{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PXHSQZ6KHTV7FOSFR4OG5MTANT","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a79aa79c79c962f8fa9e740462f86eeabf54235346ebb76be8a3985d9cad17b0","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-07T13:56:20Z","title_canon_sha256":"c89e8f40fbd6b3a865153519041a29bc53ae3171673aea742243fb75c4632331"},"schema_version":"1.0","source":{"id":"2607.06287","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.06287","created_at":"2026-07-08T01:19:20Z"},{"alias_kind":"arxiv_version","alias_value":"2607.06287v1","created_at":"2026-07-08T01:19:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06287","created_at":"2026-07-08T01:19:20Z"},{"alias_kind":"pith_short_12","alias_value":"PXHSQZ6KHTV7","created_at":"2026-07-08T01:19:20Z"},{"alias_kind":"pith_short_16","alias_value":"PXHSQZ6KHTV7FOSF","created_at":"2026-07-08T01:19:20Z"},{"alias_kind":"pith_short_8","alias_value":"PXHSQZ6K","created_at":"2026-07-08T01:19:20Z"}],"graph_snapshots":[{"event_id":"sha256:d97a23e365f94fa61279f9a98709fc0435cd935092bc1e1b4a8abdcc98edf77d","target":"graph","created_at":"2026-07-08T01:19:20Z","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/2607.06287/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study kernel-based operator learning in a two-stage sampling framework, where an offline kernel regression operator learns a discretized representation of the target operator from input-output pairs and an online kernel reconstruction operator recovers the output function from predicted observations.\n  Our main theoretical contribution is an explicit budget allocation condition relating the number $N$ of training pairs, the number $n$ of input observations, and the output resolution $m$. The condition is derived from a coupled error analysis that interprets the surrogate as a reconstruction","authors_text":"R\\\"udiger Kempf","cross_cats":["cs.LG","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-07T13:56:20Z","title":"Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06287","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":"sha256:30fd299bdb04c47ed8b618b3b041853a24dac2935056a5a7ff3032664b4baaf1","target":"record","created_at":"2026-07-08T01:19:20Z","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":"a79aa79c79c962f8fa9e740462f86eeabf54235346ebb76be8a3985d9cad17b0","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-07T13:56:20Z","title_canon_sha256":"c89e8f40fbd6b3a865153519041a29bc53ae3171673aea742243fb75c4632331"},"schema_version":"1.0","source":{"id":"2607.06287","kind":"arxiv","version":1}},"canonical_sha256":"7dcf2867ca3cebf2ba458f1c6eb2606cc420ba825eaaddec52459fa92c5971df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7dcf2867ca3cebf2ba458f1c6eb2606cc420ba825eaaddec52459fa92c5971df","first_computed_at":"2026-07-08T01:19:20.010853Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-08T01:19:20.010853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B6EYtuJ8ug+3zQSzCmmpl976UA56JV/SoA5fcwtTs7y7XDGdrn7ytHu9f5yOtFrta/9WnHhCGB+7Ld6NOF9CBA==","signature_status":"signed_v1","signed_at":"2026-07-08T01:19:20.011275Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.06287","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30fd299bdb04c47ed8b618b3b041853a24dac2935056a5a7ff3032664b4baaf1","sha256:d97a23e365f94fa61279f9a98709fc0435cd935092bc1e1b4a8abdcc98edf77d","sha256:bad5c577d36d8703daa0ee31fc9593d84cf4586062bb720721d984002ecc6865"],"state_sha256":"72e2fb63b8a40e311183bd37245a5f246ef6b948ff4a140c8e4c61d91962dfcb"}