{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:YI7L4HUPUJNBYP7JEX3E2YFW55","short_pith_number":"pith:YI7L4HUP","canonical_record":{"source":{"id":"0801.1962","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"2008-01-13T15:44:12Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"7ddf316e18507d4de6b14b6351fdec5083cb6933879fa98099e3ce728e3a3f40","abstract_canon_sha256":"aad8a9dd98af0ef549673c3e28b2d8f5642388a6a9a73d9dd9089d6db6b708fd"},"schema_version":"1.0"},"canonical_sha256":"c23ebe1e8fa25a1c3fe925f64d60b6ef4cb04ca3b3afbd99c701b48debbb91ee","source":{"kind":"arxiv","id":"0801.1962","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.1962","created_at":"2026-05-18T00:08:31Z"},{"alias_kind":"arxiv_version","alias_value":"0801.1962v1","created_at":"2026-05-18T00:08:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.1962","created_at":"2026-05-18T00:08:31Z"},{"alias_kind":"pith_short_12","alias_value":"YI7L4HUPUJNB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"YI7L4HUPUJNBYP7J","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"YI7L4HUP","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:YI7L4HUPUJNBYP7JEX3E2YFW55","target":"record","payload":{"canonical_record":{"source":{"id":"0801.1962","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"2008-01-13T15:44:12Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"7ddf316e18507d4de6b14b6351fdec5083cb6933879fa98099e3ce728e3a3f40","abstract_canon_sha256":"aad8a9dd98af0ef549673c3e28b2d8f5642388a6a9a73d9dd9089d6db6b708fd"},"schema_version":"1.0"},"canonical_sha256":"c23ebe1e8fa25a1c3fe925f64d60b6ef4cb04ca3b3afbd99c701b48debbb91ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:31.878765Z","signature_b64":"1g31izPo6ce0M4+KBzzyDfLoKVn0XVkOZXvUYUS0T5HQTca8FQPRKgeKjq/oLD4oDJ+P2N8xdIL7GSTHujkRDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c23ebe1e8fa25a1c3fe925f64d60b6ef4cb04ca3b3afbd99c701b48debbb91ee","last_reissued_at":"2026-05-18T00:08:31.878211Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:31.878211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0801.1962","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":"2026-05-18T00:08:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rLYJcD021DZHMCMdpdbqPFBvGtDDkwN7uEmRXMRgFXyVeou8mZy+41f3pROUQEdL0ijaCAj6D9Vod+Zee3FUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:53:08.692069Z"},"content_sha256":"c0b0735b0d564a9ada97d02ca58b358b7db291fbd504c4f8f8182d69ba3b9a23","schema_version":"1.0","event_id":"sha256:c0b0735b0d564a9ada97d02ca58b358b7db291fbd504c4f8f8182d69ba3b9a23"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:YI7L4HUPUJNBYP7JEX3E2YFW55","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"n-Monotone exact functionals","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Enrique Miranda, Gert de Cooman, Matthias C. M. Troffaes","submitted_at":"2008-01-13T15:44:12Z","abstract_excerpt":"We study n-monotone functionals, which constitute a generalisation of n-monotone set functions. We investigate their relation to the concepts of exactness and natural extension, which generalise the notions of coherence and natural extension in the behavioural theory of imprecise probabilities. We improve upon a number of results in the literature, and prove among other things a representation result for exact n-monotone functionals in terms of Choquet integrals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.1962","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":"2026-05-18T00:08:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H1KsR3wL0Xo3ZEfni1h3vL0HQ4ncUF4VZdBrBBecWGQwojaV5r1fxv4NU97BaEagHp1H7pqtn/lltw1l/Fg/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:53:08.692659Z"},"content_sha256":"17084a1eeeb494350a87023db8fb3787eedc42f54a0b05ed4b98bc33c7e1833d","schema_version":"1.0","event_id":"sha256:17084a1eeeb494350a87023db8fb3787eedc42f54a0b05ed4b98bc33c7e1833d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YI7L4HUPUJNBYP7JEX3E2YFW55/bundle.json","state_url":"https://pith.science/pith/YI7L4HUPUJNBYP7JEX3E2YFW55/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YI7L4HUPUJNBYP7JEX3E2YFW55/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":"2026-06-05T04:53:08Z","links":{"resolver":"https://pith.science/pith/YI7L4HUPUJNBYP7JEX3E2YFW55","bundle":"https://pith.science/pith/YI7L4HUPUJNBYP7JEX3E2YFW55/bundle.json","state":"https://pith.science/pith/YI7L4HUPUJNBYP7JEX3E2YFW55/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YI7L4HUPUJNBYP7JEX3E2YFW55/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:YI7L4HUPUJNBYP7JEX3E2YFW55","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":"aad8a9dd98af0ef549673c3e28b2d8f5642388a6a9a73d9dd9089d6db6b708fd","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"math.FA","submitted_at":"2008-01-13T15:44:12Z","title_canon_sha256":"7ddf316e18507d4de6b14b6351fdec5083cb6933879fa98099e3ce728e3a3f40"},"schema_version":"1.0","source":{"id":"0801.1962","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.1962","created_at":"2026-05-18T00:08:31Z"},{"alias_kind":"arxiv_version","alias_value":"0801.1962v1","created_at":"2026-05-18T00:08:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.1962","created_at":"2026-05-18T00:08:31Z"},{"alias_kind":"pith_short_12","alias_value":"YI7L4HUPUJNB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"YI7L4HUPUJNBYP7J","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"YI7L4HUP","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:17084a1eeeb494350a87023db8fb3787eedc42f54a0b05ed4b98bc33c7e1833d","target":"graph","created_at":"2026-05-18T00:08:31Z","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":"We study n-monotone functionals, which constitute a generalisation of n-monotone set functions. We investigate their relation to the concepts of exactness and natural extension, which generalise the notions of coherence and natural extension in the behavioural theory of imprecise probabilities. We improve upon a number of results in the literature, and prove among other things a representation result for exact n-monotone functionals in terms of Choquet integrals.","authors_text":"Enrique Miranda, Gert de Cooman, Matthias C. M. Troffaes","cross_cats":["math.PR"],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"2008-01-13T15:44:12Z","title":"n-Monotone exact functionals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.1962","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:c0b0735b0d564a9ada97d02ca58b358b7db291fbd504c4f8f8182d69ba3b9a23","target":"record","created_at":"2026-05-18T00:08:31Z","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":"aad8a9dd98af0ef549673c3e28b2d8f5642388a6a9a73d9dd9089d6db6b708fd","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"math.FA","submitted_at":"2008-01-13T15:44:12Z","title_canon_sha256":"7ddf316e18507d4de6b14b6351fdec5083cb6933879fa98099e3ce728e3a3f40"},"schema_version":"1.0","source":{"id":"0801.1962","kind":"arxiv","version":1}},"canonical_sha256":"c23ebe1e8fa25a1c3fe925f64d60b6ef4cb04ca3b3afbd99c701b48debbb91ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c23ebe1e8fa25a1c3fe925f64d60b6ef4cb04ca3b3afbd99c701b48debbb91ee","first_computed_at":"2026-05-18T00:08:31.878211Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:31.878211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1g31izPo6ce0M4+KBzzyDfLoKVn0XVkOZXvUYUS0T5HQTca8FQPRKgeKjq/oLD4oDJ+P2N8xdIL7GSTHujkRDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:31.878765Z","signed_message":"canonical_sha256_bytes"},"source_id":"0801.1962","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0b0735b0d564a9ada97d02ca58b358b7db291fbd504c4f8f8182d69ba3b9a23","sha256:17084a1eeeb494350a87023db8fb3787eedc42f54a0b05ed4b98bc33c7e1833d"],"state_sha256":"ecca09b7ca94ded7f24eacf3affb43e5cb864674023b28acf0436b8f2115bb67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jOv8iDscw6mdIZmn5l+MRRPKXCrktulZahM3d+BvWOg2JDybPEENPb60L1vIyF1ye2xUDSY2k47+JALvK7nHDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T04:53:08.695856Z","bundle_sha256":"0b1e89b26c34fc78db084572a7ef5a7b2e4c23cbcab72dd8b5d289c2fd31110e"}}