{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YRTWCLMJJCYFG56PXWCPHZANCF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7a2aead8ca7aefe2d87bc45e6217ac288aec9e80cab52c91a657945766383ba7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-10-13T11:27:47Z","title_canon_sha256":"e466e7752fd3b42944422a125bd22d9938a416cb5bbc43c8937c117b83dbac9f"},"schema_version":"1.0","source":{"id":"1510.03632","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03632","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03632v1","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03632","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"pith_short_12","alias_value":"YRTWCLMJJCYF","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YRTWCLMJJCYFG56P","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YRTWCLMJ","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:4febea84fdba7e7e50c827180a5c96e6ecdb2a94361ae0f1f36bf280300bc83f","target":"graph","created_at":"2026-05-18T01:30:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we give a characterization of all order isomorphisms on some classes of convex functions. We deal with the class $Cvx(K)$ consisting of lower-semi-continuous convex functions defined on a convex set $K$, and its subclass $Cvx_0(K)$ of non negative functions attaining the value zero at the origin. We show that any order isomorphism on these classes must be induced by a point map on the epi-graphs of the functions, and determine the exact form of this map. To this end we study convexity preserving maps on subsets of ${\\mathbb R}^n$, and also in this area we have some new interpreta","authors_text":"D.I. Florentin, S. Artstein-Avidan, V.D. Milman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-10-13T11:27:47Z","title":"Order Isomorphisms on Convex Functions in Windows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03632","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:57b1b9945599b91012cdf9210e71c3ca1febae9cab723f6bfa08e7b5e86cdf70","target":"record","created_at":"2026-05-18T01:30:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7a2aead8ca7aefe2d87bc45e6217ac288aec9e80cab52c91a657945766383ba7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-10-13T11:27:47Z","title_canon_sha256":"e466e7752fd3b42944422a125bd22d9938a416cb5bbc43c8937c117b83dbac9f"},"schema_version":"1.0","source":{"id":"1510.03632","kind":"arxiv","version":1}},"canonical_sha256":"c467612d8948b05377cfbd84f3e40d117a23a6bf684cbfff6596baab83548ced","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c467612d8948b05377cfbd84f3e40d117a23a6bf684cbfff6596baab83548ced","first_computed_at":"2026-05-18T01:30:16.619471Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:16.619471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k+u4szNjm+Q6ZAR4K2MhbY1KgJGMuk+kA5p+4zXYY3MNx3rjUHvM+V4v7jKte5e8vNmdTv/m87hms9EmT4r8Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:16.620111Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.03632","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57b1b9945599b91012cdf9210e71c3ca1febae9cab723f6bfa08e7b5e86cdf70","sha256:4febea84fdba7e7e50c827180a5c96e6ecdb2a94361ae0f1f36bf280300bc83f"],"state_sha256":"a8314c0db58bd2bf3f57e1f46f6f5ea3115a9003f4859e85d9588d7d2801b5d9"}