{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:HCMKMZGY6ZK2556MKKZH7UZRR4","short_pith_number":"pith:HCMKMZGY","canonical_record":{"source":{"id":"1212.2598","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-12-07T21:03:23Z","cross_cats_sorted":[],"title_canon_sha256":"ea19704e0f92020339961b88597e021bcee8e9638ce7f502e92ee6c055f349d1","abstract_canon_sha256":"42cbe08b456c2687094f2f2350ea9dd503134bfd6c8b646bbfd671afc3052e81"},"schema_version":"1.0"},"canonical_sha256":"3898a664d8f655aef7cc52b27fd3318f328f546654d8f11558bde4ec739f3eaa","source":{"kind":"arxiv","id":"1212.2598","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.2598","created_at":"2026-05-18T03:07:52Z"},{"alias_kind":"arxiv_version","alias_value":"1212.2598v2","created_at":"2026-05-18T03:07:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2598","created_at":"2026-05-18T03:07:52Z"},{"alias_kind":"pith_short_12","alias_value":"HCMKMZGY6ZK2","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HCMKMZGY6ZK2556M","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HCMKMZGY","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:HCMKMZGY6ZK2556MKKZH7UZRR4","target":"record","payload":{"canonical_record":{"source":{"id":"1212.2598","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-12-07T21:03:23Z","cross_cats_sorted":[],"title_canon_sha256":"ea19704e0f92020339961b88597e021bcee8e9638ce7f502e92ee6c055f349d1","abstract_canon_sha256":"42cbe08b456c2687094f2f2350ea9dd503134bfd6c8b646bbfd671afc3052e81"},"schema_version":"1.0"},"canonical_sha256":"3898a664d8f655aef7cc52b27fd3318f328f546654d8f11558bde4ec739f3eaa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:52.700720Z","signature_b64":"ZzdiyFyx7bA5YBj7smkxIPWO3SyfN+zqh8Vzc+mY3SLR1cGuY8BNi8EH6KunZWNig2m0kT7fR6gOfEyv+wDJDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3898a664d8f655aef7cc52b27fd3318f328f546654d8f11558bde4ec739f3eaa","last_reissued_at":"2026-05-18T03:07:52.699980Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:52.699980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.2598","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:07:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qOTL4gMdi8xD9slv+aMrnSkl+BXmxXnZBF4rz+ZF9W/xjxXUc7qadp6rTtTu5soWa9vSRAMfbPDm2ko/rdhPBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:38:08.519122Z"},"content_sha256":"82a68aa21384758740a1937b6edc014716f61e36bca361bfc23de216724b6e5d","schema_version":"1.0","event_id":"sha256:82a68aa21384758740a1937b6edc014716f61e36bca361bfc23de216724b6e5d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:HCMKMZGY6ZK2556MKKZH7UZRR4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simpson Type Inequalities Via m- and (alpha,m)- logarithmically Convex functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ahmet Ocak Akdemir","submitted_at":"2012-12-07T21:03:23Z","abstract_excerpt":"In this paper, we obtain some Simpson type inequalities for functions whose derivatives in absolute value are m- and (alpha,m)- logarithmically convex functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2598","kind":"arxiv","version":2},"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":"2026-05-18T03:07:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l5LVlcwDLSaUTgOLlJG9A52PKHMij0OS6egTwfinSsju4HFLl4vH9u5jW2vIgUBVfBUbQkdH8189iJP56YJyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:38:08.519498Z"},"content_sha256":"658e30358d5a904bf323455fdcbc2237d824646f8667a9b60a5b8a07b36c16f9","schema_version":"1.0","event_id":"sha256:658e30358d5a904bf323455fdcbc2237d824646f8667a9b60a5b8a07b36c16f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HCMKMZGY6ZK2556MKKZH7UZRR4/bundle.json","state_url":"https://pith.science/pith/HCMKMZGY6ZK2556MKKZH7UZRR4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HCMKMZGY6ZK2556MKKZH7UZRR4/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":"2026-06-22T16:38:08Z","links":{"resolver":"https://pith.science/pith/HCMKMZGY6ZK2556MKKZH7UZRR4","bundle":"https://pith.science/pith/HCMKMZGY6ZK2556MKKZH7UZRR4/bundle.json","state":"https://pith.science/pith/HCMKMZGY6ZK2556MKKZH7UZRR4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HCMKMZGY6ZK2556MKKZH7UZRR4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HCMKMZGY6ZK2556MKKZH7UZRR4","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":"42cbe08b456c2687094f2f2350ea9dd503134bfd6c8b646bbfd671afc3052e81","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-12-07T21:03:23Z","title_canon_sha256":"ea19704e0f92020339961b88597e021bcee8e9638ce7f502e92ee6c055f349d1"},"schema_version":"1.0","source":{"id":"1212.2598","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.2598","created_at":"2026-05-18T03:07:52Z"},{"alias_kind":"arxiv_version","alias_value":"1212.2598v2","created_at":"2026-05-18T03:07:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2598","created_at":"2026-05-18T03:07:52Z"},{"alias_kind":"pith_short_12","alias_value":"HCMKMZGY6ZK2","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HCMKMZGY6ZK2556M","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HCMKMZGY","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:658e30358d5a904bf323455fdcbc2237d824646f8667a9b60a5b8a07b36c16f9","target":"graph","created_at":"2026-05-18T03:07:52Z","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 this paper, we obtain some Simpson type inequalities for functions whose derivatives in absolute value are m- and (alpha,m)- logarithmically convex functions.","authors_text":"Ahmet Ocak Akdemir","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-12-07T21:03:23Z","title":"Simpson Type Inequalities Via m- and (alpha,m)- logarithmically Convex functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2598","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":"sha256:82a68aa21384758740a1937b6edc014716f61e36bca361bfc23de216724b6e5d","target":"record","created_at":"2026-05-18T03:07:52Z","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":"42cbe08b456c2687094f2f2350ea9dd503134bfd6c8b646bbfd671afc3052e81","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-12-07T21:03:23Z","title_canon_sha256":"ea19704e0f92020339961b88597e021bcee8e9638ce7f502e92ee6c055f349d1"},"schema_version":"1.0","source":{"id":"1212.2598","kind":"arxiv","version":2}},"canonical_sha256":"3898a664d8f655aef7cc52b27fd3318f328f546654d8f11558bde4ec739f3eaa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3898a664d8f655aef7cc52b27fd3318f328f546654d8f11558bde4ec739f3eaa","first_computed_at":"2026-05-18T03:07:52.699980Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:52.699980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZzdiyFyx7bA5YBj7smkxIPWO3SyfN+zqh8Vzc+mY3SLR1cGuY8BNi8EH6KunZWNig2m0kT7fR6gOfEyv+wDJDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:52.700720Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.2598","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82a68aa21384758740a1937b6edc014716f61e36bca361bfc23de216724b6e5d","sha256:658e30358d5a904bf323455fdcbc2237d824646f8667a9b60a5b8a07b36c16f9"],"state_sha256":"f1242029a4582d254dd2fbc7fbf43355f2e91b8a0f2a573cf76f82e21f98b04c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JeiL8NsVMCbUFY4GTthcPeivFi9WefzP0w5lMrdF3Rdbj97OCmXLG/f0eOpvKu+WzrLZS5gDelEJdIvW9qE0CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T16:38:08.521533Z","bundle_sha256":"7a4415d20da623835fde85cf89d7d4bf4e2201d483c7b05283aff83fabc16a57"}}