{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:KLT5LVSFKFKPZLCLUMELMTRETB","short_pith_number":"pith:KLT5LVSF","canonical_record":{"source":{"id":"2606.09594","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-06-08T15:04:31Z","cross_cats_sorted":["cond-mat.stat-mech","cs.NA","math-ph","math.MP","math.NA","stat.TH"],"title_canon_sha256":"86df2a3519911bd3cc6e75ae00f4e02f7009f568ee7e1125755379a80f54fb55","abstract_canon_sha256":"d02ebf016ce3e0f007c4b6bad9fee3b8a9db93a7f344baa19f24bf68cd3f812a"},"schema_version":"1.0"},"canonical_sha256":"52e7d5d6455154fcac4ba308b64e249852078f17208e9dd2216f8dc35cbd2dcb","source":{"kind":"arxiv","id":"2606.09594","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.09594","created_at":"2026-06-09T02:08:57Z"},{"alias_kind":"arxiv_version","alias_value":"2606.09594v1","created_at":"2026-06-09T02:08:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09594","created_at":"2026-06-09T02:08:57Z"},{"alias_kind":"pith_short_12","alias_value":"KLT5LVSFKFKP","created_at":"2026-06-09T02:08:57Z"},{"alias_kind":"pith_short_16","alias_value":"KLT5LVSFKFKPZLCL","created_at":"2026-06-09T02:08:57Z"},{"alias_kind":"pith_short_8","alias_value":"KLT5LVSF","created_at":"2026-06-09T02:08:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:KLT5LVSFKFKPZLCLUMELMTRETB","target":"record","payload":{"canonical_record":{"source":{"id":"2606.09594","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-06-08T15:04:31Z","cross_cats_sorted":["cond-mat.stat-mech","cs.NA","math-ph","math.MP","math.NA","stat.TH"],"title_canon_sha256":"86df2a3519911bd3cc6e75ae00f4e02f7009f568ee7e1125755379a80f54fb55","abstract_canon_sha256":"d02ebf016ce3e0f007c4b6bad9fee3b8a9db93a7f344baa19f24bf68cd3f812a"},"schema_version":"1.0"},"canonical_sha256":"52e7d5d6455154fcac4ba308b64e249852078f17208e9dd2216f8dc35cbd2dcb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:08:57.893352Z","signature_b64":"0jdX8x5+dvbAfACDCoIS1IgGzoFBJcSDlVt4GuOl6SO8T3wFKrvLitU0w+pJ2vgn0OW7EMxtTqwFAVdeWo55Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52e7d5d6455154fcac4ba308b64e249852078f17208e9dd2216f8dc35cbd2dcb","last_reissued_at":"2026-06-09T02:08:57.892549Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:08:57.892549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.09594","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":"2026-06-09T02:08:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dZ03f5m1q9FyclzRNipTz0o2aWqqjzmfSCDu5nG55LbER8sroSckH9PieXHa/Re9zXy22N+Cmb/YdRyrmUvNDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:53:41.785723Z"},"content_sha256":"e8c796bc87efc3f751e3d4f7bfb43461f1cb96cab82a1b7f940838ec797caaf1","schema_version":"1.0","event_id":"sha256:e8c796bc87efc3f751e3d4f7bfb43461f1cb96cab82a1b7f940838ec797caaf1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:KLT5LVSFKFKPZLCLUMELMTRETB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constraint residuals, graph posteriors, and determinant-corrected full-space targets in Bayesian inverse problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.NA","math-ph","math.MP","math.NA","stat.TH"],"primary_cat":"math.ST","authors_text":"Emilia Olsson, Jonathon Cottom","submitted_at":"2026-06-08T15:04:31Z","abstract_excerpt":"Bayesian inverse problems constrained by state equations are often sampled in a full parameter-state space by penalising the residual, rather than in a reduced space where the state is eliminated. We show that these formulations are not automatically equivalent as posterior measures. For finite-dimensional discretisations of equality-constrained inverse problems, assume the state equation \\(c(\\theta,u)=0\\) has a unique solution \\(u=G(\\theta)\\) and nonsingular state Jacobian \\(\\D_u c\\). The reduced posterior, its graph lift, and the zero-noise residual posterior are then distinct. A local chang"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09594","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/2606.09594/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":"2026-06-09T02:08:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dfBVrN5HTP7oKwshQF78eEDByamsj4Eyng/r2Vaqkw+az7Cmq2WMNKO+G/Q9+rrXtcOVdE1ESABcmhzdXeZvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:53:41.786450Z"},"content_sha256":"becdfad3c2492d728e285a6c22776f444539d6acbfd08a2d17623eedee256332","schema_version":"1.0","event_id":"sha256:becdfad3c2492d728e285a6c22776f444539d6acbfd08a2d17623eedee256332"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KLT5LVSFKFKPZLCLUMELMTRETB/bundle.json","state_url":"https://pith.science/pith/KLT5LVSFKFKPZLCLUMELMTRETB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KLT5LVSFKFKPZLCLUMELMTRETB/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":"2026-06-09T10:53:41Z","links":{"resolver":"https://pith.science/pith/KLT5LVSFKFKPZLCLUMELMTRETB","bundle":"https://pith.science/pith/KLT5LVSFKFKPZLCLUMELMTRETB/bundle.json","state":"https://pith.science/pith/KLT5LVSFKFKPZLCLUMELMTRETB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KLT5LVSFKFKPZLCLUMELMTRETB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KLT5LVSFKFKPZLCLUMELMTRETB","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":"d02ebf016ce3e0f007c4b6bad9fee3b8a9db93a7f344baa19f24bf68cd3f812a","cross_cats_sorted":["cond-mat.stat-mech","cs.NA","math-ph","math.MP","math.NA","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-06-08T15:04:31Z","title_canon_sha256":"86df2a3519911bd3cc6e75ae00f4e02f7009f568ee7e1125755379a80f54fb55"},"schema_version":"1.0","source":{"id":"2606.09594","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.09594","created_at":"2026-06-09T02:08:57Z"},{"alias_kind":"arxiv_version","alias_value":"2606.09594v1","created_at":"2026-06-09T02:08:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09594","created_at":"2026-06-09T02:08:57Z"},{"alias_kind":"pith_short_12","alias_value":"KLT5LVSFKFKP","created_at":"2026-06-09T02:08:57Z"},{"alias_kind":"pith_short_16","alias_value":"KLT5LVSFKFKPZLCL","created_at":"2026-06-09T02:08:57Z"},{"alias_kind":"pith_short_8","alias_value":"KLT5LVSF","created_at":"2026-06-09T02:08:57Z"}],"graph_snapshots":[{"event_id":"sha256:becdfad3c2492d728e285a6c22776f444539d6acbfd08a2d17623eedee256332","target":"graph","created_at":"2026-06-09T02:08:57Z","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/2606.09594/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Bayesian inverse problems constrained by state equations are often sampled in a full parameter-state space by penalising the residual, rather than in a reduced space where the state is eliminated. We show that these formulations are not automatically equivalent as posterior measures. For finite-dimensional discretisations of equality-constrained inverse problems, assume the state equation \\(c(\\theta,u)=0\\) has a unique solution \\(u=G(\\theta)\\) and nonsingular state Jacobian \\(\\D_u c\\). The reduced posterior, its graph lift, and the zero-noise residual posterior are then distinct. A local chang","authors_text":"Emilia Olsson, Jonathon Cottom","cross_cats":["cond-mat.stat-mech","cs.NA","math-ph","math.MP","math.NA","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-06-08T15:04:31Z","title":"Constraint residuals, graph posteriors, and determinant-corrected full-space targets in Bayesian inverse problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09594","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:e8c796bc87efc3f751e3d4f7bfb43461f1cb96cab82a1b7f940838ec797caaf1","target":"record","created_at":"2026-06-09T02:08:57Z","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":"d02ebf016ce3e0f007c4b6bad9fee3b8a9db93a7f344baa19f24bf68cd3f812a","cross_cats_sorted":["cond-mat.stat-mech","cs.NA","math-ph","math.MP","math.NA","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-06-08T15:04:31Z","title_canon_sha256":"86df2a3519911bd3cc6e75ae00f4e02f7009f568ee7e1125755379a80f54fb55"},"schema_version":"1.0","source":{"id":"2606.09594","kind":"arxiv","version":1}},"canonical_sha256":"52e7d5d6455154fcac4ba308b64e249852078f17208e9dd2216f8dc35cbd2dcb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52e7d5d6455154fcac4ba308b64e249852078f17208e9dd2216f8dc35cbd2dcb","first_computed_at":"2026-06-09T02:08:57.892549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:08:57.892549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0jdX8x5+dvbAfACDCoIS1IgGzoFBJcSDlVt4GuOl6SO8T3wFKrvLitU0w+pJ2vgn0OW7EMxtTqwFAVdeWo55Bw==","signature_status":"signed_v1","signed_at":"2026-06-09T02:08:57.893352Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.09594","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8c796bc87efc3f751e3d4f7bfb43461f1cb96cab82a1b7f940838ec797caaf1","sha256:becdfad3c2492d728e285a6c22776f444539d6acbfd08a2d17623eedee256332"],"state_sha256":"523482f9b9b4b3c72d261c0e77cf3baf1c157a083fc228b82caff7610ccf23f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zyihrjoku080mOhpTqxbMKUblEWhOzyGUKrS1QpRGs0L1ZIifMeXewAXKEo4Z6N0WKOqnouAX67bZ8MGXgMxAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T10:53:41.790802Z","bundle_sha256":"2dbd1338d6235ffe6559aa28260f8caa0d77cb4ceb9f1fc86cddcb119de606d4"}}