{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:V6E4HVOPZ2DGAGVE4YT7K4LX6W","short_pith_number":"pith:V6E4HVOP","canonical_record":{"source":{"id":"2507.19522","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-07-19T03:39:49Z","cross_cats_sorted":[],"title_canon_sha256":"208f6b0411dd201058a519b9acc49118296c508f06871bd1757fab608a2d8df3","abstract_canon_sha256":"187fa46572eef2fd1d071a752758781ef57a5a94fb4099a49fa39bf9ad357372"},"schema_version":"1.0"},"canonical_sha256":"af89c3d5cfce86601aa4e627f57177f5b1f74592ee17cf03a24af980db412f08","source":{"kind":"arxiv","id":"2507.19522","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.19522","created_at":"2026-07-05T11:43:35Z"},{"alias_kind":"arxiv_version","alias_value":"2507.19522v1","created_at":"2026-07-05T11:43:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.19522","created_at":"2026-07-05T11:43:35Z"},{"alias_kind":"pith_short_12","alias_value":"V6E4HVOPZ2DG","created_at":"2026-07-05T11:43:35Z"},{"alias_kind":"pith_short_16","alias_value":"V6E4HVOPZ2DGAGVE","created_at":"2026-07-05T11:43:35Z"},{"alias_kind":"pith_short_8","alias_value":"V6E4HVOP","created_at":"2026-07-05T11:43:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:V6E4HVOPZ2DGAGVE4YT7K4LX6W","target":"record","payload":{"canonical_record":{"source":{"id":"2507.19522","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-07-19T03:39:49Z","cross_cats_sorted":[],"title_canon_sha256":"208f6b0411dd201058a519b9acc49118296c508f06871bd1757fab608a2d8df3","abstract_canon_sha256":"187fa46572eef2fd1d071a752758781ef57a5a94fb4099a49fa39bf9ad357372"},"schema_version":"1.0"},"canonical_sha256":"af89c3d5cfce86601aa4e627f57177f5b1f74592ee17cf03a24af980db412f08","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:43:35.659430Z","signature_b64":"TcjGF9P3IwbEKFhZp2pUCHNII2jGMqQPP07yqA3BwRlP0c8iM83zy+RkiMqTFKNO5t7AoDvVTzsZ5W3pTrtdAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af89c3d5cfce86601aa4e627f57177f5b1f74592ee17cf03a24af980db412f08","last_reissued_at":"2026-07-05T11:43:35.658970Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:43:35.658970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.19522","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":"2026-07-05T11:43:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2NqByefamhQWEnHM/oYEwr7hHC/NjWvr0LpfxqzmwofHsrQpokz0ZX1k2wNoTL9fgjdEv+R6hpNlnmyHijffAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T13:07:20.107659Z"},"content_sha256":"b8cfaac8568874918413b7edd18e9c95b3a61007239b6b17502babb528905f3d","schema_version":"1.0","event_id":"sha256:b8cfaac8568874918413b7edd18e9c95b3a61007239b6b17502babb528905f3d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:V6E4HVOPZ2DGAGVE4YT7K4LX6W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Applications and Manipulations of Physics-Informed Neural Networks in Solving Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Aarush Gupta, Kendric Hsu, Syna Mathod","submitted_at":"2025-07-19T03:39:49Z","abstract_excerpt":"Mathematical models in neural networks are powerful tools for solving complex differential equations and optimizing their parameters; that is, solving the forward and inverse problems, respectively. A forward problem predicts the output of a network for a given input by optimizing weights and biases. An inverse problem finds equation parameters or coefficients that effectively model the data. A Physics-Informed Neural Network (PINN) can solve both problems. PINNs inject prior analytical information about the data into the cost function to improve model performance outside the training set boun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.19522","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/2507.19522/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":"2026-07-05T11:43:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dgcvMZY4iDFPYOtKLB//Q/fWc0zqbJ6908c6ZaM4VjUOfdWRqEtWDi037kCnrVzUq1T8cwQK/QWDezl142WzAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T13:07:20.108559Z"},"content_sha256":"b36239260bf2c1ae7889623f8b45bdea90569e825a2ad9e3acab79feb61c22f6","schema_version":"1.0","event_id":"sha256:b36239260bf2c1ae7889623f8b45bdea90569e825a2ad9e3acab79feb61c22f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V6E4HVOPZ2DGAGVE4YT7K4LX6W/bundle.json","state_url":"https://pith.science/pith/V6E4HVOPZ2DGAGVE4YT7K4LX6W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V6E4HVOPZ2DGAGVE4YT7K4LX6W/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":"2026-08-12T13:07:20Z","links":{"resolver":"https://pith.science/pith/V6E4HVOPZ2DGAGVE4YT7K4LX6W","bundle":"https://pith.science/pith/V6E4HVOPZ2DGAGVE4YT7K4LX6W/bundle.json","state":"https://pith.science/pith/V6E4HVOPZ2DGAGVE4YT7K4LX6W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V6E4HVOPZ2DGAGVE4YT7K4LX6W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:V6E4HVOPZ2DGAGVE4YT7K4LX6W","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":"187fa46572eef2fd1d071a752758781ef57a5a94fb4099a49fa39bf9ad357372","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-07-19T03:39:49Z","title_canon_sha256":"208f6b0411dd201058a519b9acc49118296c508f06871bd1757fab608a2d8df3"},"schema_version":"1.0","source":{"id":"2507.19522","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.19522","created_at":"2026-07-05T11:43:35Z"},{"alias_kind":"arxiv_version","alias_value":"2507.19522v1","created_at":"2026-07-05T11:43:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.19522","created_at":"2026-07-05T11:43:35Z"},{"alias_kind":"pith_short_12","alias_value":"V6E4HVOPZ2DG","created_at":"2026-07-05T11:43:35Z"},{"alias_kind":"pith_short_16","alias_value":"V6E4HVOPZ2DGAGVE","created_at":"2026-07-05T11:43:35Z"},{"alias_kind":"pith_short_8","alias_value":"V6E4HVOP","created_at":"2026-07-05T11:43:35Z"}],"graph_snapshots":[{"event_id":"sha256:b36239260bf2c1ae7889623f8b45bdea90569e825a2ad9e3acab79feb61c22f6","target":"graph","created_at":"2026-07-05T11:43:35Z","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/2507.19522/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Mathematical models in neural networks are powerful tools for solving complex differential equations and optimizing their parameters; that is, solving the forward and inverse problems, respectively. A forward problem predicts the output of a network for a given input by optimizing weights and biases. An inverse problem finds equation parameters or coefficients that effectively model the data. A Physics-Informed Neural Network (PINN) can solve both problems. PINNs inject prior analytical information about the data into the cost function to improve model performance outside the training set boun","authors_text":"Aarush Gupta, Kendric Hsu, Syna Mathod","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-07-19T03:39:49Z","title":"Applications and Manipulations of Physics-Informed Neural Networks in Solving Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.19522","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:b8cfaac8568874918413b7edd18e9c95b3a61007239b6b17502babb528905f3d","target":"record","created_at":"2026-07-05T11:43:35Z","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":"187fa46572eef2fd1d071a752758781ef57a5a94fb4099a49fa39bf9ad357372","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-07-19T03:39:49Z","title_canon_sha256":"208f6b0411dd201058a519b9acc49118296c508f06871bd1757fab608a2d8df3"},"schema_version":"1.0","source":{"id":"2507.19522","kind":"arxiv","version":1}},"canonical_sha256":"af89c3d5cfce86601aa4e627f57177f5b1f74592ee17cf03a24af980db412f08","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af89c3d5cfce86601aa4e627f57177f5b1f74592ee17cf03a24af980db412f08","first_computed_at":"2026-07-05T11:43:35.658970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:43:35.658970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TcjGF9P3IwbEKFhZp2pUCHNII2jGMqQPP07yqA3BwRlP0c8iM83zy+RkiMqTFKNO5t7AoDvVTzsZ5W3pTrtdAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:43:35.659430Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.19522","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8cfaac8568874918413b7edd18e9c95b3a61007239b6b17502babb528905f3d","sha256:b36239260bf2c1ae7889623f8b45bdea90569e825a2ad9e3acab79feb61c22f6"],"state_sha256":"1ce821c9eec9653126831734d5ae81dc2d85c51e7224045e7b7d77c9bf4f2eb6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yLb3OAawcCdRKNlD1hlmT+1Vcs+m43jk7cXsTuILYxt+BScWQj0CDww8ASoUjegV6mCTKQ4XLhK64HxLikI7AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T13:07:20.113953Z","bundle_sha256":"5e7f451b9a0b7642b520480e5c7f2f31dd2279d4f41bca49b136bd658385e776"}}