{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:BXQCEEWH4GYSPD6M7FBRDW6JEG","short_pith_number":"pith:BXQCEEWH","canonical_record":{"source":{"id":"1411.0773","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-04T03:27:38Z","cross_cats_sorted":[],"title_canon_sha256":"af0c6e5fb8441a0cb96b74bbb02e9c6f1d2e1b52652d3fa49619947e247d4e02","abstract_canon_sha256":"ed9092e0d74ae5c9392501f11f0fb3451b869defb36ed795c11819cdcaa79977"},"schema_version":"1.0"},"canonical_sha256":"0de02212c7e1b1278fccf94311dbc92198bbd00bcdd7010967ec677651085ce6","source":{"kind":"arxiv","id":"1411.0773","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0773","created_at":"2026-05-18T02:27:05Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0773v3","created_at":"2026-05-18T02:27:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0773","created_at":"2026-05-18T02:27:05Z"},{"alias_kind":"pith_short_12","alias_value":"BXQCEEWH4GYS","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BXQCEEWH4GYSPD6M","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BXQCEEWH","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:BXQCEEWH4GYSPD6M7FBRDW6JEG","target":"record","payload":{"canonical_record":{"source":{"id":"1411.0773","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-04T03:27:38Z","cross_cats_sorted":[],"title_canon_sha256":"af0c6e5fb8441a0cb96b74bbb02e9c6f1d2e1b52652d3fa49619947e247d4e02","abstract_canon_sha256":"ed9092e0d74ae5c9392501f11f0fb3451b869defb36ed795c11819cdcaa79977"},"schema_version":"1.0"},"canonical_sha256":"0de02212c7e1b1278fccf94311dbc92198bbd00bcdd7010967ec677651085ce6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:05.136698Z","signature_b64":"6s7On1q5c1ctXPu2W+vprMB3oL5Y21MhZFBDct/Kbh2Tv7ZFkK9poAZOkT3fnIWtcFDNx2b01AZABEFUSHA6Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0de02212c7e1b1278fccf94311dbc92198bbd00bcdd7010967ec677651085ce6","last_reissued_at":"2026-05-18T02:27:05.136281Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:05.136281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.0773","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":"2026-05-18T02:27:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xNLWvHznaA8bzogr9UE80h2NrCwTQLG43ZjUK2CsLlR5aER2KYghHVdzcEIoYjkNmAauk/iENocExwnhmHmRBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:22:26.136504Z"},"content_sha256":"601c1cd435cb07cea8042cd08ce570ae4641d98990528539c21b6b2fa093cf52","schema_version":"1.0","event_id":"sha256:601c1cd435cb07cea8042cd08ce570ae4641d98990528539c21b6b2fa093cf52"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:BXQCEEWH4GYSPD6M7FBRDW6JEG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasi-Monte Carlo methods for Choquet integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Yumiharu Nakano","submitted_at":"2014-11-04T03:27:38Z","abstract_excerpt":"We propose numerical integration methods for Choquet integrals where the capacities are given by distortion functions of an underlying probability measure. It relies on the explicit representation of the integrals for step functions and can be seen as quasi-Monte Carlo methods in this framework. We give bounds on the approximation errors in terms of the modulus of continuity of the integrand and the star discrepancy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0773","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":"2026-05-18T02:27:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"69Ekmjpqsty1Sn6NFSeLHeW8dS9KPM2QyYQezR3f4Gf+C8A0NSsO49Ch3WIJQYJYkriJskbLWd+fgiZ76dYADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:22:26.136847Z"},"content_sha256":"29f95f258aca72ba375ada2ca3ac9d7571f3837678b095b8698f13f5f05b2cdd","schema_version":"1.0","event_id":"sha256:29f95f258aca72ba375ada2ca3ac9d7571f3837678b095b8698f13f5f05b2cdd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BXQCEEWH4GYSPD6M7FBRDW6JEG/bundle.json","state_url":"https://pith.science/pith/BXQCEEWH4GYSPD6M7FBRDW6JEG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BXQCEEWH4GYSPD6M7FBRDW6JEG/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":"2026-06-23T16:22:26Z","links":{"resolver":"https://pith.science/pith/BXQCEEWH4GYSPD6M7FBRDW6JEG","bundle":"https://pith.science/pith/BXQCEEWH4GYSPD6M7FBRDW6JEG/bundle.json","state":"https://pith.science/pith/BXQCEEWH4GYSPD6M7FBRDW6JEG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BXQCEEWH4GYSPD6M7FBRDW6JEG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BXQCEEWH4GYSPD6M7FBRDW6JEG","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":"ed9092e0d74ae5c9392501f11f0fb3451b869defb36ed795c11819cdcaa79977","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-04T03:27:38Z","title_canon_sha256":"af0c6e5fb8441a0cb96b74bbb02e9c6f1d2e1b52652d3fa49619947e247d4e02"},"schema_version":"1.0","source":{"id":"1411.0773","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0773","created_at":"2026-05-18T02:27:05Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0773v3","created_at":"2026-05-18T02:27:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0773","created_at":"2026-05-18T02:27:05Z"},{"alias_kind":"pith_short_12","alias_value":"BXQCEEWH4GYS","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BXQCEEWH4GYSPD6M","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BXQCEEWH","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:29f95f258aca72ba375ada2ca3ac9d7571f3837678b095b8698f13f5f05b2cdd","target":"graph","created_at":"2026-05-18T02:27:05Z","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 propose numerical integration methods for Choquet integrals where the capacities are given by distortion functions of an underlying probability measure. It relies on the explicit representation of the integrals for step functions and can be seen as quasi-Monte Carlo methods in this framework. We give bounds on the approximation errors in terms of the modulus of continuity of the integrand and the star discrepancy.","authors_text":"Yumiharu Nakano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-04T03:27:38Z","title":"Quasi-Monte Carlo methods for Choquet integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0773","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":"sha256:601c1cd435cb07cea8042cd08ce570ae4641d98990528539c21b6b2fa093cf52","target":"record","created_at":"2026-05-18T02:27:05Z","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":"ed9092e0d74ae5c9392501f11f0fb3451b869defb36ed795c11819cdcaa79977","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-04T03:27:38Z","title_canon_sha256":"af0c6e5fb8441a0cb96b74bbb02e9c6f1d2e1b52652d3fa49619947e247d4e02"},"schema_version":"1.0","source":{"id":"1411.0773","kind":"arxiv","version":3}},"canonical_sha256":"0de02212c7e1b1278fccf94311dbc92198bbd00bcdd7010967ec677651085ce6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0de02212c7e1b1278fccf94311dbc92198bbd00bcdd7010967ec677651085ce6","first_computed_at":"2026-05-18T02:27:05.136281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:05.136281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6s7On1q5c1ctXPu2W+vprMB3oL5Y21MhZFBDct/Kbh2Tv7ZFkK9poAZOkT3fnIWtcFDNx2b01AZABEFUSHA6Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:05.136698Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.0773","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:601c1cd435cb07cea8042cd08ce570ae4641d98990528539c21b6b2fa093cf52","sha256:29f95f258aca72ba375ada2ca3ac9d7571f3837678b095b8698f13f5f05b2cdd"],"state_sha256":"81fc4bb0adb11fb8bca4e6223add3a152ac3b4a6f85745102307588dd9a49b74"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7P9mwLUqlsOcOb5L125aRftbzvLBAs11E0mSBbuEpZlGNRMyZKm2soaz5Sas92LSmr3hOHgxvz/s/gZ3bd6XAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:22:26.138823Z","bundle_sha256":"04d60a471cf98bd9636624782d75279895ca14a28842e41535e2b6c2c216e328"}}