{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NES5ISJHP3GLZ6OQL25TCYAREQ","short_pith_number":"pith:NES5ISJH","canonical_record":{"source":{"id":"1207.2435","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-07-07T17:57:04Z","cross_cats_sorted":[],"title_canon_sha256":"d87ca9715568b555691da1acd965a8b896bd64e10d0006963981f92ba5b61670","abstract_canon_sha256":"047719fb9d9dbd619d5f4fbc9ac797b6aefd221b37bad01238c4ece43c930409"},"schema_version":"1.0"},"canonical_sha256":"6925d449277eccbcf9d05ebb31601124282409b184422568d5cdcf44d74fca8e","source":{"kind":"arxiv","id":"1207.2435","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2435","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2435v1","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2435","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"pith_short_12","alias_value":"NES5ISJHP3GL","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NES5ISJHP3GLZ6OQ","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NES5ISJH","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NES5ISJHP3GLZ6OQL25TCYAREQ","target":"record","payload":{"canonical_record":{"source":{"id":"1207.2435","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-07-07T17:57:04Z","cross_cats_sorted":[],"title_canon_sha256":"d87ca9715568b555691da1acd965a8b896bd64e10d0006963981f92ba5b61670","abstract_canon_sha256":"047719fb9d9dbd619d5f4fbc9ac797b6aefd221b37bad01238c4ece43c930409"},"schema_version":"1.0"},"canonical_sha256":"6925d449277eccbcf9d05ebb31601124282409b184422568d5cdcf44d74fca8e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:24.151031Z","signature_b64":"22BsA/loLX1Aj1OPhJRHNrNZe36d01odDRIy5ZOW2dAzWF0VwhrpQ9XFdz4k9anyk4b+OK/loQzPAlp5ZTdIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6925d449277eccbcf9d05ebb31601124282409b184422568d5cdcf44d74fca8e","last_reissued_at":"2026-05-18T03:51:24.150204Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:24.150204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.2435","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":"2026-05-18T03:51:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YTg9zxeF4j/8PSCv1wTYf/5vllEolnimxfNNWT1Y6mDCBr/BF3Pt7RgAeMpiKzkI5w816YNM+UfzcsUd60DBDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:00:11.471042Z"},"content_sha256":"c2f6ca8c5fb3184929f750c5381719f388743818995b7bbc8ee919c7a137bc9b","schema_version":"1.0","event_id":"sha256:c2f6ca8c5fb3184929f750c5381719f388743818995b7bbc8ee919c7a137bc9b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NES5ISJHP3GLZ6OQL25TCYAREQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simpson Type Inequalities for Q-Class Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ahmet Ocak Akdemir, Alper Ekinci, M. Emin Ozdemir, Mustafa Gurbuz","submitted_at":"2012-07-07T17:57:04Z","abstract_excerpt":"In this paper, we obtain some Simpson type inequalities for functions whose second derivatives absolute value or q-th power of them are Q-class functions. Also we give applications to numerical integration."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2435","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":"2026-05-18T03:51:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"azjkShVg1gp0FGieWYqgNiCO9qKjDvmUD6VZfHAtdIqmlIuckeP7DlDJ/HNs7Fx8LFpc5Hv3FgsoIJirbAuJBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:00:11.471386Z"},"content_sha256":"3e0f8f804255957e8962c7d08fbc0f95e4ff4810ff11a3daf1155a6447f90a4e","schema_version":"1.0","event_id":"sha256:3e0f8f804255957e8962c7d08fbc0f95e4ff4810ff11a3daf1155a6447f90a4e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NES5ISJHP3GLZ6OQL25TCYAREQ/bundle.json","state_url":"https://pith.science/pith/NES5ISJHP3GLZ6OQL25TCYAREQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NES5ISJHP3GLZ6OQL25TCYAREQ/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":"2026-06-22T16:00:11Z","links":{"resolver":"https://pith.science/pith/NES5ISJHP3GLZ6OQL25TCYAREQ","bundle":"https://pith.science/pith/NES5ISJHP3GLZ6OQL25TCYAREQ/bundle.json","state":"https://pith.science/pith/NES5ISJHP3GLZ6OQL25TCYAREQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NES5ISJHP3GLZ6OQL25TCYAREQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NES5ISJHP3GLZ6OQL25TCYAREQ","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":"047719fb9d9dbd619d5f4fbc9ac797b6aefd221b37bad01238c4ece43c930409","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-07-07T17:57:04Z","title_canon_sha256":"d87ca9715568b555691da1acd965a8b896bd64e10d0006963981f92ba5b61670"},"schema_version":"1.0","source":{"id":"1207.2435","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2435","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2435v1","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2435","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"pith_short_12","alias_value":"NES5ISJHP3GL","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NES5ISJHP3GLZ6OQ","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NES5ISJH","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:3e0f8f804255957e8962c7d08fbc0f95e4ff4810ff11a3daf1155a6447f90a4e","target":"graph","created_at":"2026-05-18T03:51:24Z","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 second derivatives absolute value or q-th power of them are Q-class functions. Also we give applications to numerical integration.","authors_text":"Ahmet Ocak Akdemir, Alper Ekinci, M. Emin Ozdemir, Mustafa Gurbuz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-07-07T17:57:04Z","title":"Simpson Type Inequalities for Q-Class Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2435","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:c2f6ca8c5fb3184929f750c5381719f388743818995b7bbc8ee919c7a137bc9b","target":"record","created_at":"2026-05-18T03:51:24Z","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":"047719fb9d9dbd619d5f4fbc9ac797b6aefd221b37bad01238c4ece43c930409","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-07-07T17:57:04Z","title_canon_sha256":"d87ca9715568b555691da1acd965a8b896bd64e10d0006963981f92ba5b61670"},"schema_version":"1.0","source":{"id":"1207.2435","kind":"arxiv","version":1}},"canonical_sha256":"6925d449277eccbcf9d05ebb31601124282409b184422568d5cdcf44d74fca8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6925d449277eccbcf9d05ebb31601124282409b184422568d5cdcf44d74fca8e","first_computed_at":"2026-05-18T03:51:24.150204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:24.150204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"22BsA/loLX1Aj1OPhJRHNrNZe36d01odDRIy5ZOW2dAzWF0VwhrpQ9XFdz4k9anyk4b+OK/loQzPAlp5ZTdIBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:24.151031Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.2435","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2f6ca8c5fb3184929f750c5381719f388743818995b7bbc8ee919c7a137bc9b","sha256:3e0f8f804255957e8962c7d08fbc0f95e4ff4810ff11a3daf1155a6447f90a4e"],"state_sha256":"0a071c098985b4123b2b9b431ee9fb19c8d85f79bdd3376f289332292e7b13a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YUPkWMJ4nTqUleyWhmF/2fW5B4fxEYyWDjoMGvDo6cQj6TYoXh/lwZFKX8Sbd0STIMUvU/6bijyP4dCcElBTCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T16:00:11.473302Z","bundle_sha256":"1126d3415bde2cc23d13d5a6e6d2f8c8a61f8b341bce3ddebeaa5772a0f04c7b"}}