{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:TUQNNK5AOQQKU4DK22PHOITGEC","short_pith_number":"pith:TUQNNK5A","canonical_record":{"source":{"id":"1411.6636","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-11-24T21:00:46Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"4c045eed711e0dbffa35bbba3edef54c691fc1a1cf680e1c43d640a7a134c1eb","abstract_canon_sha256":"f5d173b4dcef0b13f0e5f287f6b3c48831e631d463f3450485506108df17a3b2"},"schema_version":"1.0"},"canonical_sha256":"9d20d6aba07420aa706ad69e77226620a762af482f7bc99e3f72916d426b2183","source":{"kind":"arxiv","id":"1411.6636","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6636","created_at":"2026-05-18T00:17:30Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6636v1","created_at":"2026-05-18T00:17:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6636","created_at":"2026-05-18T00:17:30Z"},{"alias_kind":"pith_short_12","alias_value":"TUQNNK5AOQQK","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TUQNNK5AOQQKU4DK","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TUQNNK5A","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:TUQNNK5AOQQKU4DK22PHOITGEC","target":"record","payload":{"canonical_record":{"source":{"id":"1411.6636","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-11-24T21:00:46Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"4c045eed711e0dbffa35bbba3edef54c691fc1a1cf680e1c43d640a7a134c1eb","abstract_canon_sha256":"f5d173b4dcef0b13f0e5f287f6b3c48831e631d463f3450485506108df17a3b2"},"schema_version":"1.0"},"canonical_sha256":"9d20d6aba07420aa706ad69e77226620a762af482f7bc99e3f72916d426b2183","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:30.869788Z","signature_b64":"URQ1+jPaMC2W4njr8ZQP6yPACmmYeFVXEHaDo9qneuhVbvSaHGmfntWT3Thuy0bnqelsCe23S5Z09LMJsisMDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d20d6aba07420aa706ad69e77226620a762af482f7bc99e3f72916d426b2183","last_reissued_at":"2026-05-18T00:17:30.869234Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:30.869234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.6636","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:17:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"02EgpirMw5JpPLwMhLiCBrzQFtg8iRtUpE5Aug2tYw0/ZUw4X5MdCitE9M7BcmtOUeeaUI80z4T1IwkcHU7MAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:04:17.923693Z"},"content_sha256":"320fb5f583d2aeb1db9583178a1341c3e858d5fc284e8107b3490b00deba15c2","schema_version":"1.0","event_id":"sha256:320fb5f583d2aeb1db9583178a1341c3e858d5fc284e8107b3490b00deba15c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:TUQNNK5AOQQKU4DK22PHOITGEC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On trace-convex noncommutative polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Christopher S. Nelson, Igor Klep, Scott A. McCullough","submitted_at":"2014-11-24T21:00:46Z","abstract_excerpt":"To each real continuous function f there is an associated trace function on real symmetric matrices Tr f. The classical Klein lemma states that f is convex if and only if Tr f is convex. In this note we present an algebraic strengthening of this lemma for univariate polynomials f: Tr f is convex if and only if the noncommutative second directional derivative of f is a sum of hermitian squares and commutators in a free algebra. We also give a localized version of this result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6636","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:17:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9/XVbfRyJ4SjuJBIfOJHIaowezpEApL0MVgaQ6l52Y+GPHBXU26qbdW5dUWdeTr807C8K/RJijkHkBFg0X3cDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:04:17.924046Z"},"content_sha256":"45cc2d3581383ff49be8fde8a503e82eea0b5d879c7c15bbc76c6d5c665db265","schema_version":"1.0","event_id":"sha256:45cc2d3581383ff49be8fde8a503e82eea0b5d879c7c15bbc76c6d5c665db265"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TUQNNK5AOQQKU4DK22PHOITGEC/bundle.json","state_url":"https://pith.science/pith/TUQNNK5AOQQKU4DK22PHOITGEC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TUQNNK5AOQQKU4DK22PHOITGEC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-12T05:04:17Z","links":{"resolver":"https://pith.science/pith/TUQNNK5AOQQKU4DK22PHOITGEC","bundle":"https://pith.science/pith/TUQNNK5AOQQKU4DK22PHOITGEC/bundle.json","state":"https://pith.science/pith/TUQNNK5AOQQKU4DK22PHOITGEC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TUQNNK5AOQQKU4DK22PHOITGEC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TUQNNK5AOQQKU4DK22PHOITGEC","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":"f5d173b4dcef0b13f0e5f287f6b3c48831e631d463f3450485506108df17a3b2","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-11-24T21:00:46Z","title_canon_sha256":"4c045eed711e0dbffa35bbba3edef54c691fc1a1cf680e1c43d640a7a134c1eb"},"schema_version":"1.0","source":{"id":"1411.6636","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6636","created_at":"2026-05-18T00:17:30Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6636v1","created_at":"2026-05-18T00:17:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6636","created_at":"2026-05-18T00:17:30Z"},{"alias_kind":"pith_short_12","alias_value":"TUQNNK5AOQQK","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TUQNNK5AOQQKU4DK","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TUQNNK5A","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:45cc2d3581383ff49be8fde8a503e82eea0b5d879c7c15bbc76c6d5c665db265","target":"graph","created_at":"2026-05-18T00:17:30Z","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":"To each real continuous function f there is an associated trace function on real symmetric matrices Tr f. The classical Klein lemma states that f is convex if and only if Tr f is convex. In this note we present an algebraic strengthening of this lemma for univariate polynomials f: Tr f is convex if and only if the noncommutative second directional derivative of f is a sum of hermitian squares and commutators in a free algebra. We also give a localized version of this result.","authors_text":"Christopher S. Nelson, Igor Klep, Scott A. McCullough","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-11-24T21:00:46Z","title":"On trace-convex noncommutative polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6636","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":"sha256:320fb5f583d2aeb1db9583178a1341c3e858d5fc284e8107b3490b00deba15c2","target":"record","created_at":"2026-05-18T00:17:30Z","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":"f5d173b4dcef0b13f0e5f287f6b3c48831e631d463f3450485506108df17a3b2","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-11-24T21:00:46Z","title_canon_sha256":"4c045eed711e0dbffa35bbba3edef54c691fc1a1cf680e1c43d640a7a134c1eb"},"schema_version":"1.0","source":{"id":"1411.6636","kind":"arxiv","version":1}},"canonical_sha256":"9d20d6aba07420aa706ad69e77226620a762af482f7bc99e3f72916d426b2183","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d20d6aba07420aa706ad69e77226620a762af482f7bc99e3f72916d426b2183","first_computed_at":"2026-05-18T00:17:30.869234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:30.869234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"URQ1+jPaMC2W4njr8ZQP6yPACmmYeFVXEHaDo9qneuhVbvSaHGmfntWT3Thuy0bnqelsCe23S5Z09LMJsisMDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:30.869788Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.6636","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:320fb5f583d2aeb1db9583178a1341c3e858d5fc284e8107b3490b00deba15c2","sha256:45cc2d3581383ff49be8fde8a503e82eea0b5d879c7c15bbc76c6d5c665db265"],"state_sha256":"e9e868b0e4f5a435c2bde04320b4f2e7a9cab3a241072b06831cb42e110b62a4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XWoUlmTOxUWspXPCLaP9eJmH8knr6pUxz60aNh9XEKy0kKIjtbEqWscKYigytC71F+rKrCt270swLwEdoVmQAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T05:04:17.926014Z","bundle_sha256":"71dc9c9bbb2f1cb488372273fb357082a476cc9bf6cc2f2cb2b767bed237c30c"}}