{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CI3JX4T4I2Z3SNPYM2PMGR4QCW","short_pith_number":"pith:CI3JX4T4","canonical_record":{"source":{"id":"1209.0873","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-05T07:05:46Z","cross_cats_sorted":[],"title_canon_sha256":"9e1674658297617a3a2263f7759b1dffafcc0bf432a8916c8a15de92fc2d323a","abstract_canon_sha256":"1228837459d7bd7acf3778a4c77aaf18a2b3e03c42f1da7f659a05eb5fc018ed"},"schema_version":"1.0"},"canonical_sha256":"12369bf27c46b3b935f8669ec3479015879986cdfe6c71b82f929284bc8f544e","source":{"kind":"arxiv","id":"1209.0873","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0873","created_at":"2026-05-18T03:46:15Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0873v1","created_at":"2026-05-18T03:46:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0873","created_at":"2026-05-18T03:46:15Z"},{"alias_kind":"pith_short_12","alias_value":"CI3JX4T4I2Z3","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CI3JX4T4I2Z3SNPY","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CI3JX4T4","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CI3JX4T4I2Z3SNPYM2PMGR4QCW","target":"record","payload":{"canonical_record":{"source":{"id":"1209.0873","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-05T07:05:46Z","cross_cats_sorted":[],"title_canon_sha256":"9e1674658297617a3a2263f7759b1dffafcc0bf432a8916c8a15de92fc2d323a","abstract_canon_sha256":"1228837459d7bd7acf3778a4c77aaf18a2b3e03c42f1da7f659a05eb5fc018ed"},"schema_version":"1.0"},"canonical_sha256":"12369bf27c46b3b935f8669ec3479015879986cdfe6c71b82f929284bc8f544e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:15.969384Z","signature_b64":"wLrtlsQIFs7PEMFpsWayLtaJwxhPCf2A95F6r1mLs+GYqdmcmCeCAxji9wuBItU9e6KeBoxr8etSdaG43QBxDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12369bf27c46b3b935f8669ec3479015879986cdfe6c71b82f929284bc8f544e","last_reissued_at":"2026-05-18T03:46:15.968762Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:15.968762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.0873","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":"2026-05-18T03:46:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CIhtJ9MD7KXIYrHS8GvVHS/EDRMRux6lpGxoed8GpKL0yr6Rb+kK3bONa1VNq5m3Sx7XX4pqXw8YorJOh/c2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T13:57:18.340779Z"},"content_sha256":"2b589181885f532ba728afc5e45925ca3f3aea2181549454ad35d17cae231031","schema_version":"1.0","event_id":"sha256:2b589181885f532ba728afc5e45925ca3f3aea2181549454ad35d17cae231031"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CI3JX4T4I2Z3SNPYM2PMGR4QCW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Power mean inequality of generalized trigonometric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Barkat Ali Bhayo, Matti Vuorinen","submitted_at":"2012-09-05T07:05:46Z","abstract_excerpt":"We study the convexity/concavity properties of the generalized $p$-trigonometric functions in the sense of P. Lindqvist with respect to the power means."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0873","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":"2026-05-18T03:46:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T5u/Dptc3PYJw5Xh1TZ+9vC1nFs/w2NiWmX/LgjBjzof6vZTT2sZA1HcUMBcSyyAdWVTaLNypWiIm12XUHbYCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T13:57:18.341135Z"},"content_sha256":"5649675555fc0ed451bc671b74b6c3efa3b4d391a2e96d09f8b26ec32372d20c","schema_version":"1.0","event_id":"sha256:5649675555fc0ed451bc671b74b6c3efa3b4d391a2e96d09f8b26ec32372d20c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CI3JX4T4I2Z3SNPYM2PMGR4QCW/bundle.json","state_url":"https://pith.science/pith/CI3JX4T4I2Z3SNPYM2PMGR4QCW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CI3JX4T4I2Z3SNPYM2PMGR4QCW/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":"2026-06-21T13:57:18Z","links":{"resolver":"https://pith.science/pith/CI3JX4T4I2Z3SNPYM2PMGR4QCW","bundle":"https://pith.science/pith/CI3JX4T4I2Z3SNPYM2PMGR4QCW/bundle.json","state":"https://pith.science/pith/CI3JX4T4I2Z3SNPYM2PMGR4QCW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CI3JX4T4I2Z3SNPYM2PMGR4QCW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CI3JX4T4I2Z3SNPYM2PMGR4QCW","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":"1228837459d7bd7acf3778a4c77aaf18a2b3e03c42f1da7f659a05eb5fc018ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-05T07:05:46Z","title_canon_sha256":"9e1674658297617a3a2263f7759b1dffafcc0bf432a8916c8a15de92fc2d323a"},"schema_version":"1.0","source":{"id":"1209.0873","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0873","created_at":"2026-05-18T03:46:15Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0873v1","created_at":"2026-05-18T03:46:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0873","created_at":"2026-05-18T03:46:15Z"},{"alias_kind":"pith_short_12","alias_value":"CI3JX4T4I2Z3","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CI3JX4T4I2Z3SNPY","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CI3JX4T4","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:5649675555fc0ed451bc671b74b6c3efa3b4d391a2e96d09f8b26ec32372d20c","target":"graph","created_at":"2026-05-18T03:46:15Z","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 study the convexity/concavity properties of the generalized $p$-trigonometric functions in the sense of P. Lindqvist with respect to the power means.","authors_text":"Barkat Ali Bhayo, Matti Vuorinen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-05T07:05:46Z","title":"Power mean inequality of generalized trigonometric functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0873","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":"sha256:2b589181885f532ba728afc5e45925ca3f3aea2181549454ad35d17cae231031","target":"record","created_at":"2026-05-18T03:46:15Z","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":"1228837459d7bd7acf3778a4c77aaf18a2b3e03c42f1da7f659a05eb5fc018ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-05T07:05:46Z","title_canon_sha256":"9e1674658297617a3a2263f7759b1dffafcc0bf432a8916c8a15de92fc2d323a"},"schema_version":"1.0","source":{"id":"1209.0873","kind":"arxiv","version":1}},"canonical_sha256":"12369bf27c46b3b935f8669ec3479015879986cdfe6c71b82f929284bc8f544e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12369bf27c46b3b935f8669ec3479015879986cdfe6c71b82f929284bc8f544e","first_computed_at":"2026-05-18T03:46:15.968762Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:15.968762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wLrtlsQIFs7PEMFpsWayLtaJwxhPCf2A95F6r1mLs+GYqdmcmCeCAxji9wuBItU9e6KeBoxr8etSdaG43QBxDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:15.969384Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.0873","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b589181885f532ba728afc5e45925ca3f3aea2181549454ad35d17cae231031","sha256:5649675555fc0ed451bc671b74b6c3efa3b4d391a2e96d09f8b26ec32372d20c"],"state_sha256":"0edd97e57dab78d8a61d7eb46791cf50d8c845981704870649b8abc6f83ccdc7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IYh2SpRrfPRfxv1jvSD/WvWHIMt95xJVwpT+m8tfctwlen3nO2R08wBvunAKBpw8WsiO/+6szFGo0Bri6wLwCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T13:57:18.344011Z","bundle_sha256":"66bb35888c25dc32360cb9cbf4e7f82623591738f7e3331180f25d21b9b024f6"}}