{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:XBFTDI67ZSILZH6GLVVBGG7XOZ","short_pith_number":"pith:XBFTDI67","canonical_record":{"source":{"id":"2006.02199","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-06-03T12:14:56Z","cross_cats_sorted":["cs.LG","cs.NA","math.AP","math.NA"],"title_canon_sha256":"1c5a2e3ae1ac0e3966ca038bf30e9d1bfb3a3707e9d3db824adfd6d588919cb3","abstract_canon_sha256":"fbd75f44b6666dbac93172118854211c6a97fb70d0ed74d6e0d95794284ef315"},"schema_version":"1.0"},"canonical_sha256":"b84b31a3dfcc90bc9fc65d6a131bf77647be34a3e4030373e1837e95ec5bee80","source":{"kind":"arxiv","id":"2006.02199","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.02199","created_at":"2026-07-05T08:26:08Z"},{"alias_kind":"arxiv_version","alias_value":"2006.02199v2","created_at":"2026-07-05T08:26:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.02199","created_at":"2026-07-05T08:26:08Z"},{"alias_kind":"pith_short_12","alias_value":"XBFTDI67ZSIL","created_at":"2026-07-05T08:26:08Z"},{"alias_kind":"pith_short_16","alias_value":"XBFTDI67ZSILZH6G","created_at":"2026-07-05T08:26:08Z"},{"alias_kind":"pith_short_8","alias_value":"XBFTDI67","created_at":"2026-07-05T08:26:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:XBFTDI67ZSILZH6GLVVBGG7XOZ","target":"record","payload":{"canonical_record":{"source":{"id":"2006.02199","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-06-03T12:14:56Z","cross_cats_sorted":["cs.LG","cs.NA","math.AP","math.NA"],"title_canon_sha256":"1c5a2e3ae1ac0e3966ca038bf30e9d1bfb3a3707e9d3db824adfd6d588919cb3","abstract_canon_sha256":"fbd75f44b6666dbac93172118854211c6a97fb70d0ed74d6e0d95794284ef315"},"schema_version":"1.0"},"canonical_sha256":"b84b31a3dfcc90bc9fc65d6a131bf77647be34a3e4030373e1837e95ec5bee80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:26:08.439186Z","signature_b64":"DWHsZ3YariQjZxzbYXvvPbfPl6waRySZGd6maLwlkT0yMU6Jz/LwFtBf+R6+iZsX/Vd3Rq1/imPpw/bpFUNwDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b84b31a3dfcc90bc9fc65d6a131bf77647be34a3e4030373e1837e95ec5bee80","last_reissued_at":"2026-07-05T08:26:08.438781Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:26:08.438781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.02199","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:26:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NkhT4TfsM6REwpqT9mX4Mo1oFX7j+bbpJjy6mOqQpLQ5Dj0N1a/4rr1HHNFADnBjeZORi6cpWgnvLPbpGyYSCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T17:23:38.800172Z"},"content_sha256":"a885c037f01c34e96eff0ee900529d784def0f4b15ef2c0a15b37139bb86d47d","schema_version":"1.0","event_id":"sha256:a885c037f01c34e96eff0ee900529d784def0f4b15ef2c0a15b37139bb86d47d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:XBFTDI67ZSILZH6GLVVBGG7XOZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Space-time deep neural network approximations for high-dimensional partial differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.AP","math.NA"],"primary_cat":"math.PR","authors_text":"Arnulf Jentzen, Diyora Salimova, Fabian Hornung","submitted_at":"2020-06-03T12:14:56Z","abstract_excerpt":"It is one of the most challenging issues in applied mathematics to approximately solve high-dimensional partial differential equations (PDEs) and most of the numerical approximation methods for PDEs in the scientific literature suffer from the so-called curse of dimensionality in the sense that the number of computational operations employed in the corresponding approximation scheme to obtain an approximation precision $\\varepsilon>0$ grows exponentially in the PDE dimension and/or the reciprocal of $\\varepsilon$. Recently, certain deep learning based approximation methods for PDEs have been p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.02199","kind":"arxiv","version":2},"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/2006.02199/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":"2026-07-05T08:26:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dZqYB/VPvWDWabpHY15aLS/M66HENjoa+0f8Oq8vZyMAiAdCGDF8l94lk5Gm1Jov1sDqz0jywI/lb5FhQjKqBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T17:23:38.800730Z"},"content_sha256":"9744a7488a42bfa1d2a643126b3c87e6bfac2f8a3c9ee2b286ad2987f06dc494","schema_version":"1.0","event_id":"sha256:9744a7488a42bfa1d2a643126b3c87e6bfac2f8a3c9ee2b286ad2987f06dc494"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XBFTDI67ZSILZH6GLVVBGG7XOZ/bundle.json","state_url":"https://pith.science/pith/XBFTDI67ZSILZH6GLVVBGG7XOZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XBFTDI67ZSILZH6GLVVBGG7XOZ/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":"2026-08-11T17:23:38Z","links":{"resolver":"https://pith.science/pith/XBFTDI67ZSILZH6GLVVBGG7XOZ","bundle":"https://pith.science/pith/XBFTDI67ZSILZH6GLVVBGG7XOZ/bundle.json","state":"https://pith.science/pith/XBFTDI67ZSILZH6GLVVBGG7XOZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XBFTDI67ZSILZH6GLVVBGG7XOZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:XBFTDI67ZSILZH6GLVVBGG7XOZ","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":"fbd75f44b6666dbac93172118854211c6a97fb70d0ed74d6e0d95794284ef315","cross_cats_sorted":["cs.LG","cs.NA","math.AP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-06-03T12:14:56Z","title_canon_sha256":"1c5a2e3ae1ac0e3966ca038bf30e9d1bfb3a3707e9d3db824adfd6d588919cb3"},"schema_version":"1.0","source":{"id":"2006.02199","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.02199","created_at":"2026-07-05T08:26:08Z"},{"alias_kind":"arxiv_version","alias_value":"2006.02199v2","created_at":"2026-07-05T08:26:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.02199","created_at":"2026-07-05T08:26:08Z"},{"alias_kind":"pith_short_12","alias_value":"XBFTDI67ZSIL","created_at":"2026-07-05T08:26:08Z"},{"alias_kind":"pith_short_16","alias_value":"XBFTDI67ZSILZH6G","created_at":"2026-07-05T08:26:08Z"},{"alias_kind":"pith_short_8","alias_value":"XBFTDI67","created_at":"2026-07-05T08:26:08Z"}],"graph_snapshots":[{"event_id":"sha256:9744a7488a42bfa1d2a643126b3c87e6bfac2f8a3c9ee2b286ad2987f06dc494","target":"graph","created_at":"2026-07-05T08:26:08Z","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/2006.02199/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is one of the most challenging issues in applied mathematics to approximately solve high-dimensional partial differential equations (PDEs) and most of the numerical approximation methods for PDEs in the scientific literature suffer from the so-called curse of dimensionality in the sense that the number of computational operations employed in the corresponding approximation scheme to obtain an approximation precision $\\varepsilon>0$ grows exponentially in the PDE dimension and/or the reciprocal of $\\varepsilon$. Recently, certain deep learning based approximation methods for PDEs have been p","authors_text":"Arnulf Jentzen, Diyora Salimova, Fabian Hornung","cross_cats":["cs.LG","cs.NA","math.AP","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-06-03T12:14:56Z","title":"Space-time deep neural network approximations for high-dimensional partial differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.02199","kind":"arxiv","version":2},"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:a885c037f01c34e96eff0ee900529d784def0f4b15ef2c0a15b37139bb86d47d","target":"record","created_at":"2026-07-05T08:26:08Z","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":"fbd75f44b6666dbac93172118854211c6a97fb70d0ed74d6e0d95794284ef315","cross_cats_sorted":["cs.LG","cs.NA","math.AP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-06-03T12:14:56Z","title_canon_sha256":"1c5a2e3ae1ac0e3966ca038bf30e9d1bfb3a3707e9d3db824adfd6d588919cb3"},"schema_version":"1.0","source":{"id":"2006.02199","kind":"arxiv","version":2}},"canonical_sha256":"b84b31a3dfcc90bc9fc65d6a131bf77647be34a3e4030373e1837e95ec5bee80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b84b31a3dfcc90bc9fc65d6a131bf77647be34a3e4030373e1837e95ec5bee80","first_computed_at":"2026-07-05T08:26:08.438781Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:26:08.438781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DWHsZ3YariQjZxzbYXvvPbfPl6waRySZGd6maLwlkT0yMU6Jz/LwFtBf+R6+iZsX/Vd3Rq1/imPpw/bpFUNwDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:26:08.439186Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.02199","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a885c037f01c34e96eff0ee900529d784def0f4b15ef2c0a15b37139bb86d47d","sha256:9744a7488a42bfa1d2a643126b3c87e6bfac2f8a3c9ee2b286ad2987f06dc494"],"state_sha256":"0e754ef63cb57fc4931f7fc22a9cbea96323fc84d6dfa6cd69cdc6c040a63a9f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kwq2WsJSioMfPabAIcs7QYKSR3oW2cj1rH7Ish7dFzIFOytxpOS6THFKwUugqy1tWs93HDXd6T/c9LydvFTVCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T17:23:38.805977Z","bundle_sha256":"e39fcd5a7b5c28db6dd3b0f76e5160bd3d21aa6d92b79178c261a94de4c52afc"}}