{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:WJZUFOXUWS24WIH37QQTR5QWCQ","short_pith_number":"pith:WJZUFOXU","canonical_record":{"source":{"id":"2501.04602","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-01-08T16:34:17Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"50798471319e79f6eba937dbbac3534f0f9c6ab969a30fe2ce31bf8abe5060a2","abstract_canon_sha256":"60fc1c55a94ec6598d3a2e7e0b5e98eb985ff6712329593e60bd382c4e5ad9f3"},"schema_version":"1.0"},"canonical_sha256":"b27342baf4b4b5cb20fbfc2138f616141f0ac50c050472ec0cf0c15e1b05ffc0","source":{"kind":"arxiv","id":"2501.04602","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.04602","created_at":"2026-07-05T10:37:42Z"},{"alias_kind":"arxiv_version","alias_value":"2501.04602v3","created_at":"2026-07-05T10:37:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.04602","created_at":"2026-07-05T10:37:42Z"},{"alias_kind":"pith_short_12","alias_value":"WJZUFOXUWS24","created_at":"2026-07-05T10:37:42Z"},{"alias_kind":"pith_short_16","alias_value":"WJZUFOXUWS24WIH3","created_at":"2026-07-05T10:37:42Z"},{"alias_kind":"pith_short_8","alias_value":"WJZUFOXU","created_at":"2026-07-05T10:37:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:WJZUFOXUWS24WIH37QQTR5QWCQ","target":"record","payload":{"canonical_record":{"source":{"id":"2501.04602","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-01-08T16:34:17Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"50798471319e79f6eba937dbbac3534f0f9c6ab969a30fe2ce31bf8abe5060a2","abstract_canon_sha256":"60fc1c55a94ec6598d3a2e7e0b5e98eb985ff6712329593e60bd382c4e5ad9f3"},"schema_version":"1.0"},"canonical_sha256":"b27342baf4b4b5cb20fbfc2138f616141f0ac50c050472ec0cf0c15e1b05ffc0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:37:42.216834Z","signature_b64":"ejL+tamGVWk1qxi5ECirEeOiI5d93q/pwrC5a7k/F30MP/0pAKOr5/8ED6YmZd/fpduDhZ9R1WfdGd+5C68WAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b27342baf4b4b5cb20fbfc2138f616141f0ac50c050472ec0cf0c15e1b05ffc0","last_reissued_at":"2026-07-05T10:37:42.216158Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:37:42.216158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.04602","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":"2026-07-05T10:37:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dXFfQFaYK7ANciDZusrG700Dp+JApMC/7jSfcwUKfQJvJ9slBE/Ck43iBKn+YXnmzdnp+QMjCWw0U6t0P60yDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T17:51:33.161935Z"},"content_sha256":"a78709953a8bba9ae140765f8ecb7385d2f0743b197c20c0f2a89af608953279","schema_version":"1.0","event_id":"sha256:a78709953a8bba9ae140765f8ecb7385d2f0743b197c20c0f2a89af608953279"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:WJZUFOXUWS24WIH37QQTR5QWCQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sobol' Matrices For Multi-Output Models With Quantified Uncertainty","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Robert A. Milton, Solomon F. Brown","submitted_at":"2025-01-08T16:34:17Z","abstract_excerpt":"Variance based global sensitivity analysis measures the relevance of inputs to a single output using Sobol' indices. This paper extends the definition in a natural way to multiple outputs, directly measuring the relevance of inputs to the linkages between outputs in a correlation-like matrix of indices. The usual Sobol' indices constitute the diagonal of this matrix. Existence, uniqueness and uncertainty quantification are established by developing the indices from a putative multi-output model with quantified uncertainty. Sobol' matrices and their standard errors are related to the moments of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.04602","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.04602/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":"2026-07-05T10:37:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z3CSGmyqiYtcB7Yn2j88af1/kRR2jsf0iBFljh4pZBFQ0UTYet/JJ6HaoWywkhh8GDD6Cu+Rl9avw2Yk6bqwAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T17:51:33.162430Z"},"content_sha256":"800cb43cc17db8e93a27e6c559a40dab3cedd3d09af6ce4ae431ce160ce7a526","schema_version":"1.0","event_id":"sha256:800cb43cc17db8e93a27e6c559a40dab3cedd3d09af6ce4ae431ce160ce7a526"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WJZUFOXUWS24WIH37QQTR5QWCQ/bundle.json","state_url":"https://pith.science/pith/WJZUFOXUWS24WIH37QQTR5QWCQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WJZUFOXUWS24WIH37QQTR5QWCQ/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":"2026-08-10T17:51:33Z","links":{"resolver":"https://pith.science/pith/WJZUFOXUWS24WIH37QQTR5QWCQ","bundle":"https://pith.science/pith/WJZUFOXUWS24WIH37QQTR5QWCQ/bundle.json","state":"https://pith.science/pith/WJZUFOXUWS24WIH37QQTR5QWCQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WJZUFOXUWS24WIH37QQTR5QWCQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WJZUFOXUWS24WIH37QQTR5QWCQ","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":"60fc1c55a94ec6598d3a2e7e0b5e98eb985ff6712329593e60bd382c4e5ad9f3","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-01-08T16:34:17Z","title_canon_sha256":"50798471319e79f6eba937dbbac3534f0f9c6ab969a30fe2ce31bf8abe5060a2"},"schema_version":"1.0","source":{"id":"2501.04602","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.04602","created_at":"2026-07-05T10:37:42Z"},{"alias_kind":"arxiv_version","alias_value":"2501.04602v3","created_at":"2026-07-05T10:37:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.04602","created_at":"2026-07-05T10:37:42Z"},{"alias_kind":"pith_short_12","alias_value":"WJZUFOXUWS24","created_at":"2026-07-05T10:37:42Z"},{"alias_kind":"pith_short_16","alias_value":"WJZUFOXUWS24WIH3","created_at":"2026-07-05T10:37:42Z"},{"alias_kind":"pith_short_8","alias_value":"WJZUFOXU","created_at":"2026-07-05T10:37:42Z"}],"graph_snapshots":[{"event_id":"sha256:800cb43cc17db8e93a27e6c559a40dab3cedd3d09af6ce4ae431ce160ce7a526","target":"graph","created_at":"2026-07-05T10:37:42Z","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/2501.04602/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Variance based global sensitivity analysis measures the relevance of inputs to a single output using Sobol' indices. This paper extends the definition in a natural way to multiple outputs, directly measuring the relevance of inputs to the linkages between outputs in a correlation-like matrix of indices. The usual Sobol' indices constitute the diagonal of this matrix. Existence, uniqueness and uncertainty quantification are established by developing the indices from a putative multi-output model with quantified uncertainty. Sobol' matrices and their standard errors are related to the moments of","authors_text":"Robert A. Milton, Solomon F. Brown","cross_cats":["stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-01-08T16:34:17Z","title":"Sobol' Matrices For Multi-Output Models With Quantified Uncertainty"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.04602","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:a78709953a8bba9ae140765f8ecb7385d2f0743b197c20c0f2a89af608953279","target":"record","created_at":"2026-07-05T10:37:42Z","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":"60fc1c55a94ec6598d3a2e7e0b5e98eb985ff6712329593e60bd382c4e5ad9f3","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-01-08T16:34:17Z","title_canon_sha256":"50798471319e79f6eba937dbbac3534f0f9c6ab969a30fe2ce31bf8abe5060a2"},"schema_version":"1.0","source":{"id":"2501.04602","kind":"arxiv","version":3}},"canonical_sha256":"b27342baf4b4b5cb20fbfc2138f616141f0ac50c050472ec0cf0c15e1b05ffc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b27342baf4b4b5cb20fbfc2138f616141f0ac50c050472ec0cf0c15e1b05ffc0","first_computed_at":"2026-07-05T10:37:42.216158Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:37:42.216158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ejL+tamGVWk1qxi5ECirEeOiI5d93q/pwrC5a7k/F30MP/0pAKOr5/8ED6YmZd/fpduDhZ9R1WfdGd+5C68WAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:37:42.216834Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.04602","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a78709953a8bba9ae140765f8ecb7385d2f0743b197c20c0f2a89af608953279","sha256:800cb43cc17db8e93a27e6c559a40dab3cedd3d09af6ce4ae431ce160ce7a526"],"state_sha256":"f41951914cb6907000b0d3fcb90cb28e3501f461d4661384f8434041e8bb09ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7sYY7Rfig/N8j4XlTyXnOdNV8H4OCPr47X4peiWJwL1xwDl7pd3YMpF222v4tqrvSCWx5DWLoD8OHfZl527eBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T17:51:33.187015Z","bundle_sha256":"e82c929570340c68dd3abd2ed02da1cb130c9d22d07ea9850e3f335ec24a649a"}}