{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:YFIQI5EUVDDCQR2FMWRETTGW5G","short_pith_number":"pith:YFIQI5EU","canonical_record":{"source":{"id":"1207.5650","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-07-24T10:36:11Z","cross_cats_sorted":[],"title_canon_sha256":"ba364d353b46f3bc015dd12943c92057df9b6a0f5e031587d3468959d56f69a1","abstract_canon_sha256":"6bbb9d2b729c8759f30492068e3ca723445e1d18ddacda582194273b72a230e0"},"schema_version":"1.0"},"canonical_sha256":"c151047494a8c628474565a249ccd6e9babd41dbc738d76ca52d925cbf615c53","source":{"kind":"arxiv","id":"1207.5650","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5650","created_at":"2026-05-18T03:50:11Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5650v1","created_at":"2026-05-18T03:50:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5650","created_at":"2026-05-18T03:50:11Z"},{"alias_kind":"pith_short_12","alias_value":"YFIQI5EUVDDC","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YFIQI5EUVDDCQR2F","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YFIQI5EU","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:YFIQI5EUVDDCQR2FMWRETTGW5G","target":"record","payload":{"canonical_record":{"source":{"id":"1207.5650","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-07-24T10:36:11Z","cross_cats_sorted":[],"title_canon_sha256":"ba364d353b46f3bc015dd12943c92057df9b6a0f5e031587d3468959d56f69a1","abstract_canon_sha256":"6bbb9d2b729c8759f30492068e3ca723445e1d18ddacda582194273b72a230e0"},"schema_version":"1.0"},"canonical_sha256":"c151047494a8c628474565a249ccd6e9babd41dbc738d76ca52d925cbf615c53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:11.769973Z","signature_b64":"38jEL+f/q2s/+AzIFkQZuwrCFlnphax4Nb6MS3ZtcJhMMddfNBNCdEjAEoodH4QLeOBoUFCEwGcWmGzAizSrDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c151047494a8c628474565a249ccd6e9babd41dbc738d76ca52d925cbf615c53","last_reissued_at":"2026-05-18T03:50:11.769111Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:11.769111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.5650","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":"2026-05-18T03:50:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7wjg0LhIvhEzzlXywSWcjPjOh4Q8azLp/xELv8K3r6QDAkPU+N1wx89CA9jRzY+gx9RNiyWcQdjbK8O6KmPlAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:59:44.954053Z"},"content_sha256":"1abd696c52441d13aed2fa0d79d9f1b1772bdf7ef4af1d40385ef212c719f0a5","schema_version":"1.0","event_id":"sha256:1abd696c52441d13aed2fa0d79d9f1b1772bdf7ef4af1d40385ef212c719f0a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:YFIQI5EUVDDCQR2FMWRETTGW5G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New estimates on generalization of some integral inequalities for quasi-convex functions and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Imdat Iscan","submitted_at":"2012-07-24T10:36:11Z","abstract_excerpt":"In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are quasi-convex. Some applications to special means of real numbers are also given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5650","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":"2026-05-18T03:50:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QohLAvZZoGYZjvDw7/9Nztpc6KfoflmBN0ZO+5Uvyv4jqTX5vpvJLuvMm22Lb0FKrNL4SNWHku73GBUDDZyDAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:59:44.954404Z"},"content_sha256":"c0f542782ec83439f6aeacc2c5065d83d42865063cfdb109eec9d4abd1b00d00","schema_version":"1.0","event_id":"sha256:c0f542782ec83439f6aeacc2c5065d83d42865063cfdb109eec9d4abd1b00d00"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YFIQI5EUVDDCQR2FMWRETTGW5G/bundle.json","state_url":"https://pith.science/pith/YFIQI5EUVDDCQR2FMWRETTGW5G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YFIQI5EUVDDCQR2FMWRETTGW5G/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":"2026-06-22T14:59:44Z","links":{"resolver":"https://pith.science/pith/YFIQI5EUVDDCQR2FMWRETTGW5G","bundle":"https://pith.science/pith/YFIQI5EUVDDCQR2FMWRETTGW5G/bundle.json","state":"https://pith.science/pith/YFIQI5EUVDDCQR2FMWRETTGW5G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YFIQI5EUVDDCQR2FMWRETTGW5G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YFIQI5EUVDDCQR2FMWRETTGW5G","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":"6bbb9d2b729c8759f30492068e3ca723445e1d18ddacda582194273b72a230e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-07-24T10:36:11Z","title_canon_sha256":"ba364d353b46f3bc015dd12943c92057df9b6a0f5e031587d3468959d56f69a1"},"schema_version":"1.0","source":{"id":"1207.5650","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5650","created_at":"2026-05-18T03:50:11Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5650v1","created_at":"2026-05-18T03:50:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5650","created_at":"2026-05-18T03:50:11Z"},{"alias_kind":"pith_short_12","alias_value":"YFIQI5EUVDDC","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YFIQI5EUVDDCQR2F","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YFIQI5EU","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:c0f542782ec83439f6aeacc2c5065d83d42865063cfdb109eec9d4abd1b00d00","target":"graph","created_at":"2026-05-18T03:50:11Z","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 derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are quasi-convex. Some applications to special means of real numbers are also given.","authors_text":"Imdat Iscan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-07-24T10:36:11Z","title":"New estimates on generalization of some integral inequalities for quasi-convex functions and their applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5650","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":"sha256:1abd696c52441d13aed2fa0d79d9f1b1772bdf7ef4af1d40385ef212c719f0a5","target":"record","created_at":"2026-05-18T03:50:11Z","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":"6bbb9d2b729c8759f30492068e3ca723445e1d18ddacda582194273b72a230e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-07-24T10:36:11Z","title_canon_sha256":"ba364d353b46f3bc015dd12943c92057df9b6a0f5e031587d3468959d56f69a1"},"schema_version":"1.0","source":{"id":"1207.5650","kind":"arxiv","version":1}},"canonical_sha256":"c151047494a8c628474565a249ccd6e9babd41dbc738d76ca52d925cbf615c53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c151047494a8c628474565a249ccd6e9babd41dbc738d76ca52d925cbf615c53","first_computed_at":"2026-05-18T03:50:11.769111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:11.769111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"38jEL+f/q2s/+AzIFkQZuwrCFlnphax4Nb6MS3ZtcJhMMddfNBNCdEjAEoodH4QLeOBoUFCEwGcWmGzAizSrDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:11.769973Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5650","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1abd696c52441d13aed2fa0d79d9f1b1772bdf7ef4af1d40385ef212c719f0a5","sha256:c0f542782ec83439f6aeacc2c5065d83d42865063cfdb109eec9d4abd1b00d00"],"state_sha256":"d6a65bd6400101f9014929a2ac3793ee6bb515c63f5a3da4e8f3fb43e53d7eb4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PzGOKvq2n4qyhbbEe/sTIPQBFEcm2BgHrz/y+p5uK3DabS5RERcXBng58BCzHHI2ZJOWQJNGmZ53mH23Y/RpBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T14:59:44.956380Z","bundle_sha256":"eb0e7e5010ad7ee3b0490d63aaf0f72c70b039c108d5d823f872689f2ebf1d4a"}}