{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:57TQEE3PWR7UGVJ5YN7YJD5ANM","short_pith_number":"pith:57TQEE3P","canonical_record":{"source":{"id":"2607.13382","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-15T02:21:24Z","cross_cats_sorted":["cs.NA","physics.comp-ph"],"title_canon_sha256":"7bee92737b479f95593cbc9bef6c4fe6de7e0a70d7c625b06ea8221641b23d72","abstract_canon_sha256":"300f2b73d9ebbf84cd1d935dfd1eadcae9ceede13578ad8ec6b3b1473046362d"},"schema_version":"1.0"},"canonical_sha256":"efe702136fb47f43553dc37f848fa06b3326cf9c7bee451a4069000757d5334f","source":{"kind":"arxiv","id":"2607.13382","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.13382","created_at":"2026-07-16T00:22:14Z"},{"alias_kind":"arxiv_version","alias_value":"2607.13382v1","created_at":"2026-07-16T00:22:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13382","created_at":"2026-07-16T00:22:14Z"},{"alias_kind":"pith_short_12","alias_value":"57TQEE3PWR7U","created_at":"2026-07-16T00:22:14Z"},{"alias_kind":"pith_short_16","alias_value":"57TQEE3PWR7UGVJ5","created_at":"2026-07-16T00:22:14Z"},{"alias_kind":"pith_short_8","alias_value":"57TQEE3P","created_at":"2026-07-16T00:22:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:57TQEE3PWR7UGVJ5YN7YJD5ANM","target":"record","payload":{"canonical_record":{"source":{"id":"2607.13382","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-15T02:21:24Z","cross_cats_sorted":["cs.NA","physics.comp-ph"],"title_canon_sha256":"7bee92737b479f95593cbc9bef6c4fe6de7e0a70d7c625b06ea8221641b23d72","abstract_canon_sha256":"300f2b73d9ebbf84cd1d935dfd1eadcae9ceede13578ad8ec6b3b1473046362d"},"schema_version":"1.0"},"canonical_sha256":"efe702136fb47f43553dc37f848fa06b3326cf9c7bee451a4069000757d5334f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T00:22:14.980747Z","signature_b64":"eVJj2rfGclc3IfKiE9F9HX/3/+AF3fd2zRO6I2Yu9GjeCUOusCDBV89U2BvGqYW7hYfNiVzQO5flRy5Lybz+Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efe702136fb47f43553dc37f848fa06b3326cf9c7bee451a4069000757d5334f","last_reissued_at":"2026-07-16T00:22:14.979844Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T00:22:14.979844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.13382","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":"2026-07-16T00:22:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"stIqme1lKIMqxrihgRx+7+ggY9HX6fZsQ0eZ6Hyy4E6fInXn98p/lKNccCdXLt6SE6ELVggzl7TbQH1IuPOHDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T19:31:09.904150Z"},"content_sha256":"9f119866f479d819bd90ebc53fd021653d048db1ee0a9d9b9c5762712ea4ac13","schema_version":"1.0","event_id":"sha256:9f119866f479d819bd90ebc53fd021653d048db1ee0a9d9b9c5762712ea4ac13"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:57TQEE3PWR7UGVJ5YN7YJD5ANM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Residual-Christoffel Sampling for Random Feature Collocation of Linear PDEs","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cs.NA","physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Jiale Linghu, Yangshuai Wang","submitted_at":"2026-07-15T02:21:24Z","abstract_excerpt":"Random feature collocation fixes a randomly generated trial space and determines its coefficients from a linear least-squares system. Stability then depends on whether the sampled residual equations represent the geometry induced by the differential operator. We construct an operator-aware discretization in which the operator-applied features determine both the collocation measure and a coefficient whitening map. The randomized scheme combines a residual-Christoffel density with inverse-density weights, while a deterministic scalar-row alternative maximizes successive regularized log-determina"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13382","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/2607.13382/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":"2026-07-16T00:22:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Nd9jhQEED1cNldDakom/YH6tU8TDNuR7t7Y9VAXYiK8WxWRBtoUX07rSam44HFXuAUooJJGH8O+pXvLspQ1Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T19:31:09.904646Z"},"content_sha256":"6adf4116e5e2646dc4a75852377a90e5605f8c75597936ada30f12e4c7f11231","schema_version":"1.0","event_id":"sha256:6adf4116e5e2646dc4a75852377a90e5605f8c75597936ada30f12e4c7f11231"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:57TQEE3PWR7UGVJ5YN7YJD5ANM","target":"integrity","payload":{"note":"DOI is split by whitespace or line breaks in the printed bibliography. Reconstructed DOI 10.1016/j.cma.2021.114129 resolves to 'Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations'. A reader following the printed text alone cannot reach it.","snippet":"Dong, S., Li, Z.: Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations. Computer Methods in Applied Me- chanics and Engineering387, 114129 (2021).https://doi.org/10.1016/j.","arxiv_id":"2607.13382","detector":"doi_compliance","evidence":{"ref_index":13,"verdict_class":"incontrovertible","resolved_title":"Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations","printed_excerpt":"10.1016/j.cma.2021","reconstructed_doi":"10.1016/j.cma.2021.114129"},"severity":"advisory","ref_index":13,"audited_at":"2026-08-02T05:30:49.194172Z","event_type":"pith.integrity.v1","detected_doi":"10.1016/j.cma.2021.114129","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"c50b009dbdf4af90c5c90719315bd582e55c0cbe398605e7bb5f813df9838165","paper_version":1,"verdict_class":"incontrovertible","resolved_title":"Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations","detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":17254,"payload_sha256":"9b2530d37a49544eb4159976f7e55570f6e35ae8ee8fdd413bc6ae0b631ee155","signature_b64":"sHtZXHQbyRTIoJSKJryeigpfhxhOPb81CG7daK7QTJqWuZpc/udxmBcXWijnJXrDYHx8MhF4XwOjQsguJ6h/Cw==","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":"2026-08-02T05:33:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6COF0DefqwIrC/Bd94aOVqsBt/ZF3nWJg+mZwz3O1Vqi7N08ZkYoUfFHByGjOCbJ0L9XVJNy9PvWeqImcseCBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T19:31:09.908390Z"},"content_sha256":"e129e6dc65b855d632191a9dabd70c80ed56ba0e5ec31664c1d188e36e618304","schema_version":"1.0","event_id":"sha256:e129e6dc65b855d632191a9dabd70c80ed56ba0e5ec31664c1d188e36e618304"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:57TQEE3PWR7UGVJ5YN7YJD5ANM","target":"integrity","payload":{"note":"DOI is split by whitespace or line breaks in the printed bibliography. Reconstructed DOI 10.1016/j.jcp.2015.04.045 resolves to 'Computing the ground state and dynamics of the nonlinear Schrödinger equation with nonlocal interactions via the nonunif'. A reader following the printed text alone cannot reach it.","snippet":"Bao, W., Jiang, S., Tang, Q., Zhang, Y.: Computing the ground state and dynamics of the nonlinear Schr¨ odinger equation with nonlocal interactions via the nonuniform FFT. Journal of Computational Physics296, 72–89 (2015).https://doi.org/10","arxiv_id":"2607.13382","detector":"doi_compliance","evidence":{"ref_index":6,"verdict_class":"incontrovertible","resolved_title":"Computing the ground state and dynamics of the nonlinear Schrödinger equation with nonlocal interactions via the nonuniform FFT","printed_excerpt":"10.1016/j","reconstructed_doi":"10.1016/j.jcp.2015.04.045"},"severity":"advisory","ref_index":6,"audited_at":"2026-08-02T05:30:49.194172Z","event_type":"pith.integrity.v1","detected_doi":"10.1016/j.jcp.2015.04.045","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"351e061b6b1ee1b8b11700990045c2d0491b99f240321cdecba781c9a8afa2f3","paper_version":1,"verdict_class":"incontrovertible","resolved_title":"Computing the ground state and dynamics of the nonlinear Schrödinger equation with nonlocal interactions via the nonuniform FFT","detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":17253,"payload_sha256":"58a75cd4863b51dfc9e77f4df7fe28f768ce55b29b16b5e63fdd8d00ef86fe9e","signature_b64":"eLorwzfNjauI4gUL7w8YUraEazqobP0kaDy0GodjcprZ7eFdwyYo6gTOUxxZtEZeOjCpyIRO8ABasWzongpDDg==","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":"2026-08-02T05:33:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q6bHSqKbJE5BMDUugXPYQ/49J5pBw5pVSTXAz8k0jmJSM9cCLUeDcXetd1PrccTXlSQ6/ih5LXffFjdFOvGuBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T19:31:09.908783Z"},"content_sha256":"8d2ee3c67cc9f095272731350304a7dce0a8879cc6875389a79d5ac3b0781f4d","schema_version":"1.0","event_id":"sha256:8d2ee3c67cc9f095272731350304a7dce0a8879cc6875389a79d5ac3b0781f4d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/57TQEE3PWR7UGVJ5YN7YJD5ANM/bundle.json","state_url":"https://pith.science/pith/57TQEE3PWR7UGVJ5YN7YJD5ANM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/57TQEE3PWR7UGVJ5YN7YJD5ANM/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":"2026-08-23T19:31:09Z","links":{"resolver":"https://pith.science/pith/57TQEE3PWR7UGVJ5YN7YJD5ANM","bundle":"https://pith.science/pith/57TQEE3PWR7UGVJ5YN7YJD5ANM/bundle.json","state":"https://pith.science/pith/57TQEE3PWR7UGVJ5YN7YJD5ANM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/57TQEE3PWR7UGVJ5YN7YJD5ANM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:57TQEE3PWR7UGVJ5YN7YJD5ANM","merge_version":"pith-open-graph-merge-v1","event_count":4,"valid_event_count":4,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"300f2b73d9ebbf84cd1d935dfd1eadcae9ceede13578ad8ec6b3b1473046362d","cross_cats_sorted":["cs.NA","physics.comp-ph"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-15T02:21:24Z","title_canon_sha256":"7bee92737b479f95593cbc9bef6c4fe6de7e0a70d7c625b06ea8221641b23d72"},"schema_version":"1.0","source":{"id":"2607.13382","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.13382","created_at":"2026-07-16T00:22:14Z"},{"alias_kind":"arxiv_version","alias_value":"2607.13382v1","created_at":"2026-07-16T00:22:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13382","created_at":"2026-07-16T00:22:14Z"},{"alias_kind":"pith_short_12","alias_value":"57TQEE3PWR7U","created_at":"2026-07-16T00:22:14Z"},{"alias_kind":"pith_short_16","alias_value":"57TQEE3PWR7UGVJ5","created_at":"2026-07-16T00:22:14Z"},{"alias_kind":"pith_short_8","alias_value":"57TQEE3P","created_at":"2026-07-16T00:22:14Z"}],"graph_snapshots":[{"event_id":"sha256:6adf4116e5e2646dc4a75852377a90e5605f8c75597936ada30f12e4c7f11231","target":"graph","created_at":"2026-07-16T00:22:14Z","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/2607.13382/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Random feature collocation fixes a randomly generated trial space and determines its coefficients from a linear least-squares system. Stability then depends on whether the sampled residual equations represent the geometry induced by the differential operator. We construct an operator-aware discretization in which the operator-applied features determine both the collocation measure and a coefficient whitening map. The randomized scheme combines a residual-Christoffel density with inverse-density weights, while a deterministic scalar-row alternative maximizes successive regularized log-determina","authors_text":"Jiale Linghu, Yangshuai Wang","cross_cats":["cs.NA","physics.comp-ph"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-15T02:21:24Z","title":"Residual-Christoffel Sampling for Random Feature Collocation of Linear PDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13382","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":"sha256:9f119866f479d819bd90ebc53fd021653d048db1ee0a9d9b9c5762712ea4ac13","target":"record","created_at":"2026-07-16T00:22:14Z","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":"300f2b73d9ebbf84cd1d935dfd1eadcae9ceede13578ad8ec6b3b1473046362d","cross_cats_sorted":["cs.NA","physics.comp-ph"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-15T02:21:24Z","title_canon_sha256":"7bee92737b479f95593cbc9bef6c4fe6de7e0a70d7c625b06ea8221641b23d72"},"schema_version":"1.0","source":{"id":"2607.13382","kind":"arxiv","version":1}},"canonical_sha256":"efe702136fb47f43553dc37f848fa06b3326cf9c7bee451a4069000757d5334f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efe702136fb47f43553dc37f848fa06b3326cf9c7bee451a4069000757d5334f","first_computed_at":"2026-07-16T00:22:14.979844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-16T00:22:14.979844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eVJj2rfGclc3IfKiE9F9HX/3/+AF3fd2zRO6I2Yu9GjeCUOusCDBV89U2BvGqYW7hYfNiVzQO5flRy5Lybz+Dw==","signature_status":"signed_v1","signed_at":"2026-07-16T00:22:14.980747Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.13382","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:8d2ee3c67cc9f095272731350304a7dce0a8879cc6875389a79d5ac3b0781f4d","sha256:e129e6dc65b855d632191a9dabd70c80ed56ba0e5ec31664c1d188e36e618304"]}],"invalid_events":[],"applied_event_ids":["sha256:9f119866f479d819bd90ebc53fd021653d048db1ee0a9d9b9c5762712ea4ac13","sha256:6adf4116e5e2646dc4a75852377a90e5605f8c75597936ada30f12e4c7f11231"],"state_sha256":"c768f6d6528e25ecf0c46199139e97a792168f274cc8ff368c46e06b30a20ce9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ltchL9eLGvWOAXkCggf1leeIT82Ck5NK0YmPL9N4kEQF5HYeqQAfjDz39TFfF8I7It+rd3jUXlQH23VMNo/9BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T19:31:09.911313Z","bundle_sha256":"05b9fa860073bca3a5c4d3b174c96269ef61265143c8300001e8ff63fa0a0418"}}