{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SUOTAKVNVEWS7BQKOWX773EQGS","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":"4f2aaa1aab7b01e82edff7dc7f3ba93b9ec2c1136a6ef9f14e5529b0589381d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-01-31T09:09:47Z","title_canon_sha256":"c20a6371bffb01b8685ab351e6400004b2eee0199ded653f77bb74d2bbfbcbd3"},"schema_version":"1.0","source":{"id":"1201.6480","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.6480","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"arxiv_version","alias_value":"1201.6480v1","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.6480","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"pith_short_12","alias_value":"SUOTAKVNVEWS","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"SUOTAKVNVEWS7BQK","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"SUOTAKVN","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:707cecd5cfbdeebf4d9f3464b9c6f3adec3cb1ec660f426c3929170314fdd9a0","target":"graph","created_at":"2026-05-18T03:35:26Z","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":"In the paper, by establishing the monotonicity of some functions involving the sine and cosine functions, the authors provide concise proofs of some known inequalities and find some new sharp inequalities involving the Seiffert, contra-harmonic, centroidal, arithmetic, geometric, harmonic, and root-square means of two positive real numbers $a$ and $b$ with $a\\ne b$.","authors_text":"Feng Qi, Wei-Dong Jiang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-01-31T09:09:47Z","title":"Some sharp inequalities involving Seiffert and other means and their concise proofs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6480","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:b10b57ee070d57371f2ccca8e9f6ec88b883864338ed6e4d58cc9bc3b937c432","target":"record","created_at":"2026-05-18T03:35:26Z","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":"4f2aaa1aab7b01e82edff7dc7f3ba93b9ec2c1136a6ef9f14e5529b0589381d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-01-31T09:09:47Z","title_canon_sha256":"c20a6371bffb01b8685ab351e6400004b2eee0199ded653f77bb74d2bbfbcbd3"},"schema_version":"1.0","source":{"id":"1201.6480","kind":"arxiv","version":1}},"canonical_sha256":"951d302aada92d2f860a75afffec9034a208b6088e52f6c5338b980bac3ad946","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"951d302aada92d2f860a75afffec9034a208b6088e52f6c5338b980bac3ad946","first_computed_at":"2026-05-18T03:35:26.163021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:26.163021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xB2z9svPlcCTl/MRBmGVi8dQxivRdz4N13vwsZyfjaXMp27xoRIQwYtOdnSnKetU8gxSzAozQxUTaWuIaoKPBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:26.163811Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.6480","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b10b57ee070d57371f2ccca8e9f6ec88b883864338ed6e4d58cc9bc3b937c432","sha256:707cecd5cfbdeebf4d9f3464b9c6f3adec3cb1ec660f426c3929170314fdd9a0"],"state_sha256":"f768a2de0567a117d029f42a7e4198666876b1e0d4194adef71d27d8f5b5e618"}