{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:A6T42YFGKBDFSJ5SOW4NYTHB3R","short_pith_number":"pith:A6T42YFG","canonical_record":{"source":{"id":"1703.10230","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-03-29T20:17:30Z","cross_cats_sorted":["cs.NA","math.AP","math.DS","math.NA"],"title_canon_sha256":"8c27f8a6063ccc8afe91e2231e3cd5fd2ca9ce0554f572c2248efa7b53732150","abstract_canon_sha256":"af9f97981df1d524945e907e73d17f2d94999ccea4c193344aff13c949e4bf5f"},"schema_version":"1.0"},"canonical_sha256":"07a7cd60a650465927b275b8dc4ce1dc415ebd220109505498f865fe950d86b7","source":{"kind":"arxiv","id":"1703.10230","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10230","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10230v1","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10230","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"pith_short_12","alias_value":"A6T42YFGKBDF","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"A6T42YFGKBDFSJ5S","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"A6T42YFG","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:A6T42YFGKBDFSJ5SOW4NYTHB3R","target":"record","payload":{"canonical_record":{"source":{"id":"1703.10230","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-03-29T20:17:30Z","cross_cats_sorted":["cs.NA","math.AP","math.DS","math.NA"],"title_canon_sha256":"8c27f8a6063ccc8afe91e2231e3cd5fd2ca9ce0554f572c2248efa7b53732150","abstract_canon_sha256":"af9f97981df1d524945e907e73d17f2d94999ccea4c193344aff13c949e4bf5f"},"schema_version":"1.0"},"canonical_sha256":"07a7cd60a650465927b275b8dc4ce1dc415ebd220109505498f865fe950d86b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:37.607589Z","signature_b64":"U0ApeUVCLZ8Hyx+Infsvf5rynN0a6Z2g1qAuW7j2CXeuBUT6twVIz5KBmq2nZ3qZMDZ4Z+ck+JJ/jJSrSJGZAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07a7cd60a650465927b275b8dc4ce1dc415ebd220109505498f865fe950d86b7","last_reissued_at":"2026-05-18T00:47:37.607156Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:37.607156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.10230","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":"2026-05-18T00:47:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k0B40osxcOBk8m+PxJESyOstYPh7lwSvFcsGIXhAKMXb4BOu9nCr+DcX4xwHyEEZGqd1JLyVtRBE2hb7/u4bDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:01:40.628061Z"},"content_sha256":"c77f3ceb7487d33a855a1029ab5f6d99a50475c1c0c1b671007b55bbbed69bff","schema_version":"1.0","event_id":"sha256:c77f3ceb7487d33a855a1029ab5f6d99a50475c1c0c1b671007b55bbbed69bff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:A6T42YFGKBDFSJ5SOW4NYTHB3R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP","math.DS","math.NA"],"primary_cat":"stat.ML","authors_text":"George Em Karniadakis, Maziar Raissi, Paris Perdikaris","submitted_at":"2017-03-29T20:17:30Z","abstract_excerpt":"We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes, by construction, are designed to deal with cases where: (1) all we observe are noisy data on black-box initial conditions, and (2) we are interested in quantifying the uncertainty associated with such noisy data in our solutions to time-dependent partial differential equations. Our method circumvents the need for spatial discretization of the differential o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10230","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":""},"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":"2026-05-18T00:47:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wquvBNGe5Iqcl5aDecORlOZYO94RzyQPTPdgO9rxqklaIOzSPQyTnJdUZl7ASvbjuo95MsZAI39IuRyw8UaBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:01:40.628726Z"},"content_sha256":"4f53f5502a5a3f5ce8cc7922a6d93e196dd599eec54fa1418af473c732e2df68","schema_version":"1.0","event_id":"sha256:4f53f5502a5a3f5ce8cc7922a6d93e196dd599eec54fa1418af473c732e2df68"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A6T42YFGKBDFSJ5SOW4NYTHB3R/bundle.json","state_url":"https://pith.science/pith/A6T42YFGKBDFSJ5SOW4NYTHB3R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A6T42YFGKBDFSJ5SOW4NYTHB3R/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":"2026-06-05T20:01:40Z","links":{"resolver":"https://pith.science/pith/A6T42YFGKBDFSJ5SOW4NYTHB3R","bundle":"https://pith.science/pith/A6T42YFGKBDFSJ5SOW4NYTHB3R/bundle.json","state":"https://pith.science/pith/A6T42YFGKBDFSJ5SOW4NYTHB3R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A6T42YFGKBDFSJ5SOW4NYTHB3R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:A6T42YFGKBDFSJ5SOW4NYTHB3R","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":"af9f97981df1d524945e907e73d17f2d94999ccea4c193344aff13c949e4bf5f","cross_cats_sorted":["cs.NA","math.AP","math.DS","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-03-29T20:17:30Z","title_canon_sha256":"8c27f8a6063ccc8afe91e2231e3cd5fd2ca9ce0554f572c2248efa7b53732150"},"schema_version":"1.0","source":{"id":"1703.10230","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10230","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10230v1","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10230","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"pith_short_12","alias_value":"A6T42YFGKBDF","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"A6T42YFGKBDFSJ5S","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"A6T42YFG","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:4f53f5502a5a3f5ce8cc7922a6d93e196dd599eec54fa1418af473c732e2df68","target":"graph","created_at":"2026-05-18T00:47:37Z","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"},"paper":{"abstract_excerpt":"We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes, by construction, are designed to deal with cases where: (1) all we observe are noisy data on black-box initial conditions, and (2) we are interested in quantifying the uncertainty associated with such noisy data in our solutions to time-dependent partial differential equations. Our method circumvents the need for spatial discretization of the differential o","authors_text":"George Em Karniadakis, Maziar Raissi, Paris Perdikaris","cross_cats":["cs.NA","math.AP","math.DS","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-03-29T20:17:30Z","title":"Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10230","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:c77f3ceb7487d33a855a1029ab5f6d99a50475c1c0c1b671007b55bbbed69bff","target":"record","created_at":"2026-05-18T00:47:37Z","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":"af9f97981df1d524945e907e73d17f2d94999ccea4c193344aff13c949e4bf5f","cross_cats_sorted":["cs.NA","math.AP","math.DS","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-03-29T20:17:30Z","title_canon_sha256":"8c27f8a6063ccc8afe91e2231e3cd5fd2ca9ce0554f572c2248efa7b53732150"},"schema_version":"1.0","source":{"id":"1703.10230","kind":"arxiv","version":1}},"canonical_sha256":"07a7cd60a650465927b275b8dc4ce1dc415ebd220109505498f865fe950d86b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07a7cd60a650465927b275b8dc4ce1dc415ebd220109505498f865fe950d86b7","first_computed_at":"2026-05-18T00:47:37.607156Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:37.607156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U0ApeUVCLZ8Hyx+Infsvf5rynN0a6Z2g1qAuW7j2CXeuBUT6twVIz5KBmq2nZ3qZMDZ4Z+ck+JJ/jJSrSJGZAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:37.607589Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.10230","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c77f3ceb7487d33a855a1029ab5f6d99a50475c1c0c1b671007b55bbbed69bff","sha256:4f53f5502a5a3f5ce8cc7922a6d93e196dd599eec54fa1418af473c732e2df68"],"state_sha256":"c797bedda6098893f304833cc36b87ba54e850684bddc1d17644e3db827972a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WRGYVlXXvN49DmzBhocMfL3ePa48SJdckTtJTj/1T2gw67WA0K065dn0CB/pfXxnIFzbbd0X8pH5sL/Kof2NBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T20:01:40.633211Z","bundle_sha256":"0ca2d1a529cd720bcfae106f580aa9b3dce20a3829bd430c83afec31fc73160d"}}