{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:EUKQP7CSEP5SZGBGIJVC7AWJOP","short_pith_number":"pith:EUKQP7CS","canonical_record":{"source":{"id":"2606.08203","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-06T14:42:03Z","cross_cats_sorted":["cs.LG","cs.NA","stat.ML"],"title_canon_sha256":"eb5ef9c3c20a38ca8c8656f21796a6e920c32b65acf0ea0f90e6025ed1db0653","abstract_canon_sha256":"621a385355a4d6e005a5ed32f97e6bc9018a0c937903471d87a3a0b92bec6bbd"},"schema_version":"1.0"},"canonical_sha256":"251507fc5223fb2c9826426a2f82c973f87ec5c799c454297218f412b47ca1d6","source":{"kind":"arxiv","id":"2606.08203","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08203","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08203v1","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08203","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"pith_short_12","alias_value":"EUKQP7CSEP5S","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"pith_short_16","alias_value":"EUKQP7CSEP5SZGBG","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"pith_short_8","alias_value":"EUKQP7CS","created_at":"2026-06-09T01:05:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:EUKQP7CSEP5SZGBGIJVC7AWJOP","target":"record","payload":{"canonical_record":{"source":{"id":"2606.08203","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-06T14:42:03Z","cross_cats_sorted":["cs.LG","cs.NA","stat.ML"],"title_canon_sha256":"eb5ef9c3c20a38ca8c8656f21796a6e920c32b65acf0ea0f90e6025ed1db0653","abstract_canon_sha256":"621a385355a4d6e005a5ed32f97e6bc9018a0c937903471d87a3a0b92bec6bbd"},"schema_version":"1.0"},"canonical_sha256":"251507fc5223fb2c9826426a2f82c973f87ec5c799c454297218f412b47ca1d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:05:29.929055Z","signature_b64":"UYUeIAnj+XLQ+wW9xjfIvK6zUDQyMFd3xqwHWTLYAEvjyn7gk1z0rxjwHyeASxyplkxsuIUBloq6UpRsTod9CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"251507fc5223fb2c9826426a2f82c973f87ec5c799c454297218f412b47ca1d6","last_reissued_at":"2026-06-09T01:05:29.928551Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:05:29.928551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.08203","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":"2026-06-09T01:05:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GGC0UPdsSpo7UG4bufyAbo57ud6Nn3DWsPR7+QXSv2ciy7QHU3KT3ChWf76qW3o+gyCmZYojavtUNBb727AVBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-26T20:43:35.157911Z"},"content_sha256":"a3db8bf3a19cfadfbc6b292b2436801e08f9d6c86b8a641566d28a0a76cc2563","schema_version":"1.0","event_id":"sha256:a3db8bf3a19cfadfbc6b292b2436801e08f9d6c86b8a641566d28a0a76cc2563"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:EUKQP7CSEP5SZGBGIJVC7AWJOP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stable and Scalable Probabilistic Numerical Solvers for Stiff and High-Dimensional ODEs","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.LG","cs.NA","stat.ML"],"primary_cat":"math.NA","authors_text":"Nathanael Bosch","submitted_at":"2026-06-06T14:42:03Z","abstract_excerpt":"Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs) have been established as a flexible and efficient simulation framework with built-in numerical uncertainty quantification. However, problems that are both stiff and high-dimensional remain a challenge, as current methods are either stable and have cubic cost in the ODE dimension, or scale linearly at the expense of stability. In this paper, we close this gap and develop probabilistic ODE solvers that are both stable and scalable. We propose two complementary strategies. First, we develop a matrix-free up"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08203","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/2606.08203/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":"2026-06-09T01:05:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UFqDuaKJdrF/TXxOXnbcOGI2vCMb9/wrDdAi6TGhIzckjCY/G9AYKZhYvAJtAvkXPyEJzWFL/romW9Q8rmbaCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-26T20:43:35.158547Z"},"content_sha256":"a245f6cd038de30477f17fa8c9e1d339b87a84ac333cee0b9b4e570f50970ac0","schema_version":"1.0","event_id":"sha256:a245f6cd038de30477f17fa8c9e1d339b87a84ac333cee0b9b4e570f50970ac0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EUKQP7CSEP5SZGBGIJVC7AWJOP/bundle.json","state_url":"https://pith.science/pith/EUKQP7CSEP5SZGBGIJVC7AWJOP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EUKQP7CSEP5SZGBGIJVC7AWJOP/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":"2026-07-26T20:43:35Z","links":{"resolver":"https://pith.science/pith/EUKQP7CSEP5SZGBGIJVC7AWJOP","bundle":"https://pith.science/pith/EUKQP7CSEP5SZGBGIJVC7AWJOP/bundle.json","state":"https://pith.science/pith/EUKQP7CSEP5SZGBGIJVC7AWJOP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EUKQP7CSEP5SZGBGIJVC7AWJOP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EUKQP7CSEP5SZGBGIJVC7AWJOP","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":"621a385355a4d6e005a5ed32f97e6bc9018a0c937903471d87a3a0b92bec6bbd","cross_cats_sorted":["cs.LG","cs.NA","stat.ML"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-06T14:42:03Z","title_canon_sha256":"eb5ef9c3c20a38ca8c8656f21796a6e920c32b65acf0ea0f90e6025ed1db0653"},"schema_version":"1.0","source":{"id":"2606.08203","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08203","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08203v1","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08203","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"pith_short_12","alias_value":"EUKQP7CSEP5S","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"pith_short_16","alias_value":"EUKQP7CSEP5SZGBG","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"pith_short_8","alias_value":"EUKQP7CS","created_at":"2026-06-09T01:05:29Z"}],"graph_snapshots":[{"event_id":"sha256:a245f6cd038de30477f17fa8c9e1d339b87a84ac333cee0b9b4e570f50970ac0","target":"graph","created_at":"2026-06-09T01:05:29Z","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/2606.08203/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs) have been established as a flexible and efficient simulation framework with built-in numerical uncertainty quantification. However, problems that are both stiff and high-dimensional remain a challenge, as current methods are either stable and have cubic cost in the ODE dimension, or scale linearly at the expense of stability. In this paper, we close this gap and develop probabilistic ODE solvers that are both stable and scalable. We propose two complementary strategies. First, we develop a matrix-free up","authors_text":"Nathanael Bosch","cross_cats":["cs.LG","cs.NA","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-06T14:42:03Z","title":"Stable and Scalable Probabilistic Numerical Solvers for Stiff and High-Dimensional ODEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08203","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:a3db8bf3a19cfadfbc6b292b2436801e08f9d6c86b8a641566d28a0a76cc2563","target":"record","created_at":"2026-06-09T01:05:29Z","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":"621a385355a4d6e005a5ed32f97e6bc9018a0c937903471d87a3a0b92bec6bbd","cross_cats_sorted":["cs.LG","cs.NA","stat.ML"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-06T14:42:03Z","title_canon_sha256":"eb5ef9c3c20a38ca8c8656f21796a6e920c32b65acf0ea0f90e6025ed1db0653"},"schema_version":"1.0","source":{"id":"2606.08203","kind":"arxiv","version":1}},"canonical_sha256":"251507fc5223fb2c9826426a2f82c973f87ec5c799c454297218f412b47ca1d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"251507fc5223fb2c9826426a2f82c973f87ec5c799c454297218f412b47ca1d6","first_computed_at":"2026-06-09T01:05:29.928551Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:29.928551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UYUeIAnj+XLQ+wW9xjfIvK6zUDQyMFd3xqwHWTLYAEvjyn7gk1z0rxjwHyeASxyplkxsuIUBloq6UpRsTod9CA==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:29.929055Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.08203","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3db8bf3a19cfadfbc6b292b2436801e08f9d6c86b8a641566d28a0a76cc2563","sha256:a245f6cd038de30477f17fa8c9e1d339b87a84ac333cee0b9b4e570f50970ac0"],"state_sha256":"a7f626f1a822cb9602cf73637684476fb08aa84cfca9ca34ca83b03a14099480"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0wdFofFdXmR2ueCvHjX41Fr3gKgJPVvugv2FdDi8J9Yzb23XWNN5UVJWW22UnmuXyUPWiftnWZTnRPfvNwrfBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-26T20:43:35.161073Z","bundle_sha256":"ae2dec2c5513595b17965f4a26f1992a26d3098db53a1d26652a8dd08868342e"}}