{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6W4SI6EH4E2QJNJTK2OHZDO4VK","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":"99b913c1e17ae475d2962d60acb9baad879c9769a4b0836a88268cbedec73df3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-02-14T12:17:16Z","title_canon_sha256":"436d688f5f218390dc816b9d96b6e4fedb9df8e06bb247375d051b3e15e13dd1"},"schema_version":"1.0","source":{"id":"1502.04201","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04201","created_at":"2026-05-18T01:14:26Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04201v2","created_at":"2026-05-18T01:14:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04201","created_at":"2026-05-18T01:14:26Z"},{"alias_kind":"pith_short_12","alias_value":"6W4SI6EH4E2Q","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6W4SI6EH4E2QJNJT","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6W4SI6EH","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:eb86ab00ae94f9e67a93deefff3c4e64b9830bced3b199b505739b4cd180ae9c","target":"graph","created_at":"2026-05-18T01:14:26Z","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":"Given positive numbers $a$ and $b$, the function $\\sqrt{at^2+b}$ is exponentially convex function of $t$ on the whole real axis. Three proofs of this result are presented.","authors_text":"Victor Katsnelson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-02-14T12:17:16Z","title":"The function $(\\cosh\\sqrt{at^2+b})$ is exponentially convex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04201","kind":"arxiv","version":2},"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:e3ce0b053fe35217a9907e097e1c2754ac9e25ed0868880346ed1d0bfe0a941f","target":"record","created_at":"2026-05-18T01:14:26Z","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":"99b913c1e17ae475d2962d60acb9baad879c9769a4b0836a88268cbedec73df3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-02-14T12:17:16Z","title_canon_sha256":"436d688f5f218390dc816b9d96b6e4fedb9df8e06bb247375d051b3e15e13dd1"},"schema_version":"1.0","source":{"id":"1502.04201","kind":"arxiv","version":2}},"canonical_sha256":"f5b9247887e13504b533569c7c8ddcaa89d32e515f7e453a4cc3fe18c27951ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5b9247887e13504b533569c7c8ddcaa89d32e515f7e453a4cc3fe18c27951ce","first_computed_at":"2026-05-18T01:14:26.140090Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:26.140090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mMZ0ifZKSH0YwcgV9C3bBFtDiPQxzwmpz+cAAbLIWsJtY0qcoGi74C8ynSd6RDsAj+CIdKcZ60tb4arAtukOAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:26.140859Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.04201","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3ce0b053fe35217a9907e097e1c2754ac9e25ed0868880346ed1d0bfe0a941f","sha256:eb86ab00ae94f9e67a93deefff3c4e64b9830bced3b199b505739b4cd180ae9c"],"state_sha256":"3611f9d93d73236293cabc8dd3800446b05d6890a77b69fcddc6880a97e4d0a6"}