{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZHAZETLGL2KFLILBLELTIU77H2","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":"9c7802b4089efc898eff939623ad45a96ae1cfb21b16dee43c04ca15d0350918","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-05T07:12:25Z","title_canon_sha256":"d4432a7a98d04db048cb3ecb800606d3217a81db8ba897e1130f15e944045a91"},"schema_version":"1.0","source":{"id":"1309.1244","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1244","created_at":"2026-05-18T00:26:47Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1244v1","created_at":"2026-05-18T00:26:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1244","created_at":"2026-05-18T00:26:47Z"},{"alias_kind":"pith_short_12","alias_value":"ZHAZETLGL2KF","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZHAZETLGL2KFLILB","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZHAZETLG","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:17a186bb51f89971ebc939c20b03d3891850f0bd5152e5ecafb1c9410782e931","target":"graph","created_at":"2026-05-18T00:26:47Z","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":"We investigate the representation of homogeneous, symmetric means in the form M(x,y)=\\frac{x-y}{2f((x-y)/(x+y))}. This allows for a new approach to comparing means. As an example, we provide optimal estimate of the form (1-\\mu)min(x,y)+ \\mu max(x,y)<= M(x,y)<= (1-\\nu)min(x,y)+ \\nu max(x,y) and M((x+y)/2-\\mu(x-y)/2,(x+y)/2+\\mu(x-y)/2)<= N(x,y)<= M((x+y)/2-\\nu(x-y)/2,(x+y)/2+\\nu(x-y)/2) for some known means.","authors_text":"Alfred Witkowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-05T07:12:25Z","title":"On Seiffert-like means"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1244","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":"sha256:3286f7c02e440423d77e447290f6009a98cbf544d5b0fde3ee409fdff5eda3e6","target":"record","created_at":"2026-05-18T00:26:47Z","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":"9c7802b4089efc898eff939623ad45a96ae1cfb21b16dee43c04ca15d0350918","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-05T07:12:25Z","title_canon_sha256":"d4432a7a98d04db048cb3ecb800606d3217a81db8ba897e1130f15e944045a91"},"schema_version":"1.0","source":{"id":"1309.1244","kind":"arxiv","version":1}},"canonical_sha256":"c9c1924d665e9455a16159173453ff3e8ebb5faeed0c8ddf8892a599f235c489","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9c1924d665e9455a16159173453ff3e8ebb5faeed0c8ddf8892a599f235c489","first_computed_at":"2026-05-18T00:26:47.548745Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:47.548745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"buyV7T0EojTYYUXEQRA9tL6yRuoPB5ZxlAGMShv4BbWDlDhDE8cDjot42Q8nbNEzQnIZLxoV7NWlDgdsFkFKBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:47.549349Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1244","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3286f7c02e440423d77e447290f6009a98cbf544d5b0fde3ee409fdff5eda3e6","sha256:17a186bb51f89971ebc939c20b03d3891850f0bd5152e5ecafb1c9410782e931"],"state_sha256":"ca0ea3879fc1ae9c745598a3b074f7730b1024a3ac07b24ccfdb45a5668e85d6"}