{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:BNFM7CDIGDZFR6DDXYRNPJQBOW","short_pith_number":"pith:BNFM7CDI","canonical_record":{"source":{"id":"0807.4133","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-07-25T16:09:37Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"a90e40d2770c420195a1edfa7a18dfb312406d16b44c341cf7465b868455a219","abstract_canon_sha256":"0badeec679ca873617b0c90ee877d0a299356c3885c5620c932077e0d70e334a"},"schema_version":"1.0"},"canonical_sha256":"0b4acf886830f258f863be22d7a601758a9dadc743708f6aefa8bb50499d8de0","source":{"kind":"arxiv","id":"0807.4133","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.4133","created_at":"2026-05-18T03:51:02Z"},{"alias_kind":"arxiv_version","alias_value":"0807.4133v3","created_at":"2026-05-18T03:51:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.4133","created_at":"2026-05-18T03:51:02Z"},{"alias_kind":"pith_short_12","alias_value":"BNFM7CDIGDZF","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"BNFM7CDIGDZFR6DD","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"BNFM7CDI","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:BNFM7CDIGDZFR6DDXYRNPJQBOW","target":"record","payload":{"canonical_record":{"source":{"id":"0807.4133","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-07-25T16:09:37Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"a90e40d2770c420195a1edfa7a18dfb312406d16b44c341cf7465b868455a219","abstract_canon_sha256":"0badeec679ca873617b0c90ee877d0a299356c3885c5620c932077e0d70e334a"},"schema_version":"1.0"},"canonical_sha256":"0b4acf886830f258f863be22d7a601758a9dadc743708f6aefa8bb50499d8de0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:02.587299Z","signature_b64":"1YEnlK/OhSS+QIQNU5P/9z56TK4NDsOjvL78/fRd7PRGqZYLW2MVLgGEOhTP2ydo0+xZL/ph4RshLHTA36zFAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b4acf886830f258f863be22d7a601758a9dadc743708f6aefa8bb50499d8de0","last_reissued_at":"2026-05-18T03:51:02.586547Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:02.586547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0807.4133","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:51:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k3GfeEeUC9RYx5FNeZdnuBCHzrzMxqqHL/8JaqasgqmkmkVHZ6JMAq3GOv7NErhjEkVAQKxWO78JPqnOEEJpCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T17:00:43.332840Z"},"content_sha256":"28dac41cefe97c7cf52b036e52ea3661b8e62d4a4a021ffac774af49432bb641","schema_version":"1.0","event_id":"sha256:28dac41cefe97c7cf52b036e52ea3661b8e62d4a4a021ffac774af49432bb641"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:BNFM7CDIGDZFR6DDXYRNPJQBOW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On some extremalities in the approximate integration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Szymon Wasowicz","submitted_at":"2008-07-25T16:09:37Z","abstract_excerpt":"Some extremalities for quadrature operators are proved for convex functions of higher order. Such results are known in the numerical analysis, however they are often proved under suitable differentiability assumptions. In our considerations we do not use any other assumptions apart from higher order convexity itself. The obtained inequalities refine the inequalities of Hadamard type. They are applied to give error bounds of quadrature operators under the assumptions weaker from the commonly used."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.4133","kind":"arxiv","version":3},"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":"2026-05-18T03:51:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bcw95t9dUovBg71Nq4P1JM5as/HIKKmCZJdG7hZrIpKcO93t0BQ78MNgnhvpyDpyx+YjZidCbuKK6illLZ1FBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T17:00:43.333188Z"},"content_sha256":"63c1685a28ea965ee3aaf7bbcec72dddd684b9103d9d9924ba9f6efbd246b313","schema_version":"1.0","event_id":"sha256:63c1685a28ea965ee3aaf7bbcec72dddd684b9103d9d9924ba9f6efbd246b313"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BNFM7CDIGDZFR6DDXYRNPJQBOW/bundle.json","state_url":"https://pith.science/pith/BNFM7CDIGDZFR6DDXYRNPJQBOW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BNFM7CDIGDZFR6DDXYRNPJQBOW/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":"2026-06-21T17:00:43Z","links":{"resolver":"https://pith.science/pith/BNFM7CDIGDZFR6DDXYRNPJQBOW","bundle":"https://pith.science/pith/BNFM7CDIGDZFR6DDXYRNPJQBOW/bundle.json","state":"https://pith.science/pith/BNFM7CDIGDZFR6DDXYRNPJQBOW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BNFM7CDIGDZFR6DDXYRNPJQBOW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:BNFM7CDIGDZFR6DDXYRNPJQBOW","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":"0badeec679ca873617b0c90ee877d0a299356c3885c5620c932077e0d70e334a","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-07-25T16:09:37Z","title_canon_sha256":"a90e40d2770c420195a1edfa7a18dfb312406d16b44c341cf7465b868455a219"},"schema_version":"1.0","source":{"id":"0807.4133","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.4133","created_at":"2026-05-18T03:51:02Z"},{"alias_kind":"arxiv_version","alias_value":"0807.4133v3","created_at":"2026-05-18T03:51:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.4133","created_at":"2026-05-18T03:51:02Z"},{"alias_kind":"pith_short_12","alias_value":"BNFM7CDIGDZF","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"BNFM7CDIGDZFR6DD","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"BNFM7CDI","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:63c1685a28ea965ee3aaf7bbcec72dddd684b9103d9d9924ba9f6efbd246b313","target":"graph","created_at":"2026-05-18T03:51:02Z","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":"Some extremalities for quadrature operators are proved for convex functions of higher order. Such results are known in the numerical analysis, however they are often proved under suitable differentiability assumptions. In our considerations we do not use any other assumptions apart from higher order convexity itself. The obtained inequalities refine the inequalities of Hadamard type. They are applied to give error bounds of quadrature operators under the assumptions weaker from the commonly used.","authors_text":"Szymon Wasowicz","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-07-25T16:09:37Z","title":"On some extremalities in the approximate integration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.4133","kind":"arxiv","version":3},"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":"sha256:28dac41cefe97c7cf52b036e52ea3661b8e62d4a4a021ffac774af49432bb641","target":"record","created_at":"2026-05-18T03:51:02Z","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":"0badeec679ca873617b0c90ee877d0a299356c3885c5620c932077e0d70e334a","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-07-25T16:09:37Z","title_canon_sha256":"a90e40d2770c420195a1edfa7a18dfb312406d16b44c341cf7465b868455a219"},"schema_version":"1.0","source":{"id":"0807.4133","kind":"arxiv","version":3}},"canonical_sha256":"0b4acf886830f258f863be22d7a601758a9dadc743708f6aefa8bb50499d8de0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b4acf886830f258f863be22d7a601758a9dadc743708f6aefa8bb50499d8de0","first_computed_at":"2026-05-18T03:51:02.586547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:02.586547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1YEnlK/OhSS+QIQNU5P/9z56TK4NDsOjvL78/fRd7PRGqZYLW2MVLgGEOhTP2ydo0+xZL/ph4RshLHTA36zFAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:02.587299Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.4133","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28dac41cefe97c7cf52b036e52ea3661b8e62d4a4a021ffac774af49432bb641","sha256:63c1685a28ea965ee3aaf7bbcec72dddd684b9103d9d9924ba9f6efbd246b313"],"state_sha256":"6a6d66837377fdd80764ce4b57e873153f6c0cdf2ec4eb4f1e31a6dbd2c53855"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nthGKsNBrZfN3Stks9QPfBt4Z2GgQ8U8gajpJv0nJR4l5+X9Jv/xdBXKWJ2w5llZb9PDc7aJzfYCv2F9SRF7DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T17:00:43.335310Z","bundle_sha256":"7828eabc305d08e57a1a35284b59eb28c2f92436563d392431467da3ea47f727"}}