{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ARG7JWNUIPKERSO6B3IVI22YTB","short_pith_number":"pith:ARG7JWNU","canonical_record":{"source":{"id":"2607.01229","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.TH","submitted_at":"2026-07-01T17:59:24Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"e31c4b49ea5457627264d43c612df0c0ac76b76f7ce937f734f93d0b6efebd54","abstract_canon_sha256":"e62753af9f3bd5b5aeee52f8eeca82bac2b5721a6ac927db82e276a0e550ae56"},"schema_version":"1.0"},"canonical_sha256":"044df4d9b443d448c9de0ed1546b58986b1e417a72899fa8179294070a40a5e5","source":{"kind":"arxiv","id":"2607.01229","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01229","created_at":"2026-07-02T01:18:33Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01229v1","created_at":"2026-07-02T01:18:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01229","created_at":"2026-07-02T01:18:33Z"},{"alias_kind":"pith_short_12","alias_value":"ARG7JWNUIPKE","created_at":"2026-07-02T01:18:33Z"},{"alias_kind":"pith_short_16","alias_value":"ARG7JWNUIPKERSO6","created_at":"2026-07-02T01:18:33Z"},{"alias_kind":"pith_short_8","alias_value":"ARG7JWNU","created_at":"2026-07-02T01:18:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ARG7JWNUIPKERSO6B3IVI22YTB","target":"record","payload":{"canonical_record":{"source":{"id":"2607.01229","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.TH","submitted_at":"2026-07-01T17:59:24Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"e31c4b49ea5457627264d43c612df0c0ac76b76f7ce937f734f93d0b6efebd54","abstract_canon_sha256":"e62753af9f3bd5b5aeee52f8eeca82bac2b5721a6ac927db82e276a0e550ae56"},"schema_version":"1.0"},"canonical_sha256":"044df4d9b443d448c9de0ed1546b58986b1e417a72899fa8179294070a40a5e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T01:18:33.349418Z","signature_b64":"VBtFhO+DQJwHE95xN4eUkkpFB6VLHNw7H7avolSze+95Js41bIpx2HUHydsv5+j9s198KscsNgxNAZmqCWPfDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"044df4d9b443d448c9de0ed1546b58986b1e417a72899fa8179294070a40a5e5","last_reissued_at":"2026-07-02T01:18:33.349051Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T01:18:33.349051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.01229","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":"2026-07-02T01:18:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GTqZZnvuXJZUzLGLLGktFRsL0LkXXwqWLRejrZGJAShbx0vRCN8ueoWsOSkJQbonEa+7h9ZwxmIUuSn1puqGBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T14:33:42.169677Z"},"content_sha256":"69bdc007611573c4931a9ce9810840b75460024e7a7d63cf14b646b3a1294287","schema_version":"1.0","event_id":"sha256:69bdc007611573c4931a9ce9810840b75460024e7a7d63cf14b646b3a1294287"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ARG7JWNUIPKERSO6B3IVI22YTB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multidimensional Risk Made Easy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"econ.TH","authors_text":"Mark Whitmeyer","submitted_at":"2026-07-01T17:59:24Z","abstract_excerpt":"Suppose we want to assign a certainty equivalent--one number--to a multivariate risk. Which such assignments are law-invariant, monotone with respect to vector stochastic dominance, and invariant to independent background risk? I show that every such certainty equivalent is a positive mixture of scalar entropic certainty equivalents applied to positive projections of the vector risk. The same representation yields a robust-order characterization: unanimity across such certainty equivalents is equivalent, up to closure, to dominance after adding independent multidimensional background risk. In "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01229","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.01229/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-02T01:18:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zyp4rX/svJWiJPirFSp/EdCAnTRnYmtPya5mTs/7PUCJQjHCnAFychL9dvpcznjNGwKo4a6GINfejzMiSGtoBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T14:33:42.170042Z"},"content_sha256":"1144bad830ab29ceab49657d29d7360f993577e0f8f57401ddb8081538d94336","schema_version":"1.0","event_id":"sha256:1144bad830ab29ceab49657d29d7360f993577e0f8f57401ddb8081538d94336"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ARG7JWNUIPKERSO6B3IVI22YTB/bundle.json","state_url":"https://pith.science/pith/ARG7JWNUIPKERSO6B3IVI22YTB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ARG7JWNUIPKERSO6B3IVI22YTB/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":"2026-07-03T14:33:42Z","links":{"resolver":"https://pith.science/pith/ARG7JWNUIPKERSO6B3IVI22YTB","bundle":"https://pith.science/pith/ARG7JWNUIPKERSO6B3IVI22YTB/bundle.json","state":"https://pith.science/pith/ARG7JWNUIPKERSO6B3IVI22YTB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ARG7JWNUIPKERSO6B3IVI22YTB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ARG7JWNUIPKERSO6B3IVI22YTB","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":"e62753af9f3bd5b5aeee52f8eeca82bac2b5721a6ac927db82e276a0e550ae56","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.TH","submitted_at":"2026-07-01T17:59:24Z","title_canon_sha256":"e31c4b49ea5457627264d43c612df0c0ac76b76f7ce937f734f93d0b6efebd54"},"schema_version":"1.0","source":{"id":"2607.01229","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01229","created_at":"2026-07-02T01:18:33Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01229v1","created_at":"2026-07-02T01:18:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01229","created_at":"2026-07-02T01:18:33Z"},{"alias_kind":"pith_short_12","alias_value":"ARG7JWNUIPKE","created_at":"2026-07-02T01:18:33Z"},{"alias_kind":"pith_short_16","alias_value":"ARG7JWNUIPKERSO6","created_at":"2026-07-02T01:18:33Z"},{"alias_kind":"pith_short_8","alias_value":"ARG7JWNU","created_at":"2026-07-02T01:18:33Z"}],"graph_snapshots":[{"event_id":"sha256:1144bad830ab29ceab49657d29d7360f993577e0f8f57401ddb8081538d94336","target":"graph","created_at":"2026-07-02T01:18:33Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.01229/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Suppose we want to assign a certainty equivalent--one number--to a multivariate risk. Which such assignments are law-invariant, monotone with respect to vector stochastic dominance, and invariant to independent background risk? I show that every such certainty equivalent is a positive mixture of scalar entropic certainty equivalents applied to positive projections of the vector risk. The same representation yields a robust-order characterization: unanimity across such certainty equivalents is equivalent, up to closure, to dominance after adding independent multidimensional background risk. In ","authors_text":"Mark Whitmeyer","cross_cats":["math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.TH","submitted_at":"2026-07-01T17:59:24Z","title":"Multidimensional Risk Made Easy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01229","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":"sha256:69bdc007611573c4931a9ce9810840b75460024e7a7d63cf14b646b3a1294287","target":"record","created_at":"2026-07-02T01:18:33Z","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":"e62753af9f3bd5b5aeee52f8eeca82bac2b5721a6ac927db82e276a0e550ae56","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.TH","submitted_at":"2026-07-01T17:59:24Z","title_canon_sha256":"e31c4b49ea5457627264d43c612df0c0ac76b76f7ce937f734f93d0b6efebd54"},"schema_version":"1.0","source":{"id":"2607.01229","kind":"arxiv","version":1}},"canonical_sha256":"044df4d9b443d448c9de0ed1546b58986b1e417a72899fa8179294070a40a5e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"044df4d9b443d448c9de0ed1546b58986b1e417a72899fa8179294070a40a5e5","first_computed_at":"2026-07-02T01:18:33.349051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T01:18:33.349051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VBtFhO+DQJwHE95xN4eUkkpFB6VLHNw7H7avolSze+95Js41bIpx2HUHydsv5+j9s198KscsNgxNAZmqCWPfDA==","signature_status":"signed_v1","signed_at":"2026-07-02T01:18:33.349418Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.01229","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69bdc007611573c4931a9ce9810840b75460024e7a7d63cf14b646b3a1294287","sha256:1144bad830ab29ceab49657d29d7360f993577e0f8f57401ddb8081538d94336"],"state_sha256":"a0aac035e02077a9d130638d3591704fd0e3d7ea39bc4f924821e99b6438e50b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ofgpii0ZMsmYU2pgI4nlhiJMqhLDrodDIHj48Zd3CGqsXKrKR+A78/Xe3yhPDF6cQZYFa9johuQl0Z5RQ7KAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T14:33:42.172158Z","bundle_sha256":"e71d0f7c7e60dbcfa8ff9df404ed64d9086f29144df2efcd459ff361c2e7cdff"}}