{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SUDPUL3S6DKDHS7NHGU4WO2XO6","short_pith_number":"pith:SUDPUL3S","canonical_record":{"source":{"id":"2606.19138","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-17T14:46:23Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"c4871801b5a78bf5f04920517b33f4d46a3381cb00e9685d2fddbcedec740cf5","abstract_canon_sha256":"520e5f3d5fabaccc4b7b595e165d187f04a2acc98e832eb1e522e99237ed7c0a"},"schema_version":"1.0"},"canonical_sha256":"9506fa2f72f0d433cbed39a9cb3b5777ae3d23354df00cb59f2a19f1b2faf822","source":{"kind":"arxiv","id":"2606.19138","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.19138","created_at":"2026-06-19T16:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"2606.19138v1","created_at":"2026-06-19T16:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19138","created_at":"2026-06-19T16:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"SUDPUL3S6DKD","created_at":"2026-06-19T16:11:57Z"},{"alias_kind":"pith_short_16","alias_value":"SUDPUL3S6DKDHS7N","created_at":"2026-06-19T16:11:57Z"},{"alias_kind":"pith_short_8","alias_value":"SUDPUL3S","created_at":"2026-06-19T16:11:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SUDPUL3S6DKDHS7NHGU4WO2XO6","target":"record","payload":{"canonical_record":{"source":{"id":"2606.19138","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-17T14:46:23Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"c4871801b5a78bf5f04920517b33f4d46a3381cb00e9685d2fddbcedec740cf5","abstract_canon_sha256":"520e5f3d5fabaccc4b7b595e165d187f04a2acc98e832eb1e522e99237ed7c0a"},"schema_version":"1.0"},"canonical_sha256":"9506fa2f72f0d433cbed39a9cb3b5777ae3d23354df00cb59f2a19f1b2faf822","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:11:57.590752Z","signature_b64":"LSsbw+aLrsf7WI6XpuiR2alYJOCkPtZscFx3/DN8PEg0JA2dM6Fcr3MsKJhzZ8ETeip1Qb7DQjW7Acs7XcI9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9506fa2f72f0d433cbed39a9cb3b5777ae3d23354df00cb59f2a19f1b2faf822","last_reissued_at":"2026-06-19T16:11:57.590357Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:11:57.590357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.19138","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":"2026-06-19T16:11:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oNFxwX9T2jXI+5DrYKQPyIeBMoEBfVpaBSDNtFklotgKwg/vHbjVFaapezqpS0YHf0oIEO8sbkJQ+By+teNmDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T13:51:27.535760Z"},"content_sha256":"0b8dda7985fb3dfa132222bd17600e1daa1948c1227fa964b04bd45a936db964","schema_version":"1.0","event_id":"sha256:0b8dda7985fb3dfa132222bd17600e1daa1948c1227fa964b04bd45a936db964"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SUDPUL3S6DKDHS7NHGU4WO2XO6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"INDEQS: Informed Neural controlled Differential EQuationS","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Gabriel Nobis, Jackie Ma, Juri Schubert, Kristiyan Blagov, Michael Detzel, Wojciech Samek","submitted_at":"2026-06-17T14:46:23Z","abstract_excerpt":"Neural Controlled Differential Equations (NCDE) provide a powerful continuous-time framework for forecasting time series, but standard graph-based extensions typically learn spatial structure purely from data, even in settings where a directed graph structure is known a priori. We introduce Informed Neural controlled Differential EQuationS (INDEQS), a graph-based NCDE forecasting method that incorporates prior knowledge of a directed graph at distinct architectural positions. INDEQS separates inner mixing of hidden states across graph nodes from outer mixing between vector field and control, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19138","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/2606.19138/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":"2026-06-19T16:11:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"noPo0daqvhj6VqzXQtXck2+mhNOfYSuKT3c/n8LIVi/FGapgE0hthU93TDRjn35q+iExwd732zW0UuwwPBpqDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T13:51:27.536154Z"},"content_sha256":"544c46acb1aa3791bb1362f2bb8816ca41441f0b8305920f8ce77c118a73f894","schema_version":"1.0","event_id":"sha256:544c46acb1aa3791bb1362f2bb8816ca41441f0b8305920f8ce77c118a73f894"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SUDPUL3S6DKDHS7NHGU4WO2XO6/bundle.json","state_url":"https://pith.science/pith/SUDPUL3S6DKDHS7NHGU4WO2XO6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SUDPUL3S6DKDHS7NHGU4WO2XO6/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":"2026-06-29T13:51:27Z","links":{"resolver":"https://pith.science/pith/SUDPUL3S6DKDHS7NHGU4WO2XO6","bundle":"https://pith.science/pith/SUDPUL3S6DKDHS7NHGU4WO2XO6/bundle.json","state":"https://pith.science/pith/SUDPUL3S6DKDHS7NHGU4WO2XO6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SUDPUL3S6DKDHS7NHGU4WO2XO6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SUDPUL3S6DKDHS7NHGU4WO2XO6","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":"520e5f3d5fabaccc4b7b595e165d187f04a2acc98e832eb1e522e99237ed7c0a","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-17T14:46:23Z","title_canon_sha256":"c4871801b5a78bf5f04920517b33f4d46a3381cb00e9685d2fddbcedec740cf5"},"schema_version":"1.0","source":{"id":"2606.19138","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.19138","created_at":"2026-06-19T16:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"2606.19138v1","created_at":"2026-06-19T16:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19138","created_at":"2026-06-19T16:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"SUDPUL3S6DKD","created_at":"2026-06-19T16:11:57Z"},{"alias_kind":"pith_short_16","alias_value":"SUDPUL3S6DKDHS7N","created_at":"2026-06-19T16:11:57Z"},{"alias_kind":"pith_short_8","alias_value":"SUDPUL3S","created_at":"2026-06-19T16:11:57Z"}],"graph_snapshots":[{"event_id":"sha256:544c46acb1aa3791bb1362f2bb8816ca41441f0b8305920f8ce77c118a73f894","target":"graph","created_at":"2026-06-19T16:11:57Z","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/2606.19138/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Neural Controlled Differential Equations (NCDE) provide a powerful continuous-time framework for forecasting time series, but standard graph-based extensions typically learn spatial structure purely from data, even in settings where a directed graph structure is known a priori. We introduce Informed Neural controlled Differential EQuationS (INDEQS), a graph-based NCDE forecasting method that incorporates prior knowledge of a directed graph at distinct architectural positions. INDEQS separates inner mixing of hidden states across graph nodes from outer mixing between vector field and control, a","authors_text":"Gabriel Nobis, Jackie Ma, Juri Schubert, Kristiyan Blagov, Michael Detzel, Wojciech Samek","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-17T14:46:23Z","title":"INDEQS: Informed Neural controlled Differential EQuationS"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19138","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":"sha256:0b8dda7985fb3dfa132222bd17600e1daa1948c1227fa964b04bd45a936db964","target":"record","created_at":"2026-06-19T16:11:57Z","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":"520e5f3d5fabaccc4b7b595e165d187f04a2acc98e832eb1e522e99237ed7c0a","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-17T14:46:23Z","title_canon_sha256":"c4871801b5a78bf5f04920517b33f4d46a3381cb00e9685d2fddbcedec740cf5"},"schema_version":"1.0","source":{"id":"2606.19138","kind":"arxiv","version":1}},"canonical_sha256":"9506fa2f72f0d433cbed39a9cb3b5777ae3d23354df00cb59f2a19f1b2faf822","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9506fa2f72f0d433cbed39a9cb3b5777ae3d23354df00cb59f2a19f1b2faf822","first_computed_at":"2026-06-19T16:11:57.590357Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:57.590357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LSsbw+aLrsf7WI6XpuiR2alYJOCkPtZscFx3/DN8PEg0JA2dM6Fcr3MsKJhzZ8ETeip1Qb7DQjW7Acs7XcI9DA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:57.590752Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.19138","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b8dda7985fb3dfa132222bd17600e1daa1948c1227fa964b04bd45a936db964","sha256:544c46acb1aa3791bb1362f2bb8816ca41441f0b8305920f8ce77c118a73f894"],"state_sha256":"4df5e2bd21d2af587e1613c8948458ebf2700eaf942f651aa6ae571868756597"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PZhkGGIGCJcFDHcNGbLoE6Z7l+GUqtvzD4hihBH3f5AP+2qGIQuV2NhkZBQXwyTYZByS5xXHDiq/RKvkoaOSDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T13:51:27.538538Z","bundle_sha256":"91ed3950c74e9fcca9d2f1e6c785d84ebf191c720f8a100df3945bad8379fb14"}}