{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DMY3RI2FKJNPEFMBVFSC5H66AL","short_pith_number":"pith:DMY3RI2F","canonical_record":{"source":{"id":"1805.01462","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-05-03T11:33:10Z","cross_cats_sorted":[],"title_canon_sha256":"f84c741f5d010294baafb78dce6bb4c516cec6c5bec9b59809e98e62c60c9215","abstract_canon_sha256":"80de25ed1a8d489f25da8813c170dae177887ddfff22c786ec545341bcc687fc"},"schema_version":"1.0"},"canonical_sha256":"1b31b8a345525af21581a9642e9fde02c20c47adf21a7a70edb608383503d817","source":{"kind":"arxiv","id":"1805.01462","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.01462","created_at":"2026-05-18T00:00:30Z"},{"alias_kind":"arxiv_version","alias_value":"1805.01462v2","created_at":"2026-05-18T00:00:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01462","created_at":"2026-05-18T00:00:30Z"},{"alias_kind":"pith_short_12","alias_value":"DMY3RI2FKJNP","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DMY3RI2FKJNPEFMB","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DMY3RI2F","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DMY3RI2FKJNPEFMBVFSC5H66AL","target":"record","payload":{"canonical_record":{"source":{"id":"1805.01462","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-05-03T11:33:10Z","cross_cats_sorted":[],"title_canon_sha256":"f84c741f5d010294baafb78dce6bb4c516cec6c5bec9b59809e98e62c60c9215","abstract_canon_sha256":"80de25ed1a8d489f25da8813c170dae177887ddfff22c786ec545341bcc687fc"},"schema_version":"1.0"},"canonical_sha256":"1b31b8a345525af21581a9642e9fde02c20c47adf21a7a70edb608383503d817","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:30.367072Z","signature_b64":"MmmK15eZZDqLKQDjpZ8jMaKi85wDtb+sEDKymRGflxzO0EKQuTXZkfHRUl1Z55Zk9hEYu3npxFp5wZXLB7EuCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b31b8a345525af21581a9642e9fde02c20c47adf21a7a70edb608383503d817","last_reissued_at":"2026-05-18T00:00:30.366483Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:30.366483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.01462","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":"2026-05-18T00:00:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GFwzXzgQIZr90n0xmdI9nh7NIlsuf4hSOCVdB0uNUj/QHIfBbQWY18kUxViuEb18JGu7l9qI40Zlz3aFTKCoDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:46:17.325773Z"},"content_sha256":"1c6916ec14f39475226cef91158d3415e046c87b4614cda0d565dcb5a15648be","schema_version":"1.0","event_id":"sha256:1c6916ec14f39475226cef91158d3415e046c87b4614cda0d565dcb5a15648be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DMY3RI2FKJNPEFMBVFSC5H66AL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monotonicity Properties and functional inequalities for the Volterra and incomplete Volterra functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Khaled Mehrez, Sergei M. Sitnik","submitted_at":"2018-05-03T11:33:10Z","abstract_excerpt":"In this paper we prove some monotonicity, log--convexity and log--concavity properties for the Volterra and incomplete Volterra functions. Moreover, as consequences of these results, we present some functional inequalities (like Tur\\'an type inequalities) as well as we determined sharp upper and lower bounds for the normalized incomplete Volterra functions in terms of weighted power means."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01462","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":"2026-05-18T00:00:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BhnlZOqDIJuVSHq4313d7g2cJI8+pSoFCNZDWS3uMuqz2xlA2tlf7SUIi+GtvcW8oTJ87XyIFxxZS6Be+ph5Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:46:17.326371Z"},"content_sha256":"c5c73c0305268ffd7cd3821c69ebd54871155a27b7fa515c933264c6983901e4","schema_version":"1.0","event_id":"sha256:c5c73c0305268ffd7cd3821c69ebd54871155a27b7fa515c933264c6983901e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DMY3RI2FKJNPEFMBVFSC5H66AL/bundle.json","state_url":"https://pith.science/pith/DMY3RI2FKJNPEFMBVFSC5H66AL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DMY3RI2FKJNPEFMBVFSC5H66AL/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":"2026-06-23T06:46:17Z","links":{"resolver":"https://pith.science/pith/DMY3RI2FKJNPEFMBVFSC5H66AL","bundle":"https://pith.science/pith/DMY3RI2FKJNPEFMBVFSC5H66AL/bundle.json","state":"https://pith.science/pith/DMY3RI2FKJNPEFMBVFSC5H66AL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DMY3RI2FKJNPEFMBVFSC5H66AL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DMY3RI2FKJNPEFMBVFSC5H66AL","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":"80de25ed1a8d489f25da8813c170dae177887ddfff22c786ec545341bcc687fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-05-03T11:33:10Z","title_canon_sha256":"f84c741f5d010294baafb78dce6bb4c516cec6c5bec9b59809e98e62c60c9215"},"schema_version":"1.0","source":{"id":"1805.01462","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.01462","created_at":"2026-05-18T00:00:30Z"},{"alias_kind":"arxiv_version","alias_value":"1805.01462v2","created_at":"2026-05-18T00:00:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01462","created_at":"2026-05-18T00:00:30Z"},{"alias_kind":"pith_short_12","alias_value":"DMY3RI2FKJNP","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DMY3RI2FKJNPEFMB","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DMY3RI2F","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:c5c73c0305268ffd7cd3821c69ebd54871155a27b7fa515c933264c6983901e4","target":"graph","created_at":"2026-05-18T00:00:30Z","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 prove some monotonicity, log--convexity and log--concavity properties for the Volterra and incomplete Volterra functions. Moreover, as consequences of these results, we present some functional inequalities (like Tur\\'an type inequalities) as well as we determined sharp upper and lower bounds for the normalized incomplete Volterra functions in terms of weighted power means.","authors_text":"Khaled Mehrez, Sergei M. Sitnik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-05-03T11:33:10Z","title":"Monotonicity Properties and functional inequalities for the Volterra and incomplete Volterra functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01462","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":"sha256:1c6916ec14f39475226cef91158d3415e046c87b4614cda0d565dcb5a15648be","target":"record","created_at":"2026-05-18T00:00:30Z","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":"80de25ed1a8d489f25da8813c170dae177887ddfff22c786ec545341bcc687fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-05-03T11:33:10Z","title_canon_sha256":"f84c741f5d010294baafb78dce6bb4c516cec6c5bec9b59809e98e62c60c9215"},"schema_version":"1.0","source":{"id":"1805.01462","kind":"arxiv","version":2}},"canonical_sha256":"1b31b8a345525af21581a9642e9fde02c20c47adf21a7a70edb608383503d817","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b31b8a345525af21581a9642e9fde02c20c47adf21a7a70edb608383503d817","first_computed_at":"2026-05-18T00:00:30.366483Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:30.366483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MmmK15eZZDqLKQDjpZ8jMaKi85wDtb+sEDKymRGflxzO0EKQuTXZkfHRUl1Z55Zk9hEYu3npxFp5wZXLB7EuCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:30.367072Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.01462","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c6916ec14f39475226cef91158d3415e046c87b4614cda0d565dcb5a15648be","sha256:c5c73c0305268ffd7cd3821c69ebd54871155a27b7fa515c933264c6983901e4"],"state_sha256":"5338989910a784dbbf5f6a8b532ff0ecd3da452c6907bf58d4f102ada5aa60be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iDK7XssAMxoTDc1HbDm+Hjt3aFk54a6jGjHEilw/GCRfu6ezd3lokuCQTDJ6dQLJBRkHDVGuM8IUzAEfD5Z7Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T06:46:17.329057Z","bundle_sha256":"f0eccea8224d6d8b4ea6948ccc553404b1a240a98caf7226d369568e0ff9f6e2"}}