{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:M3C77RS3BU76STTYAWB6BSMNJV","short_pith_number":"pith:M3C77RS3","canonical_record":{"source":{"id":"2408.11266","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-08-21T01:34:20Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"7e090a481e1372b162b66504c9f324bd953573cfebde6a9ff59a0907a8cd1186","abstract_canon_sha256":"e581aa218d9dce49190612ff044db5fb771cea6e3b8acd6dcff6951df8d01110"},"schema_version":"1.0"},"canonical_sha256":"66c5ffc65b0d3fe94e780583e0c98d4d4bb4d27667bef6f11698d17cb74f4278","source":{"kind":"arxiv","id":"2408.11266","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.11266","created_at":"2026-06-02T02:04:45Z"},{"alias_kind":"arxiv_version","alias_value":"2408.11266v5","created_at":"2026-06-02T02:04:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.11266","created_at":"2026-06-02T02:04:45Z"},{"alias_kind":"pith_short_12","alias_value":"M3C77RS3BU76","created_at":"2026-06-02T02:04:45Z"},{"alias_kind":"pith_short_16","alias_value":"M3C77RS3BU76STTY","created_at":"2026-06-02T02:04:45Z"},{"alias_kind":"pith_short_8","alias_value":"M3C77RS3","created_at":"2026-06-02T02:04:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:M3C77RS3BU76STTYAWB6BSMNJV","target":"record","payload":{"canonical_record":{"source":{"id":"2408.11266","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-08-21T01:34:20Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"7e090a481e1372b162b66504c9f324bd953573cfebde6a9ff59a0907a8cd1186","abstract_canon_sha256":"e581aa218d9dce49190612ff044db5fb771cea6e3b8acd6dcff6951df8d01110"},"schema_version":"1.0"},"canonical_sha256":"66c5ffc65b0d3fe94e780583e0c98d4d4bb4d27667bef6f11698d17cb74f4278","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:45.041374Z","signature_b64":"/fXWf8Wpu7UikSlrRohm69D9QBacFce67mxmmfwcFaE8Wn0gOWB9py3ENxxU3MFZSEzZ4lGwtCPFuEYze724CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66c5ffc65b0d3fe94e780583e0c98d4d4bb4d27667bef6f11698d17cb74f4278","last_reissued_at":"2026-06-02T02:04:45.040895Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:45.040895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2408.11266","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-02T02:04:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JUPl4FrsAaDWaEVjXtPRqELUn14UjyLkVlfWLINUs2Q39267xuK+Sxyg4tVXq6cb1H7B9LkQl4y+XEy7rq6FDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:33:55.187488Z"},"content_sha256":"734f27fa02b205fa5102d1a6f5c8ec4e487ff65e5021f1ae120fa9b654cfc045","schema_version":"1.0","event_id":"sha256:734f27fa02b205fa5102d1a6f5c8ec4e487ff65e5021f1ae120fa9b654cfc045"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:M3C77RS3BU76STTYAWB6BSMNJV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Practical Aspects on Solving Differential Equations Using Deep Learning: A Primer","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.LG","authors_text":"Georgios Is. Detorakis","submitted_at":"2024-08-21T01:34:20Z","abstract_excerpt":"Deep learning is now common across many scientific fields, including the study of partial differential equations. This article provides a brief, accessible introduction to core deep learning concepts, including neural networks, backpropagation, and the universal approximation theorem. It mainly covers how to use deep learning in solving differential equations. The article aims to help undergraduate and graduate students in mathematics, physics, and related areas learn how to use Deep Learning to solve partial differential equations. Instructors in mathematics or physics can also use this artic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.11266","kind":"arxiv","version":5},"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/2408.11266/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":"2026-06-02T02:04:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IdBnrTYucOvKrLgKTurte5w/vO8IgOztNeDTI/PkUvWppYutTwnQsFzI6WTOUAZ1EZPWVgty8571ge/ZaeCVAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:33:55.188121Z"},"content_sha256":"70859f1b9813de64db34b82ee38b30677df6cff16f547dd544fd991606f11e6a","schema_version":"1.0","event_id":"sha256:70859f1b9813de64db34b82ee38b30677df6cff16f547dd544fd991606f11e6a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M3C77RS3BU76STTYAWB6BSMNJV/bundle.json","state_url":"https://pith.science/pith/M3C77RS3BU76STTYAWB6BSMNJV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M3C77RS3BU76STTYAWB6BSMNJV/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":"2026-06-07T10:33:55Z","links":{"resolver":"https://pith.science/pith/M3C77RS3BU76STTYAWB6BSMNJV","bundle":"https://pith.science/pith/M3C77RS3BU76STTYAWB6BSMNJV/bundle.json","state":"https://pith.science/pith/M3C77RS3BU76STTYAWB6BSMNJV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M3C77RS3BU76STTYAWB6BSMNJV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:M3C77RS3BU76STTYAWB6BSMNJV","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":"e581aa218d9dce49190612ff044db5fb771cea6e3b8acd6dcff6951df8d01110","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-08-21T01:34:20Z","title_canon_sha256":"7e090a481e1372b162b66504c9f324bd953573cfebde6a9ff59a0907a8cd1186"},"schema_version":"1.0","source":{"id":"2408.11266","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.11266","created_at":"2026-06-02T02:04:45Z"},{"alias_kind":"arxiv_version","alias_value":"2408.11266v5","created_at":"2026-06-02T02:04:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.11266","created_at":"2026-06-02T02:04:45Z"},{"alias_kind":"pith_short_12","alias_value":"M3C77RS3BU76","created_at":"2026-06-02T02:04:45Z"},{"alias_kind":"pith_short_16","alias_value":"M3C77RS3BU76STTY","created_at":"2026-06-02T02:04:45Z"},{"alias_kind":"pith_short_8","alias_value":"M3C77RS3","created_at":"2026-06-02T02:04:45Z"}],"graph_snapshots":[{"event_id":"sha256:70859f1b9813de64db34b82ee38b30677df6cff16f547dd544fd991606f11e6a","target":"graph","created_at":"2026-06-02T02:04:45Z","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/2408.11266/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Deep learning is now common across many scientific fields, including the study of partial differential equations. This article provides a brief, accessible introduction to core deep learning concepts, including neural networks, backpropagation, and the universal approximation theorem. It mainly covers how to use deep learning in solving differential equations. The article aims to help undergraduate and graduate students in mathematics, physics, and related areas learn how to use Deep Learning to solve partial differential equations. Instructors in mathematics or physics can also use this artic","authors_text":"Georgios Is. Detorakis","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-08-21T01:34:20Z","title":"Practical Aspects on Solving Differential Equations Using Deep Learning: A Primer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.11266","kind":"arxiv","version":5},"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":"sha256:734f27fa02b205fa5102d1a6f5c8ec4e487ff65e5021f1ae120fa9b654cfc045","target":"record","created_at":"2026-06-02T02:04:45Z","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":"e581aa218d9dce49190612ff044db5fb771cea6e3b8acd6dcff6951df8d01110","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-08-21T01:34:20Z","title_canon_sha256":"7e090a481e1372b162b66504c9f324bd953573cfebde6a9ff59a0907a8cd1186"},"schema_version":"1.0","source":{"id":"2408.11266","kind":"arxiv","version":5}},"canonical_sha256":"66c5ffc65b0d3fe94e780583e0c98d4d4bb4d27667bef6f11698d17cb74f4278","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66c5ffc65b0d3fe94e780583e0c98d4d4bb4d27667bef6f11698d17cb74f4278","first_computed_at":"2026-06-02T02:04:45.040895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:45.040895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/fXWf8Wpu7UikSlrRohm69D9QBacFce67mxmmfwcFaE8Wn0gOWB9py3ENxxU3MFZSEzZ4lGwtCPFuEYze724CA==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:45.041374Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.11266","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:734f27fa02b205fa5102d1a6f5c8ec4e487ff65e5021f1ae120fa9b654cfc045","sha256:70859f1b9813de64db34b82ee38b30677df6cff16f547dd544fd991606f11e6a"],"state_sha256":"fa0c070e6c9d9af19228a0070bfb4c28d532992fb2cdbb367fd5ede761c9dba6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xhyUFyDxd4irZVdCH133wPjS0oqsjrt/ZNiV4qtr92o+RAwqa2yTneSUBL2hqVaZeh5mYTL318fbj8gmoZoJBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T10:33:55.190962Z","bundle_sha256":"4a612a2f118e87695f29b57993bca9955e7a4bc740e6882241e4962acccebd57"}}