{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:RC2KUCIAK6ZR6IUGKSDXBJDWDJ","short_pith_number":"pith:RC2KUCIA","canonical_record":{"source":{"id":"2606.21828","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-20T01:34:19Z","cross_cats_sorted":["cs.LG","cs.NA"],"title_canon_sha256":"0498bced63ca624d6396bc8edb3c5116b2d1cb9716dc7e53e76ce7a8038477ed","abstract_canon_sha256":"36f8db9ee49cc0dafb9d538779739a8ce9f4bebf572b5afce36fd89774557f78"},"schema_version":"1.0"},"canonical_sha256":"88b4aa090057b31f2286548770a4761a400b40537c6cdadd8b1ea9f583c25864","source":{"kind":"arxiv","id":"2606.21828","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.21828","created_at":"2026-06-23T02:13:00Z"},{"alias_kind":"arxiv_version","alias_value":"2606.21828v1","created_at":"2026-06-23T02:13:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.21828","created_at":"2026-06-23T02:13:00Z"},{"alias_kind":"pith_short_12","alias_value":"RC2KUCIAK6ZR","created_at":"2026-06-23T02:13:00Z"},{"alias_kind":"pith_short_16","alias_value":"RC2KUCIAK6ZR6IUG","created_at":"2026-06-23T02:13:00Z"},{"alias_kind":"pith_short_8","alias_value":"RC2KUCIA","created_at":"2026-06-23T02:13:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:RC2KUCIAK6ZR6IUGKSDXBJDWDJ","target":"record","payload":{"canonical_record":{"source":{"id":"2606.21828","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-20T01:34:19Z","cross_cats_sorted":["cs.LG","cs.NA"],"title_canon_sha256":"0498bced63ca624d6396bc8edb3c5116b2d1cb9716dc7e53e76ce7a8038477ed","abstract_canon_sha256":"36f8db9ee49cc0dafb9d538779739a8ce9f4bebf572b5afce36fd89774557f78"},"schema_version":"1.0"},"canonical_sha256":"88b4aa090057b31f2286548770a4761a400b40537c6cdadd8b1ea9f583c25864","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:00.200482Z","signature_b64":"wrZodGtejBX+5bxJyglFrpbwmmRQ9jBafprscQpEgFArs9ANb7k+KOWSsDScZe1Getvfp02kf+5K0dZwKFRgBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88b4aa090057b31f2286548770a4761a400b40537c6cdadd8b1ea9f583c25864","last_reissued_at":"2026-06-23T02:13:00.200001Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:00.200001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.21828","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":"2026-06-23T02:13:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rMrpgUA9Gj4vcHfpB3qLjFiQE7dHmMt13k5TuJ9MaHBb66gEE5ivdh6Ywb+5zXe57rq4x+4KWLGr0ohzJNb4BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T16:30:09.855927Z"},"content_sha256":"079e61efb1648fef1bf6a6fc555e52b31740bc409a801bfaa04eadc4b4eb47a1","schema_version":"1.0","event_id":"sha256:079e61efb1648fef1bf6a6fc555e52b31740bc409a801bfaa04eadc4b4eb47a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:RC2KUCIAK6ZR6IUGKSDXBJDWDJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectrally Safe Neural Operator Warm-Starts for Large-Scale Newton Solvers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA"],"primary_cat":"math.NA","authors_text":"George Em Karniadakis, Jaemin Oh, Jerome Darbon, Youngkyu Lee","submitted_at":"2026-06-20T01:34:19Z","abstract_excerpt":"Neural operators are increasingly used to warm-start Newton solvers for nonlinear PDEs, on the premise that a low test error places the initial guess inside the basin of attraction. We show that this premise is unreliable. An operator trained to the relative \\(L^2\\) error \\(O(10^{-3})\\) can still produce an initial state in which the discrete Jacobian is indefinite, because the mean-squared training controls error on average while leaving localized pointwise violations of the underlying physics. For a nearly incompressible hyperelasticity problem, we trace this to the predicted volume change: "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21828","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/2606.21828/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":"2026-06-23T02:13:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MXgxZTnUo8cidVml227RwTfWUN9lv3CZQxbr9WqS2H9ZIHi3W/qt5WePF+caCbXeU0zYJQfm8QqY2fMo3sL+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T16:30:09.856328Z"},"content_sha256":"4906106be22d7c5b42a54b71e9591b3d190bc8c2399e7714333b02e1171e34d7","schema_version":"1.0","event_id":"sha256:4906106be22d7c5b42a54b71e9591b3d190bc8c2399e7714333b02e1171e34d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RC2KUCIAK6ZR6IUGKSDXBJDWDJ/bundle.json","state_url":"https://pith.science/pith/RC2KUCIAK6ZR6IUGKSDXBJDWDJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RC2KUCIAK6ZR6IUGKSDXBJDWDJ/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":"2026-06-24T16:30:09Z","links":{"resolver":"https://pith.science/pith/RC2KUCIAK6ZR6IUGKSDXBJDWDJ","bundle":"https://pith.science/pith/RC2KUCIAK6ZR6IUGKSDXBJDWDJ/bundle.json","state":"https://pith.science/pith/RC2KUCIAK6ZR6IUGKSDXBJDWDJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RC2KUCIAK6ZR6IUGKSDXBJDWDJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RC2KUCIAK6ZR6IUGKSDXBJDWDJ","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":"36f8db9ee49cc0dafb9d538779739a8ce9f4bebf572b5afce36fd89774557f78","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-20T01:34:19Z","title_canon_sha256":"0498bced63ca624d6396bc8edb3c5116b2d1cb9716dc7e53e76ce7a8038477ed"},"schema_version":"1.0","source":{"id":"2606.21828","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.21828","created_at":"2026-06-23T02:13:00Z"},{"alias_kind":"arxiv_version","alias_value":"2606.21828v1","created_at":"2026-06-23T02:13:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.21828","created_at":"2026-06-23T02:13:00Z"},{"alias_kind":"pith_short_12","alias_value":"RC2KUCIAK6ZR","created_at":"2026-06-23T02:13:00Z"},{"alias_kind":"pith_short_16","alias_value":"RC2KUCIAK6ZR6IUG","created_at":"2026-06-23T02:13:00Z"},{"alias_kind":"pith_short_8","alias_value":"RC2KUCIA","created_at":"2026-06-23T02:13:00Z"}],"graph_snapshots":[{"event_id":"sha256:4906106be22d7c5b42a54b71e9591b3d190bc8c2399e7714333b02e1171e34d7","target":"graph","created_at":"2026-06-23T02:13:00Z","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/2606.21828/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Neural operators are increasingly used to warm-start Newton solvers for nonlinear PDEs, on the premise that a low test error places the initial guess inside the basin of attraction. We show that this premise is unreliable. An operator trained to the relative \\(L^2\\) error \\(O(10^{-3})\\) can still produce an initial state in which the discrete Jacobian is indefinite, because the mean-squared training controls error on average while leaving localized pointwise violations of the underlying physics. For a nearly incompressible hyperelasticity problem, we trace this to the predicted volume change: ","authors_text":"George Em Karniadakis, Jaemin Oh, Jerome Darbon, Youngkyu Lee","cross_cats":["cs.LG","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-20T01:34:19Z","title":"Spectrally Safe Neural Operator Warm-Starts for Large-Scale Newton Solvers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21828","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":"sha256:079e61efb1648fef1bf6a6fc555e52b31740bc409a801bfaa04eadc4b4eb47a1","target":"record","created_at":"2026-06-23T02:13:00Z","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":"36f8db9ee49cc0dafb9d538779739a8ce9f4bebf572b5afce36fd89774557f78","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-20T01:34:19Z","title_canon_sha256":"0498bced63ca624d6396bc8edb3c5116b2d1cb9716dc7e53e76ce7a8038477ed"},"schema_version":"1.0","source":{"id":"2606.21828","kind":"arxiv","version":1}},"canonical_sha256":"88b4aa090057b31f2286548770a4761a400b40537c6cdadd8b1ea9f583c25864","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88b4aa090057b31f2286548770a4761a400b40537c6cdadd8b1ea9f583c25864","first_computed_at":"2026-06-23T02:13:00.200001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T02:13:00.200001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wrZodGtejBX+5bxJyglFrpbwmmRQ9jBafprscQpEgFArs9ANb7k+KOWSsDScZe1Getvfp02kf+5K0dZwKFRgBA==","signature_status":"signed_v1","signed_at":"2026-06-23T02:13:00.200482Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.21828","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:079e61efb1648fef1bf6a6fc555e52b31740bc409a801bfaa04eadc4b4eb47a1","sha256:4906106be22d7c5b42a54b71e9591b3d190bc8c2399e7714333b02e1171e34d7"],"state_sha256":"20cc8a2483784428ffb060b8b0509183882880278ef4e3039b7fcec737201bd1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XXQDKDCg0TUKGFwiCjFxW4LmYzBO2PHlbmjeUQvqphRorKhMzZvy4VprInNkRX1uUGOLC9Cfm9pgwvZVVlChDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T16:30:09.858439Z","bundle_sha256":"db6c303d586b7190ad394ecafe2be14209b4d675e1b437ccc7e416876799bfd2"}}