{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:AQF6AMMCKOR664KSN766TRJNOP","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":"bb727300d9d5741de59ba35c04cfe3862a14b5653e728870ccc9b7769ff8ccda","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-07-25T08:45:45Z","title_canon_sha256":"edb92831f5799e1ba892687ac17bfc868e41de6219f3e7eda76aecbe1fc409d6"},"schema_version":"1.0","source":{"id":"2607.23110","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.23110","created_at":"2026-07-28T01:22:07Z"},{"alias_kind":"arxiv_version","alias_value":"2607.23110v1","created_at":"2026-07-28T01:22:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.23110","created_at":"2026-07-28T01:22:07Z"},{"alias_kind":"pith_short_12","alias_value":"AQF6AMMCKOR6","created_at":"2026-07-28T01:22:07Z"},{"alias_kind":"pith_short_16","alias_value":"AQF6AMMCKOR664KS","created_at":"2026-07-28T01:22:07Z"},{"alias_kind":"pith_short_8","alias_value":"AQF6AMMC","created_at":"2026-07-28T01:22:07Z"}],"graph_snapshots":[{"event_id":"sha256:669610c64849cc86000b294ccad2f067864e1a1a915734fb5e30b429a78708c6","target":"graph","created_at":"2026-07-28T01:22:07Z","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/2607.23110/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the extension of Neural Jump ODEs to infinite-dimensional function spaces. In particular, the underlying process $X$ now takes values in $L^2(\\Xi, \\mathbb{R}^{d_X})$ instead of $\\mathbb{R}^{d_X}$ and the Operator NJ-ODE approximates the optimal predictor of this process by producing a representative of the conditional expectation. The NJ-ODE model is a framework for online learning the optimal prediction of continuous-time stochastic processes, given discrete, possibly irregular and incomplete past observations. In a series of works, this model has been extended to deal","authors_text":"Florian Krach, Josef Teichmann, Oliver L\\\"othgren","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-07-25T08:45:45Z","title":"Operator Neural Jump ODEs: $L^2$-optimal prediction in function spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23110","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":"sha256:52e3f6b776c63909ba46f41e0c3ac1cd1b0ff6f4034c9efa507883688c83c876","target":"record","created_at":"2026-07-28T01:22:07Z","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":"bb727300d9d5741de59ba35c04cfe3862a14b5653e728870ccc9b7769ff8ccda","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-07-25T08:45:45Z","title_canon_sha256":"edb92831f5799e1ba892687ac17bfc868e41de6219f3e7eda76aecbe1fc409d6"},"schema_version":"1.0","source":{"id":"2607.23110","kind":"arxiv","version":1}},"canonical_sha256":"040be0318253a3ef71526ffde9c52d73e7ad1831bd4b026e3a409561a918db6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"040be0318253a3ef71526ffde9c52d73e7ad1831bd4b026e3a409561a918db6a","first_computed_at":"2026-07-28T01:22:07.193016Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-28T01:22:07.193016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"asktgKyaKfwn9wrKrEEuGJIgLFdM59mN2mab5o68VE48D7RLiPr8L+Rt4rZsGaakscjg9DTIPumPRuPSj7znDA==","signature_status":"signed_v1","signed_at":"2026-07-28T01:22:07.193819Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.23110","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52e3f6b776c63909ba46f41e0c3ac1cd1b0ff6f4034c9efa507883688c83c876","sha256:669610c64849cc86000b294ccad2f067864e1a1a915734fb5e30b429a78708c6"],"state_sha256":"186461d43b8ab85cdc5f44e79f93a7d4ea6e9633653e0ecc6a8f934202df2862"}