{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:QYWIKYNCKUO5L73FRCR2FYGI5Q","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":"9373b47dcd1c4af20966fb4038050560387cc4c99a4842c29ff7d94604d279b4","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-01-19T22:32:52Z","title_canon_sha256":"e2362a28765b46ded89490b37e825ca68c18bdd74c5e1f7988ba2c40f64a0d4b"},"schema_version":"1.0","source":{"id":"2301.08342","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.08342","created_at":"2026-07-05T05:34:35Z"},{"alias_kind":"arxiv_version","alias_value":"2301.08342v1","created_at":"2026-07-05T05:34:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.08342","created_at":"2026-07-05T05:34:35Z"},{"alias_kind":"pith_short_12","alias_value":"QYWIKYNCKUO5","created_at":"2026-07-05T05:34:35Z"},{"alias_kind":"pith_short_16","alias_value":"QYWIKYNCKUO5L73F","created_at":"2026-07-05T05:34:35Z"},{"alias_kind":"pith_short_8","alias_value":"QYWIKYNC","created_at":"2026-07-05T05:34:35Z"}],"graph_snapshots":[{"event_id":"sha256:2f7500236e1122038d98a30169e21191b3536af335e369209fada78fb845e980","target":"graph","created_at":"2026-07-05T05:34:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2301.08342/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We analyze the role played by $n$-convexity for the fulfillment of a series of linear functional inequalities that extend the Hornich-Hlawka functional inequality, $f\\left( x\\right) +f\\left( y\\right) +f\\left( z\\right) +f\\left( x+y+z\\right) \\geq f\\left( x+y\\right) +f\\left( y+z\\right)+f\\left( z+x\\right) +f(0),$ including extensions to the case of positive operators.","authors_text":"Constantin P. Niculescu, Suvrit Sra","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-01-19T22:32:52Z","title":"The Hornich-Hlawka functional inequality for functions with positive differences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.08342","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":"sha256:23437f7f169998727c68b75420be62735e7755c2c2cebaa0cb5f9fd4cdad3bbb","target":"record","created_at":"2026-07-05T05:34:35Z","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":"9373b47dcd1c4af20966fb4038050560387cc4c99a4842c29ff7d94604d279b4","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-01-19T22:32:52Z","title_canon_sha256":"e2362a28765b46ded89490b37e825ca68c18bdd74c5e1f7988ba2c40f64a0d4b"},"schema_version":"1.0","source":{"id":"2301.08342","kind":"arxiv","version":1}},"canonical_sha256":"862c8561a2551dd5ff6588a3a2e0c8ec2a27abd030fa9b78cea2b170f6cc159c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"862c8561a2551dd5ff6588a3a2e0c8ec2a27abd030fa9b78cea2b170f6cc159c","first_computed_at":"2026-07-05T05:34:35.184945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:34:35.184945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c3YMNRVuAaeEEpXVakur3LLuyNK7H8K9X2CCaU2Mc3JecIs1felUMxDIfLEulqh4WSocG+Gfitt0ApUQlt3eCw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:34:35.185452Z","signed_message":"canonical_sha256_bytes"},"source_id":"2301.08342","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23437f7f169998727c68b75420be62735e7755c2c2cebaa0cb5f9fd4cdad3bbb","sha256:2f7500236e1122038d98a30169e21191b3536af335e369209fada78fb845e980"],"state_sha256":"dca77fb09c04681e85222425a066f699fde6564b4e342ed4db340c8c08870b76"}