{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:PLY5OKRBLIOUPMBOG4WTA6JZQ4","short_pith_number":"pith:PLY5OKRB","canonical_record":{"source":{"id":"2605.28076","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2026-05-27T07:31:42Z","cross_cats_sorted":["cs.NA","math.NA","nlin.CD","physics.data-an"],"title_canon_sha256":"4496fffd5071217aca880c430b71533ba54340a9079f559cb8aa9dc10b369be3","abstract_canon_sha256":"a765ba1905538ad35ae60a7b5819d9b07e53835c802bc449cd02fe0bb07290fa"},"schema_version":"1.0"},"canonical_sha256":"7af1d72a215a1d47b02e372d307939873b75ad586efb23cafe57e3f451004b67","source":{"kind":"arxiv","id":"2605.28076","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.28076","created_at":"2026-05-28T01:04:57Z"},{"alias_kind":"arxiv_version","alias_value":"2605.28076v1","created_at":"2026-05-28T01:04:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.28076","created_at":"2026-05-28T01:04:57Z"},{"alias_kind":"pith_short_12","alias_value":"PLY5OKRBLIOU","created_at":"2026-05-28T01:04:57Z"},{"alias_kind":"pith_short_16","alias_value":"PLY5OKRBLIOUPMBO","created_at":"2026-05-28T01:04:57Z"},{"alias_kind":"pith_short_8","alias_value":"PLY5OKRB","created_at":"2026-05-28T01:04:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:PLY5OKRBLIOUPMBOG4WTA6JZQ4","target":"record","payload":{"canonical_record":{"source":{"id":"2605.28076","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2026-05-27T07:31:42Z","cross_cats_sorted":["cs.NA","math.NA","nlin.CD","physics.data-an"],"title_canon_sha256":"4496fffd5071217aca880c430b71533ba54340a9079f559cb8aa9dc10b369be3","abstract_canon_sha256":"a765ba1905538ad35ae60a7b5819d9b07e53835c802bc449cd02fe0bb07290fa"},"schema_version":"1.0"},"canonical_sha256":"7af1d72a215a1d47b02e372d307939873b75ad586efb23cafe57e3f451004b67","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T01:04:57.887141Z","signature_b64":"nJfJ5oQmf7OMN66ocqRj73Kxes7nlAUUhtnB/UnJYSYypGzEu989E9k6qqmNeNsG8hTEWweEVF/jJXo+OSWoCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7af1d72a215a1d47b02e372d307939873b75ad586efb23cafe57e3f451004b67","last_reissued_at":"2026-05-28T01:04:57.886754Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T01:04:57.886754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.28076","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":"2026-05-28T01:04:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RFI3c5iYivJUm+VNqgKcbr+kuIXJdHzf4kTJ5LQTKqF/zQyuwchj2to+G3CrJd50UQxi2svGbPjEKhZilCcADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:01:06.551191Z"},"content_sha256":"be3baeed1ab0ae064fe92b74dda7d2f771f8e46ce948a5236d2cb560d335369f","schema_version":"1.0","event_id":"sha256:be3baeed1ab0ae064fe92b74dda7d2f771f8e46ce948a5236d2cb560d335369f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:PLY5OKRBLIOUPMBOG4WTA6JZQ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The conditional-mean barrier: From deterministic regression to conditional distribution learning","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA","math.NA","nlin.CD","physics.data-an"],"primary_cat":"stat.ML","authors_text":"Junfeng Chen","submitted_at":"2026-05-27T07:31:42Z","abstract_excerpt":"Many problems in computational science and engineering become one-to-many after coarse graining, partial observation, or inverse reconstruction: a resolved state may not determine a unique subgrid forcing, a structural descriptor may not determine a unique effective response, and a low-resolution observation may correspond to many plausible high-resolution fields. In such settings, deterministic surrogates may learn a well-defined mathematical object while still missing application-relevant uncertainty. This tutorial develops a self-contained module centered on the conditional-mean barrier: th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28076","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/2605.28076/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":"2026-05-28T01:04:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lQf1e/nPEVadsd/GJhSCJup3yfL1y/n7eorN+Yezngz1Cgw0s3oU+WF8i+pAjFLvbL7Lr4NRua7JKAcOPA7RCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:01:06.552008Z"},"content_sha256":"3a12ead79ac179956b4c2d74acc15d7dfd58a72b1cb8fc6846b4aee76ddbe11c","schema_version":"1.0","event_id":"sha256:3a12ead79ac179956b4c2d74acc15d7dfd58a72b1cb8fc6846b4aee76ddbe11c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PLY5OKRBLIOUPMBOG4WTA6JZQ4/bundle.json","state_url":"https://pith.science/pith/PLY5OKRBLIOUPMBOG4WTA6JZQ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PLY5OKRBLIOUPMBOG4WTA6JZQ4/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":"2026-06-10T01:01:06Z","links":{"resolver":"https://pith.science/pith/PLY5OKRBLIOUPMBOG4WTA6JZQ4","bundle":"https://pith.science/pith/PLY5OKRBLIOUPMBOG4WTA6JZQ4/bundle.json","state":"https://pith.science/pith/PLY5OKRBLIOUPMBOG4WTA6JZQ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PLY5OKRBLIOUPMBOG4WTA6JZQ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PLY5OKRBLIOUPMBOG4WTA6JZQ4","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":"a765ba1905538ad35ae60a7b5819d9b07e53835c802bc449cd02fe0bb07290fa","cross_cats_sorted":["cs.NA","math.NA","nlin.CD","physics.data-an"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2026-05-27T07:31:42Z","title_canon_sha256":"4496fffd5071217aca880c430b71533ba54340a9079f559cb8aa9dc10b369be3"},"schema_version":"1.0","source":{"id":"2605.28076","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.28076","created_at":"2026-05-28T01:04:57Z"},{"alias_kind":"arxiv_version","alias_value":"2605.28076v1","created_at":"2026-05-28T01:04:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.28076","created_at":"2026-05-28T01:04:57Z"},{"alias_kind":"pith_short_12","alias_value":"PLY5OKRBLIOU","created_at":"2026-05-28T01:04:57Z"},{"alias_kind":"pith_short_16","alias_value":"PLY5OKRBLIOUPMBO","created_at":"2026-05-28T01:04:57Z"},{"alias_kind":"pith_short_8","alias_value":"PLY5OKRB","created_at":"2026-05-28T01:04:57Z"}],"graph_snapshots":[{"event_id":"sha256:3a12ead79ac179956b4c2d74acc15d7dfd58a72b1cb8fc6846b4aee76ddbe11c","target":"graph","created_at":"2026-05-28T01:04:57Z","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/2605.28076/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Many problems in computational science and engineering become one-to-many after coarse graining, partial observation, or inverse reconstruction: a resolved state may not determine a unique subgrid forcing, a structural descriptor may not determine a unique effective response, and a low-resolution observation may correspond to many plausible high-resolution fields. In such settings, deterministic surrogates may learn a well-defined mathematical object while still missing application-relevant uncertainty. This tutorial develops a self-contained module centered on the conditional-mean barrier: th","authors_text":"Junfeng Chen","cross_cats":["cs.NA","math.NA","nlin.CD","physics.data-an"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2026-05-27T07:31:42Z","title":"The conditional-mean barrier: From deterministic regression to conditional distribution learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28076","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:be3baeed1ab0ae064fe92b74dda7d2f771f8e46ce948a5236d2cb560d335369f","target":"record","created_at":"2026-05-28T01:04:57Z","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":"a765ba1905538ad35ae60a7b5819d9b07e53835c802bc449cd02fe0bb07290fa","cross_cats_sorted":["cs.NA","math.NA","nlin.CD","physics.data-an"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2026-05-27T07:31:42Z","title_canon_sha256":"4496fffd5071217aca880c430b71533ba54340a9079f559cb8aa9dc10b369be3"},"schema_version":"1.0","source":{"id":"2605.28076","kind":"arxiv","version":1}},"canonical_sha256":"7af1d72a215a1d47b02e372d307939873b75ad586efb23cafe57e3f451004b67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7af1d72a215a1d47b02e372d307939873b75ad586efb23cafe57e3f451004b67","first_computed_at":"2026-05-28T01:04:57.886754Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T01:04:57.886754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nJfJ5oQmf7OMN66ocqRj73Kxes7nlAUUhtnB/UnJYSYypGzEu989E9k6qqmNeNsG8hTEWweEVF/jJXo+OSWoCA==","signature_status":"signed_v1","signed_at":"2026-05-28T01:04:57.887141Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.28076","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be3baeed1ab0ae064fe92b74dda7d2f771f8e46ce948a5236d2cb560d335369f","sha256:3a12ead79ac179956b4c2d74acc15d7dfd58a72b1cb8fc6846b4aee76ddbe11c"],"state_sha256":"7fc122cbae9d45a3102aa265c3e6549d462f3cbde1afed6e8b31e301f22f5972"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/ehvsUrnFzTEUH4/z8NYL6+Pi6hRAIk6KFF/IvjXjwlNdM04tyGmjK+yRlhqDX0/2kn8IbSQRh2UPvGzOQuLBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T01:01:06.556170Z","bundle_sha256":"3cc038a47f3cc6b0b1589e8e010fbef459dd631a409c5e1fec73b35d8e777e22"}}