{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:TAIOOJ3JNBB6MKH5IAJW3226TV","short_pith_number":"pith:TAIOOJ3J","canonical_record":{"source":{"id":"1011.1543","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-11-06T08:02:32Z","cross_cats_sorted":[],"title_canon_sha256":"ee5ec94fabe8d23d958578b5eebd42ba97c15203721d2980c9dad8cd83816ad2","abstract_canon_sha256":"a9d367908dc74b61061f0b2a131eb36f765868acf8b33cfa70efc1dc4bf1178e"},"schema_version":"1.0"},"canonical_sha256":"9810e727696843e628fd40136deb5e9d64f7eea9e0113adfd6f7787291d85c47","source":{"kind":"arxiv","id":"1011.1543","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1543","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1543v1","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1543","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"pith_short_12","alias_value":"TAIOOJ3JNBB6","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"TAIOOJ3JNBB6MKH5","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"TAIOOJ3J","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:TAIOOJ3JNBB6MKH5IAJW3226TV","target":"record","payload":{"canonical_record":{"source":{"id":"1011.1543","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-11-06T08:02:32Z","cross_cats_sorted":[],"title_canon_sha256":"ee5ec94fabe8d23d958578b5eebd42ba97c15203721d2980c9dad8cd83816ad2","abstract_canon_sha256":"a9d367908dc74b61061f0b2a131eb36f765868acf8b33cfa70efc1dc4bf1178e"},"schema_version":"1.0"},"canonical_sha256":"9810e727696843e628fd40136deb5e9d64f7eea9e0113adfd6f7787291d85c47","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:50.950456Z","signature_b64":"wZ3KAegauT1pewUaqNRvGf3sZR2XC1bUZWsQBsiORs0jnhfUB078+5Urv+TSCDqfrC9CKCCEJVp93OFmEcmTAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9810e727696843e628fd40136deb5e9d64f7eea9e0113adfd6f7787291d85c47","last_reissued_at":"2026-05-18T04:36:50.950031Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:50.950031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.1543","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":"2026-05-18T04:36:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2heEpNPjf61XGYB4eapnHUc5y+h3Xzs9xNXjEk2mqceVpTfkYh7nlEdXmkQ2pR6i9C6pHBFAccA9QdYizCiDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:10:01.750509Z"},"content_sha256":"0422fbdc742872bf86b9a08e1326bc1e58de8daa7dafb6f261f4d637b0eb3002","schema_version":"1.0","event_id":"sha256:0422fbdc742872bf86b9a08e1326bc1e58de8daa7dafb6f261f4d637b0eb3002"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:TAIOOJ3JNBB6MKH5IAJW3226TV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Hadamard Type Inequalities for M-Convex Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ahmet Ocak Akdemir, Cetin Yildiz, Mustafa Gurbuz","submitted_at":"2010-11-06T08:02:32Z","abstract_excerpt":"In this paper we obtained some new Hadamard-Type inequalities for functions whose derivatives absolute values m-convex. Some applications to special means of real numbers are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1543","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":"2026-05-18T04:36:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6g5kiGWb343qILYIHZym+FFEEYGDMyuhZbyXQNE/IumuEFsvxlxmzRoAhfVjpZKjSas3+lb3etkQ9z0BZ1wGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:10:01.750834Z"},"content_sha256":"01f7718237c8dc0b56b45ae70631775967684db742d8745dc5d663ec227aafe8","schema_version":"1.0","event_id":"sha256:01f7718237c8dc0b56b45ae70631775967684db742d8745dc5d663ec227aafe8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TAIOOJ3JNBB6MKH5IAJW3226TV/bundle.json","state_url":"https://pith.science/pith/TAIOOJ3JNBB6MKH5IAJW3226TV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TAIOOJ3JNBB6MKH5IAJW3226TV/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":"2026-06-22T16:10:01Z","links":{"resolver":"https://pith.science/pith/TAIOOJ3JNBB6MKH5IAJW3226TV","bundle":"https://pith.science/pith/TAIOOJ3JNBB6MKH5IAJW3226TV/bundle.json","state":"https://pith.science/pith/TAIOOJ3JNBB6MKH5IAJW3226TV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TAIOOJ3JNBB6MKH5IAJW3226TV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:TAIOOJ3JNBB6MKH5IAJW3226TV","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":"a9d367908dc74b61061f0b2a131eb36f765868acf8b33cfa70efc1dc4bf1178e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-11-06T08:02:32Z","title_canon_sha256":"ee5ec94fabe8d23d958578b5eebd42ba97c15203721d2980c9dad8cd83816ad2"},"schema_version":"1.0","source":{"id":"1011.1543","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1543","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1543v1","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1543","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"pith_short_12","alias_value":"TAIOOJ3JNBB6","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"TAIOOJ3JNBB6MKH5","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"TAIOOJ3J","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:01f7718237c8dc0b56b45ae70631775967684db742d8745dc5d663ec227aafe8","target":"graph","created_at":"2026-05-18T04:36:50Z","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 obtained some new Hadamard-Type inequalities for functions whose derivatives absolute values m-convex. Some applications to special means of real numbers are given.","authors_text":"Ahmet Ocak Akdemir, Cetin Yildiz, Mustafa Gurbuz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-11-06T08:02:32Z","title":"The Hadamard Type Inequalities for M-Convex Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1543","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":"sha256:0422fbdc742872bf86b9a08e1326bc1e58de8daa7dafb6f261f4d637b0eb3002","target":"record","created_at":"2026-05-18T04:36:50Z","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":"a9d367908dc74b61061f0b2a131eb36f765868acf8b33cfa70efc1dc4bf1178e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-11-06T08:02:32Z","title_canon_sha256":"ee5ec94fabe8d23d958578b5eebd42ba97c15203721d2980c9dad8cd83816ad2"},"schema_version":"1.0","source":{"id":"1011.1543","kind":"arxiv","version":1}},"canonical_sha256":"9810e727696843e628fd40136deb5e9d64f7eea9e0113adfd6f7787291d85c47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9810e727696843e628fd40136deb5e9d64f7eea9e0113adfd6f7787291d85c47","first_computed_at":"2026-05-18T04:36:50.950031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:50.950031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wZ3KAegauT1pewUaqNRvGf3sZR2XC1bUZWsQBsiORs0jnhfUB078+5Urv+TSCDqfrC9CKCCEJVp93OFmEcmTAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:50.950456Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.1543","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0422fbdc742872bf86b9a08e1326bc1e58de8daa7dafb6f261f4d637b0eb3002","sha256:01f7718237c8dc0b56b45ae70631775967684db742d8745dc5d663ec227aafe8"],"state_sha256":"f0f20cab277fefc7b38fd9bfb87a66bf59d91780fc6ec2fcf9e64676d9cded80"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ej5gT4fyKCr4MteZs6VjyDvnT0ohNYB5sUtea/eW4Z4k7KqaSZONjTmUsNI/I58BnC4VgtJmm1xksweAxL0RBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T16:10:01.755082Z","bundle_sha256":"b190278493291afd5354bd9c71ffc8e4a5674fafd8ae4bbdff1740980ce86e54"}}