{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:K6ZY3UNNT65ZKEU3GLCD7POB4X","short_pith_number":"pith:K6ZY3UNN","canonical_record":{"source":{"id":"2607.23940","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-27T02:32:22Z","cross_cats_sorted":[],"title_canon_sha256":"1729a15a619cd6229a90b8584688cdbcb896505701bf3b1db2f1ef6d15beab5b","abstract_canon_sha256":"7c2b0bfe9649d202fd7fc51609a2896e02a3a52523b13155ca6d1eba5b5df9b5"},"schema_version":"1.0"},"canonical_sha256":"57b38dd1ad9fbb95129b32c43fbdc1e5f1a461cd13309057a883da1f7019053e","source":{"kind":"arxiv","id":"2607.23940","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.23940","created_at":"2026-07-28T01:23:36Z"},{"alias_kind":"arxiv_version","alias_value":"2607.23940v1","created_at":"2026-07-28T01:23:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.23940","created_at":"2026-07-28T01:23:36Z"},{"alias_kind":"pith_short_12","alias_value":"K6ZY3UNNT65Z","created_at":"2026-07-28T01:23:36Z"},{"alias_kind":"pith_short_16","alias_value":"K6ZY3UNNT65ZKEU3","created_at":"2026-07-28T01:23:36Z"},{"alias_kind":"pith_short_8","alias_value":"K6ZY3UNN","created_at":"2026-07-28T01:23:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:K6ZY3UNNT65ZKEU3GLCD7POB4X","target":"record","payload":{"canonical_record":{"source":{"id":"2607.23940","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-27T02:32:22Z","cross_cats_sorted":[],"title_canon_sha256":"1729a15a619cd6229a90b8584688cdbcb896505701bf3b1db2f1ef6d15beab5b","abstract_canon_sha256":"7c2b0bfe9649d202fd7fc51609a2896e02a3a52523b13155ca6d1eba5b5df9b5"},"schema_version":"1.0"},"canonical_sha256":"57b38dd1ad9fbb95129b32c43fbdc1e5f1a461cd13309057a883da1f7019053e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T01:23:36.871182Z","signature_b64":"az1ZlfHsUMyLEJu0YIBXQKf2avVNHAOZHfSORUxVCed19qeovGSyHp1zBGFWE7TL7Sr5rRKmS1CVCzXpdRkBCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57b38dd1ad9fbb95129b32c43fbdc1e5f1a461cd13309057a883da1f7019053e","last_reissued_at":"2026-07-28T01:23:36.870225Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T01:23:36.870225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.23940","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":"2026-07-28T01:23:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1qvc5GvtES4MkGNyamHy04nmI50fqSDAjFp6bf9UQH6aRwu0gJUdR02nKWsBtYRq7xolaqLWmDr2zU+S+rC3BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:16:11.192280Z"},"content_sha256":"5ffc10bc9509c00cd84df73d06b93f96af15fa84fb3fdd25a8d0124a8411aea0","schema_version":"1.0","event_id":"sha256:5ffc10bc9509c00cd84df73d06b93f96af15fa84fb3fdd25a8d0124a8411aea0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:K6ZY3UNNT65ZKEU3GLCD7POB4X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variational Boosting for Physics-Informed Neural Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Kaylee Vo, Pavlos Protopapas","submitted_at":"2026-07-27T02:32:22Z","abstract_excerpt":"Physics-Informed Neural Networks (PINNs) solve differential equations by minimizing the residual of a nonlinear operator over a neural parameterization of the solution. However, monolithic PINNs often suffer from ill-conditioning, spectral bias, and optimization instability.\n  We introduce a variational boosting framework in which solutions are constructed additively in function space. Each stage trains a weak learner whose converged correction satisfies a local orthogonality condition, equivalent to a projected functional gradient descent step onto the tangent space of the network's function "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23940","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/2607.23940/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":"2026-07-28T01:23:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"62LgSYVBXPeGvdy06ypp6gNJLcCvAAUYB2Koq7tjxctuvneaT2J4S2XaYYAQK7RfQGXmnK03pHKOGgr0xZyVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:16:11.193317Z"},"content_sha256":"c7ffc1b505b4cd799032dbe6780d018ae40369ba973732845f448024ff3c97ff","schema_version":"1.0","event_id":"sha256:c7ffc1b505b4cd799032dbe6780d018ae40369ba973732845f448024ff3c97ff"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:K6ZY3UNNT65ZKEU3GLCD7POB4X","target":"integrity","payload":{"note":"DOI is split by whitespace or line breaks in the printed bibliography. Reconstructed DOI 10.1016/j.jcp.2018.10.045 resolves to 'Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear'. A reader following the printed text alone cannot reach it.","snippet":"doi: 10.1016/j. jcp.2018.10.045. URLhttps://doi.org/10.1016/j.jcp.2018.10.045. Emilien Seiler, Wanzhou Lei, and Pavlos Protopapas. Stiff transfer learning for physics-informed neural networks.ArXiv.org,","arxiv_id":"2607.23940","detector":"doi_compliance","evidence":{"ref_index":2019,"verdict_class":"incontrovertible","resolved_title":"Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations","printed_excerpt":"10.1016/j","reconstructed_doi":"10.1016/j.jcp.2018.10.045"},"severity":"advisory","ref_index":2019,"audited_at":"2026-07-31T23:42:06.212462Z","event_type":"pith.integrity.v1","detected_doi":"10.1016/j.jcp.2018.10.045","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"b1f886ee99b62bc420062c99a3561ebad0e1104228acac3450ba223fdd34e63d","paper_version":1,"verdict_class":"incontrovertible","resolved_title":"Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations","detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":14613,"payload_sha256":"5fa9b2522a0e40cb40a66a578afbe63c6a02ba021063458d98acabb684157286","signature_b64":"r/lhbuARPl4H1cN2Cr4PwoXUjHOJGLIK3WMynI9NklqzXe38YfP5nc8WnLOgt8rbQgLLZPrDiQowA4zHr1tGAw==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-31T23:46:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"psS3c0nbmo2qcdfWjvVNz+kwRqEZy1pjS/G7550SPZd2Gv1AkfdW+hSo9rvBpPxekKock42Tv7RFLqnU8htGBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:16:11.197195Z"},"content_sha256":"0559973d2d611785df16847b97a09b0bd436369626eca0290186dfbd9bd65ece","schema_version":"1.0","event_id":"sha256:0559973d2d611785df16847b97a09b0bd436369626eca0290186dfbd9bd65ece"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K6ZY3UNNT65ZKEU3GLCD7POB4X/bundle.json","state_url":"https://pith.science/pith/K6ZY3UNNT65ZKEU3GLCD7POB4X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K6ZY3UNNT65ZKEU3GLCD7POB4X/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":"2026-08-09T04:16:11Z","links":{"resolver":"https://pith.science/pith/K6ZY3UNNT65ZKEU3GLCD7POB4X","bundle":"https://pith.science/pith/K6ZY3UNNT65ZKEU3GLCD7POB4X/bundle.json","state":"https://pith.science/pith/K6ZY3UNNT65ZKEU3GLCD7POB4X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K6ZY3UNNT65ZKEU3GLCD7POB4X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:K6ZY3UNNT65ZKEU3GLCD7POB4X","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7c2b0bfe9649d202fd7fc51609a2896e02a3a52523b13155ca6d1eba5b5df9b5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-27T02:32:22Z","title_canon_sha256":"1729a15a619cd6229a90b8584688cdbcb896505701bf3b1db2f1ef6d15beab5b"},"schema_version":"1.0","source":{"id":"2607.23940","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.23940","created_at":"2026-07-28T01:23:36Z"},{"alias_kind":"arxiv_version","alias_value":"2607.23940v1","created_at":"2026-07-28T01:23:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.23940","created_at":"2026-07-28T01:23:36Z"},{"alias_kind":"pith_short_12","alias_value":"K6ZY3UNNT65Z","created_at":"2026-07-28T01:23:36Z"},{"alias_kind":"pith_short_16","alias_value":"K6ZY3UNNT65ZKEU3","created_at":"2026-07-28T01:23:36Z"},{"alias_kind":"pith_short_8","alias_value":"K6ZY3UNN","created_at":"2026-07-28T01:23:36Z"}],"graph_snapshots":[{"event_id":"sha256:c7ffc1b505b4cd799032dbe6780d018ae40369ba973732845f448024ff3c97ff","target":"graph","created_at":"2026-07-28T01:23:36Z","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/2607.23940/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Physics-Informed Neural Networks (PINNs) solve differential equations by minimizing the residual of a nonlinear operator over a neural parameterization of the solution. However, monolithic PINNs often suffer from ill-conditioning, spectral bias, and optimization instability.\n  We introduce a variational boosting framework in which solutions are constructed additively in function space. Each stage trains a weak learner whose converged correction satisfies a local orthogonality condition, equivalent to a projected functional gradient descent step onto the tangent space of the network's function ","authors_text":"Kaylee Vo, Pavlos Protopapas","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-27T02:32:22Z","title":"Variational Boosting for Physics-Informed Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23940","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":"sha256:5ffc10bc9509c00cd84df73d06b93f96af15fa84fb3fdd25a8d0124a8411aea0","target":"record","created_at":"2026-07-28T01:23:36Z","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":"7c2b0bfe9649d202fd7fc51609a2896e02a3a52523b13155ca6d1eba5b5df9b5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-27T02:32:22Z","title_canon_sha256":"1729a15a619cd6229a90b8584688cdbcb896505701bf3b1db2f1ef6d15beab5b"},"schema_version":"1.0","source":{"id":"2607.23940","kind":"arxiv","version":1}},"canonical_sha256":"57b38dd1ad9fbb95129b32c43fbdc1e5f1a461cd13309057a883da1f7019053e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57b38dd1ad9fbb95129b32c43fbdc1e5f1a461cd13309057a883da1f7019053e","first_computed_at":"2026-07-28T01:23:36.870225Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-28T01:23:36.870225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"az1ZlfHsUMyLEJu0YIBXQKf2avVNHAOZHfSORUxVCed19qeovGSyHp1zBGFWE7TL7Sr5rRKmS1CVCzXpdRkBCA==","signature_status":"signed_v1","signed_at":"2026-07-28T01:23:36.871182Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.23940","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ffc10bc9509c00cd84df73d06b93f96af15fa84fb3fdd25a8d0124a8411aea0","sha256:c7ffc1b505b4cd799032dbe6780d018ae40369ba973732845f448024ff3c97ff","sha256:0559973d2d611785df16847b97a09b0bd436369626eca0290186dfbd9bd65ece"],"state_sha256":"d709694ab4da20761cc8c47cade42b3f5bcbce1fc4484d8f56c31577e25d8530"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U6hdczQqJB6VtCf4S99rlKqDQWxh2b8mYwmTY4sX1Rwsa/1qRwGdXt92qDNHbvqPW55H+bn5Hi0lLxY4w9V3Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T04:16:11.204962Z","bundle_sha256":"c1c31bc4ac672a7771a50834a0f5ed9a995293281a239fea8d5a21f25a65059e"}}