{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:7UPINXR5UVWZD6GLYI7CZPMLLM","short_pith_number":"pith:7UPINXR5","canonical_record":{"source":{"id":"1706.07193","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-22T07:39:51Z","cross_cats_sorted":["math.AP","math.SP","math.ST","stat.ML","stat.TH"],"title_canon_sha256":"211f7c3f7f90db94b2b44332858b7677c63520cff3c353302b05e1e37656a318","abstract_canon_sha256":"84b9bea6c78a497ff2b8c37b6203449983399c21904875b56954a73f938b7c02"},"schema_version":"1.0"},"canonical_sha256":"fd1e86de3da56d91f8cbc23e2cbd8b5b0057cfa52a017ea272bf3ab009e6e59e","source":{"kind":"arxiv","id":"1706.07193","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07193","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07193v1","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07193","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"7UPINXR5UVWZ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7UPINXR5UVWZD6GL","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7UPINXR5","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:7UPINXR5UVWZD6GLYI7CZPMLLM","target":"record","payload":{"canonical_record":{"source":{"id":"1706.07193","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-22T07:39:51Z","cross_cats_sorted":["math.AP","math.SP","math.ST","stat.ML","stat.TH"],"title_canon_sha256":"211f7c3f7f90db94b2b44332858b7677c63520cff3c353302b05e1e37656a318","abstract_canon_sha256":"84b9bea6c78a497ff2b8c37b6203449983399c21904875b56954a73f938b7c02"},"schema_version":"1.0"},"canonical_sha256":"fd1e86de3da56d91f8cbc23e2cbd8b5b0057cfa52a017ea272bf3ab009e6e59e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:52.371513Z","signature_b64":"q5o6TBWLpGN5XYp+Clziyn/iHObyJaIr8WJziu7+P8MEHz+umTUqvnhjLrIZnbKVaUuRFfBn8NeaGfrb004LCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd1e86de3da56d91f8cbc23e2cbd8b5b0057cfa52a017ea272bf3ab009e6e59e","last_reissued_at":"2026-05-18T00:41:52.370727Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:52.370727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.07193","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":"2026-05-18T00:41:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ubbgIenPMDNBUBtprLkZuwZ/RkcuDLw8VLEcZqDYguAll6ijaR2HM2Da8Qe0cWZPZIkn31dWtS4+jwlQ1dBbCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T12:14:51.602703Z"},"content_sha256":"e4285afccc2d633db9654720f4be3c9d4e9e280bb691a085e14ebce9c718f674","schema_version":"1.0","event_id":"sha256:e4285afccc2d633db9654720f4be3c9d4e9e280bb691a085e14ebce9c718f674"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:7UPINXR5UVWZD6GLYI7CZPMLLM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Continuum Limit of Posteriors in Graph Bayesian Inverse Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.SP","math.ST","stat.ML","stat.TH"],"primary_cat":"math.PR","authors_text":"Daniel Sanz-Alonso, Nicolas Garcia Trillos","submitted_at":"2017-06-22T07:39:51Z","abstract_excerpt":"We consider the problem of recovering a function input of a differential equation formulated on an unknown domain $M$. We assume to have access to a discrete domain $M_n=\\{x_1, \\dots, x_n\\} \\subset M$, and to noisy measurements of the output solution at $p\\le n$ of those points. We introduce a graph-based Bayesian inverse problem, and show that the graph-posterior measures over functions in $M_n$ converge, in the large $n$ limit, to a posterior over functions in $M$ that solves a Bayesian inverse problem with known domain.\n  The proofs rely on the variational formulation of the Bayesian update"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07193","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":""},"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":"2026-05-18T00:41:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"41hPzlt/ecWVDJR9BfEMVozbgsjJFgm9+RXiwRyRqSgRDg9CdV1qfJFc4Q8M5slCMQM/1vhNv042setMdoVMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T12:14:51.603150Z"},"content_sha256":"890096d1121806c3f9b980ce6d0fa271eeaac7f4bbddcd7c6883c2e235281aec","schema_version":"1.0","event_id":"sha256:890096d1121806c3f9b980ce6d0fa271eeaac7f4bbddcd7c6883c2e235281aec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7UPINXR5UVWZD6GLYI7CZPMLLM/bundle.json","state_url":"https://pith.science/pith/7UPINXR5UVWZD6GLYI7CZPMLLM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7UPINXR5UVWZD6GLYI7CZPMLLM/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":"2026-05-23T12:14:51Z","links":{"resolver":"https://pith.science/pith/7UPINXR5UVWZD6GLYI7CZPMLLM","bundle":"https://pith.science/pith/7UPINXR5UVWZD6GLYI7CZPMLLM/bundle.json","state":"https://pith.science/pith/7UPINXR5UVWZD6GLYI7CZPMLLM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7UPINXR5UVWZD6GLYI7CZPMLLM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7UPINXR5UVWZD6GLYI7CZPMLLM","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":"84b9bea6c78a497ff2b8c37b6203449983399c21904875b56954a73f938b7c02","cross_cats_sorted":["math.AP","math.SP","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-22T07:39:51Z","title_canon_sha256":"211f7c3f7f90db94b2b44332858b7677c63520cff3c353302b05e1e37656a318"},"schema_version":"1.0","source":{"id":"1706.07193","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07193","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07193v1","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07193","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"7UPINXR5UVWZ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7UPINXR5UVWZD6GL","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7UPINXR5","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:890096d1121806c3f9b980ce6d0fa271eeaac7f4bbddcd7c6883c2e235281aec","target":"graph","created_at":"2026-05-18T00:41:52Z","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 consider the problem of recovering a function input of a differential equation formulated on an unknown domain $M$. We assume to have access to a discrete domain $M_n=\\{x_1, \\dots, x_n\\} \\subset M$, and to noisy measurements of the output solution at $p\\le n$ of those points. We introduce a graph-based Bayesian inverse problem, and show that the graph-posterior measures over functions in $M_n$ converge, in the large $n$ limit, to a posterior over functions in $M$ that solves a Bayesian inverse problem with known domain.\n  The proofs rely on the variational formulation of the Bayesian update","authors_text":"Daniel Sanz-Alonso, Nicolas Garcia Trillos","cross_cats":["math.AP","math.SP","math.ST","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-22T07:39:51Z","title":"Continuum Limit of Posteriors in Graph Bayesian Inverse Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07193","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:e4285afccc2d633db9654720f4be3c9d4e9e280bb691a085e14ebce9c718f674","target":"record","created_at":"2026-05-18T00:41:52Z","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":"84b9bea6c78a497ff2b8c37b6203449983399c21904875b56954a73f938b7c02","cross_cats_sorted":["math.AP","math.SP","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-22T07:39:51Z","title_canon_sha256":"211f7c3f7f90db94b2b44332858b7677c63520cff3c353302b05e1e37656a318"},"schema_version":"1.0","source":{"id":"1706.07193","kind":"arxiv","version":1}},"canonical_sha256":"fd1e86de3da56d91f8cbc23e2cbd8b5b0057cfa52a017ea272bf3ab009e6e59e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd1e86de3da56d91f8cbc23e2cbd8b5b0057cfa52a017ea272bf3ab009e6e59e","first_computed_at":"2026-05-18T00:41:52.370727Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:52.370727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q5o6TBWLpGN5XYp+Clziyn/iHObyJaIr8WJziu7+P8MEHz+umTUqvnhjLrIZnbKVaUuRFfBn8NeaGfrb004LCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:52.371513Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.07193","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4285afccc2d633db9654720f4be3c9d4e9e280bb691a085e14ebce9c718f674","sha256:890096d1121806c3f9b980ce6d0fa271eeaac7f4bbddcd7c6883c2e235281aec"],"state_sha256":"0df4c2579276cea0e1e96990aa5219d41204875e64c6267c02d421471e276eab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MHXKUrTRRlNY9Mu2TBYlTndolGEhPxUMpGOnARuKvvysLbnAHazZnOBvF+I1monCnhhFxRYY3HY77oTbEPs8Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T12:14:51.605731Z","bundle_sha256":"4f77db2ba348bcb2b0042635887c99e40f258a5d2a983bd02472d3ba743cbcf1"}}