{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:UMNL74SMA7Y66FF2JI5DZ6U567","short_pith_number":"pith:UMNL74SM","schema_version":"1.0","canonical_sha256":"a31abff24c07f1ef14ba4a3a3cfa9df7efda098446cf94eeeb036dcd83810f49","source":{"kind":"arxiv","id":"1408.0328","version":1},"attestation_state":"computed","paper":{"title":"Weakly monotone averaging functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"cs.AI","authors_text":"Gleb Beliakov, Tim Wilkin","submitted_at":"2014-08-02T03:03:33Z","abstract_excerpt":"Monotonicity with respect to all arguments is fundamental to the definition of aggregation functions. It is also a limiting property that results in many important non-monotonic averaging functions being excluded from the theoretical framework. This work proposes a definition for weakly monotonic averaging functions, studies some properties of this class of functions and proves that several families of important non-monotonic means are actually weakly monotonic averaging functions. Specifically we provide sufficient conditions for weak monotonicity of the Lehmer mean and generalised mixture op"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1408.0328","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-08-02T03:03:33Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"3d189bd0a7ee492e69997fef775b6d0ad6e075017164c7ac7dd795ef32120606","abstract_canon_sha256":"188bc96ed6eedec56449202e89b21cf35a6d1af541bdb03c88377825ed4ab5d9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:57.349767Z","signature_b64":"xSZa2QBd1lh2kG67frxvQ8NPR0JNSFU+mnw27/9nvppq/uu1kOrhdTvScXeIV+ctEU+pMhdTN+axiB7iOr3nCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a31abff24c07f1ef14ba4a3a3cfa9df7efda098446cf94eeeb036dcd83810f49","last_reissued_at":"2026-05-18T02:45:57.349133Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:57.349133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weakly monotone averaging functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"cs.AI","authors_text":"Gleb Beliakov, Tim Wilkin","submitted_at":"2014-08-02T03:03:33Z","abstract_excerpt":"Monotonicity with respect to all arguments is fundamental to the definition of aggregation functions. It is also a limiting property that results in many important non-monotonic averaging functions being excluded from the theoretical framework. This work proposes a definition for weakly monotonic averaging functions, studies some properties of this class of functions and proves that several families of important non-monotonic means are actually weakly monotonic averaging functions. Specifically we provide sufficient conditions for weak monotonicity of the Lehmer mean and generalised mixture op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0328","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1408.0328","created_at":"2026-05-18T02:45:57.349225+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.0328v1","created_at":"2026-05-18T02:45:57.349225+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.0328","created_at":"2026-05-18T02:45:57.349225+00:00"},{"alias_kind":"pith_short_12","alias_value":"UMNL74SMA7Y6","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"UMNL74SMA7Y66FF2","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"UMNL74SM","created_at":"2026-05-18T12:28:52.271510+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UMNL74SMA7Y66FF2JI5DZ6U567","json":"https://pith.science/pith/UMNL74SMA7Y66FF2JI5DZ6U567.json","graph_json":"https://pith.science/api/pith-number/UMNL74SMA7Y66FF2JI5DZ6U567/graph.json","events_json":"https://pith.science/api/pith-number/UMNL74SMA7Y66FF2JI5DZ6U567/events.json","paper":"https://pith.science/paper/UMNL74SM"},"agent_actions":{"view_html":"https://pith.science/pith/UMNL74SMA7Y66FF2JI5DZ6U567","download_json":"https://pith.science/pith/UMNL74SMA7Y66FF2JI5DZ6U567.json","view_paper":"https://pith.science/paper/UMNL74SM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.0328&json=true","fetch_graph":"https://pith.science/api/pith-number/UMNL74SMA7Y66FF2JI5DZ6U567/graph.json","fetch_events":"https://pith.science/api/pith-number/UMNL74SMA7Y66FF2JI5DZ6U567/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UMNL74SMA7Y66FF2JI5DZ6U567/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UMNL74SMA7Y66FF2JI5DZ6U567/action/storage_attestation","attest_author":"https://pith.science/pith/UMNL74SMA7Y66FF2JI5DZ6U567/action/author_attestation","sign_citation":"https://pith.science/pith/UMNL74SMA7Y66FF2JI5DZ6U567/action/citation_signature","submit_replication":"https://pith.science/pith/UMNL74SMA7Y66FF2JI5DZ6U567/action/replication_record"}},"created_at":"2026-05-18T02:45:57.349225+00:00","updated_at":"2026-05-18T02:45:57.349225+00:00"}