HILTVUIYJCKZRSQSCSSMALGIUB/action/author_attestation","sign_citation":"https://pith.science/pith/HILTVUIYJCKZRSQSCSSMALGIUB/action/citation_signature","submit_replication":"https://pith.science/pith/HILTVUIYJCKZRSQSCSSMALGIUB/action/replication_record"}},"created_at":"2026-05-18T02:18:31.172644+00:00","updated_at":"2026-05-18T02:18:31.172644+00:00"}