{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MJXVTJNPAOMNGITJYDPORY2SDG","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":"99d314cda3294428bcbb0a4a7c13937684d804ed3a8c386e23d606a2c7bb1d32","cross_cats_sorted":["math.PR","math.ST","physics.data-an","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-16T21:49:21Z","title_canon_sha256":"705efe9aefd80d0f21a7248654cab63a31c2ab39a685d8a13a3bf5f28f6001cc"},"schema_version":"1.0","source":{"id":"1611.05475","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.05475","created_at":"2026-05-18T00:41:38Z"},{"alias_kind":"arxiv_version","alias_value":"1611.05475v1","created_at":"2026-05-18T00:41:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.05475","created_at":"2026-05-18T00:41:38Z"},{"alias_kind":"pith_short_12","alias_value":"MJXVTJNPAOMN","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MJXVTJNPAOMNGITJ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MJXVTJNP","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:b515d9538d0f41f539b217a07b0346090b596a80aedb6a54be2134b90ccc16bc","target":"graph","created_at":"2026-05-18T00:41:38Z","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 the inverse problem of recovering the order and the diffusion coefficient of an elliptic fractional partial differential equation from a finite number of noisy observations of the solution. We work in a Bayesian framework and show conditions under which the posterior distribution is given by a change of measure from the prior. Moreover, we show well-posedness of the inverse problem, in the sense that small perturbations of the observed solution lead to small Hellinger perturbations of the associated posterior measures. We thus provide a mathematical foundation to the Bayesian learning","authors_text":"Daniel Sanz-Alonso, Nicolas Garcia Trillos","cross_cats":["math.PR","math.ST","physics.data-an","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-16T21:49:21Z","title":"The Bayesian Formulation and Well-Posedness of Fractional Elliptic Inverse Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05475","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":"sha256:4370d7372a57a0d8dd056d081204e73fcfc1293e571b254406c079be4286f5e3","target":"record","created_at":"2026-05-18T00:41:38Z","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":"99d314cda3294428bcbb0a4a7c13937684d804ed3a8c386e23d606a2c7bb1d32","cross_cats_sorted":["math.PR","math.ST","physics.data-an","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-16T21:49:21Z","title_canon_sha256":"705efe9aefd80d0f21a7248654cab63a31c2ab39a685d8a13a3bf5f28f6001cc"},"schema_version":"1.0","source":{"id":"1611.05475","kind":"arxiv","version":1}},"canonical_sha256":"626f59a5af0398d32269c0dee8e3521997c337ce8d289941df2bda343cc1346c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"626f59a5af0398d32269c0dee8e3521997c337ce8d289941df2bda343cc1346c","first_computed_at":"2026-05-18T00:41:38.456653Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:38.456653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9EaxCprIXkvQWX2xr9b0r1jSCyDqBJYdfsK0+FohvFnY5T7Rwkzl6fi6A2XTE3FRLlgA2Dd7ggGdNhZFDbb6Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:38.457276Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.05475","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4370d7372a57a0d8dd056d081204e73fcfc1293e571b254406c079be4286f5e3","sha256:b515d9538d0f41f539b217a07b0346090b596a80aedb6a54be2134b90ccc16bc"],"state_sha256":"3190f2b46e7c4b535cdaa14667104b02d45a98c9d455058c54b4009079869cc9"}