{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CDMLRNP4W3UJDJ435B6V57FXW5","short_pith_number":"pith:CDMLRNP4","canonical_record":{"source":{"id":"1705.02742","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-08T05:16:03Z","cross_cats_sorted":[],"title_canon_sha256":"cf7dc6ed189d49b3d1256c447f17fca1789edddde28d7e9ee6ead94a682df86f","abstract_canon_sha256":"141bead6d5da719ba804ed5e7e18102f61d7ec52d5862f223705b4aa427cd0a4"},"schema_version":"1.0"},"canonical_sha256":"10d8b8b5fcb6e891a79be87d5efcb7b751c9c7f0b3bde2b2ad8630b27e7fc37b","source":{"kind":"arxiv","id":"1705.02742","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02742","created_at":"2026-05-18T00:31:45Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02742v2","created_at":"2026-05-18T00:31:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02742","created_at":"2026-05-18T00:31:45Z"},{"alias_kind":"pith_short_12","alias_value":"CDMLRNP4W3UJ","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CDMLRNP4W3UJDJ43","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CDMLRNP4","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CDMLRNP4W3UJDJ435B6V57FXW5","target":"record","payload":{"canonical_record":{"source":{"id":"1705.02742","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-08T05:16:03Z","cross_cats_sorted":[],"title_canon_sha256":"cf7dc6ed189d49b3d1256c447f17fca1789edddde28d7e9ee6ead94a682df86f","abstract_canon_sha256":"141bead6d5da719ba804ed5e7e18102f61d7ec52d5862f223705b4aa427cd0a4"},"schema_version":"1.0"},"canonical_sha256":"10d8b8b5fcb6e891a79be87d5efcb7b751c9c7f0b3bde2b2ad8630b27e7fc37b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:45.116467Z","signature_b64":"FYCIKRu7pSpXpTOLxJrPBtDx9ObtWk4l8kgKAdK0SG5LEUnqxRBy2+mRUmt/ZM8SCPVDrCKBFB5HHZI5cHCRDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10d8b8b5fcb6e891a79be87d5efcb7b751c9c7f0b3bde2b2ad8630b27e7fc37b","last_reissued_at":"2026-05-18T00:31:45.115726Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:45.115726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.02742","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":"2026-05-18T00:31:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kgxFsof+yb10DHjqfPMdT+dH1gBHBUmK2rgv/5szUz+OHnb+fcB6jJgiIpb41G8+CQbFtiFOtEwMVDgYyTWADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T13:49:10.577434Z"},"content_sha256":"85608cac79bbbda379d55654c6f01f97e3c3f995c26eb0f34e5c097a1a518046","schema_version":"1.0","event_id":"sha256:85608cac79bbbda379d55654c6f01f97e3c3f995c26eb0f34e5c097a1a518046"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CDMLRNP4W3UJDJ435B6V57FXW5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantifying non-monotonicity of functions and the lack of positivity in signed measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ri\\v{c}ardas Zitikis, Youri Davydov","submitted_at":"2017-05-08T05:16:03Z","abstract_excerpt":"In various research areas related to decision making, problems and their solutions frequently rely on certain functions being monotonic. In the case of non-monotonic functions, one would then wish to quantify their lack of monotonicity. In this paper we develop a method designed specifically for this task, including quantification of the lack of positivity, negativity, or sign-constancy in signed measures. We note relevant applications in Insurance, Finance, and Economics, and discuss some of them in detail."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02742","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":"2026-05-18T00:31:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ofgdbL6lZY+ke7crM8+RXMwp5XPx9mgCS25KBU3gptCpp6xNYYjCyEwn9UIjAgPqXsqVo4GK/H46h+BvjQllDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T13:49:10.577775Z"},"content_sha256":"0509de5ed54bb1fd58312ff1e56dd4842fbf69322c97a444fd282c9e1e2eb50a","schema_version":"1.0","event_id":"sha256:0509de5ed54bb1fd58312ff1e56dd4842fbf69322c97a444fd282c9e1e2eb50a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CDMLRNP4W3UJDJ435B6V57FXW5/bundle.json","state_url":"https://pith.science/pith/CDMLRNP4W3UJDJ435B6V57FXW5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CDMLRNP4W3UJDJ435B6V57FXW5/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":"2026-07-02T13:49:10Z","links":{"resolver":"https://pith.science/pith/CDMLRNP4W3UJDJ435B6V57FXW5","bundle":"https://pith.science/pith/CDMLRNP4W3UJDJ435B6V57FXW5/bundle.json","state":"https://pith.science/pith/CDMLRNP4W3UJDJ435B6V57FXW5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CDMLRNP4W3UJDJ435B6V57FXW5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CDMLRNP4W3UJDJ435B6V57FXW5","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":"141bead6d5da719ba804ed5e7e18102f61d7ec52d5862f223705b4aa427cd0a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-08T05:16:03Z","title_canon_sha256":"cf7dc6ed189d49b3d1256c447f17fca1789edddde28d7e9ee6ead94a682df86f"},"schema_version":"1.0","source":{"id":"1705.02742","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02742","created_at":"2026-05-18T00:31:45Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02742v2","created_at":"2026-05-18T00:31:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02742","created_at":"2026-05-18T00:31:45Z"},{"alias_kind":"pith_short_12","alias_value":"CDMLRNP4W3UJ","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CDMLRNP4W3UJDJ43","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CDMLRNP4","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:0509de5ed54bb1fd58312ff1e56dd4842fbf69322c97a444fd282c9e1e2eb50a","target":"graph","created_at":"2026-05-18T00:31:45Z","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 various research areas related to decision making, problems and their solutions frequently rely on certain functions being monotonic. In the case of non-monotonic functions, one would then wish to quantify their lack of monotonicity. In this paper we develop a method designed specifically for this task, including quantification of the lack of positivity, negativity, or sign-constancy in signed measures. We note relevant applications in Insurance, Finance, and Economics, and discuss some of them in detail.","authors_text":"Ri\\v{c}ardas Zitikis, Youri Davydov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-08T05:16:03Z","title":"Quantifying non-monotonicity of functions and the lack of positivity in signed measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02742","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":"sha256:85608cac79bbbda379d55654c6f01f97e3c3f995c26eb0f34e5c097a1a518046","target":"record","created_at":"2026-05-18T00:31:45Z","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":"141bead6d5da719ba804ed5e7e18102f61d7ec52d5862f223705b4aa427cd0a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-08T05:16:03Z","title_canon_sha256":"cf7dc6ed189d49b3d1256c447f17fca1789edddde28d7e9ee6ead94a682df86f"},"schema_version":"1.0","source":{"id":"1705.02742","kind":"arxiv","version":2}},"canonical_sha256":"10d8b8b5fcb6e891a79be87d5efcb7b751c9c7f0b3bde2b2ad8630b27e7fc37b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10d8b8b5fcb6e891a79be87d5efcb7b751c9c7f0b3bde2b2ad8630b27e7fc37b","first_computed_at":"2026-05-18T00:31:45.115726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:45.115726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FYCIKRu7pSpXpTOLxJrPBtDx9ObtWk4l8kgKAdK0SG5LEUnqxRBy2+mRUmt/ZM8SCPVDrCKBFB5HHZI5cHCRDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:45.116467Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.02742","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85608cac79bbbda379d55654c6f01f97e3c3f995c26eb0f34e5c097a1a518046","sha256:0509de5ed54bb1fd58312ff1e56dd4842fbf69322c97a444fd282c9e1e2eb50a"],"state_sha256":"2d8afb6b9b3e53187503a9099c75aba9df512048eb56d595925f43224d21b0c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cbw1kT+v/42M9f28fdnWIIdAApeSf+coxWbxgO/Lwl+yANAmJHi6przcKkWQzjpbYuqWbqJvkFb0EQqDldfNCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T13:49:10.579673Z","bundle_sha256":"946a4e0f904f950ed1e6c632e149b3b34b9b104e3ab0dee8ea8b84c3fc0794e7"}}