{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:2INVOHUCHWDEDI4OXQSAY3LKN3","short_pith_number":"pith:2INVOHUC","canonical_record":{"source":{"id":"2408.08540","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-08-16T05:52:29Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"952324614f4f7dc4c791ec6abc240298fc4bf154b974d38a8f8ac859128c813f","abstract_canon_sha256":"1cdf8145ea8913805b92c6210d9f170aee2977fbdf04b8dd8820482bf614be21"},"schema_version":"1.0"},"canonical_sha256":"d21b571e823d8641a38ebc240c6d6a6eca2ae6274af810650bc491675a5c962d","source":{"kind":"arxiv","id":"2408.08540","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.08540","created_at":"2026-07-05T11:16:50Z"},{"alias_kind":"arxiv_version","alias_value":"2408.08540v3","created_at":"2026-07-05T11:16:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.08540","created_at":"2026-07-05T11:16:50Z"},{"alias_kind":"pith_short_12","alias_value":"2INVOHUCHWDE","created_at":"2026-07-05T11:16:50Z"},{"alias_kind":"pith_short_16","alias_value":"2INVOHUCHWDEDI4O","created_at":"2026-07-05T11:16:50Z"},{"alias_kind":"pith_short_8","alias_value":"2INVOHUC","created_at":"2026-07-05T11:16:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:2INVOHUCHWDEDI4OXQSAY3LKN3","target":"record","payload":{"canonical_record":{"source":{"id":"2408.08540","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-08-16T05:52:29Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"952324614f4f7dc4c791ec6abc240298fc4bf154b974d38a8f8ac859128c813f","abstract_canon_sha256":"1cdf8145ea8913805b92c6210d9f170aee2977fbdf04b8dd8820482bf614be21"},"schema_version":"1.0"},"canonical_sha256":"d21b571e823d8641a38ebc240c6d6a6eca2ae6274af810650bc491675a5c962d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:16:50.376817Z","signature_b64":"hfHMu3rDJHV+Q8bow0lVntYQHPmjFL6R0jiHpPnSlAIVscoKwLlGjiPig3yGpD9+PZ/swkcGPsT3JsHN0GmJBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d21b571e823d8641a38ebc240c6d6a6eca2ae6274af810650bc491675a5c962d","last_reissued_at":"2026-07-05T11:16:50.376087Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:16:50.376087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2408.08540","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:16:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ClwEYSks+Vk7gouyqPeT9+7U8YxzX+V+f5kWvoYIR9oNh6E8PQ2FmutTMjzriIFyHmxQRV9tfLGjQepd2im/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T13:11:04.705784Z"},"content_sha256":"cfa3ec2f49d61fa809365089ab7c10c9d649aa0594696b63fa9fa50077c48d4f","schema_version":"1.0","event_id":"sha256:cfa3ec2f49d61fa809365089ab7c10c9d649aa0594696b63fa9fa50077c48d4f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:2INVOHUCHWDEDI4OXQSAY3LKN3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Hybrid Iterative Neural Solver Based on Spectral Analysis for Parametric PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Chen Cui, Kai Jiang, Shi Shu, Yun Liu","submitted_at":"2024-08-16T05:52:29Z","abstract_excerpt":"Deep learning-based hybrid iterative methods (DL-HIM) have emerged as a promising approach for designing fast neural solvers to tackle large-scale sparse linear systems. DL-HIM combine the smoothing effect of simple iterative methods with the spectral bias of neural networks, which allows them to effectively eliminate both high-frequency and low-frequency error components. However, their efficiency may decrease if simple iterative methods can not provide effective smoothing, making it difficult for the neural network to learn mid-frequency and high-frequency components. This paper first conduc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.08540","kind":"arxiv","version":3},"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/2408.08540/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":"2026-07-05T11:16:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v4aiMx1K6FiGbr8EzJrBwm3WL1e4skqH6DyLIqBwYf5qzgmu14hBGkcghYGg9RdpBt7ko375DNO+odVlDxyHDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T13:11:04.706080Z"},"content_sha256":"04afdc1f26778cb8db4466e88ea337779c7c39f41e7f80ca2d3a80284590f632","schema_version":"1.0","event_id":"sha256:04afdc1f26778cb8db4466e88ea337779c7c39f41e7f80ca2d3a80284590f632"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2INVOHUCHWDEDI4OXQSAY3LKN3/bundle.json","state_url":"https://pith.science/pith/2INVOHUCHWDEDI4OXQSAY3LKN3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2INVOHUCHWDEDI4OXQSAY3LKN3/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":"2026-08-14T13:11:04Z","links":{"resolver":"https://pith.science/pith/2INVOHUCHWDEDI4OXQSAY3LKN3","bundle":"https://pith.science/pith/2INVOHUCHWDEDI4OXQSAY3LKN3/bundle.json","state":"https://pith.science/pith/2INVOHUCHWDEDI4OXQSAY3LKN3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2INVOHUCHWDEDI4OXQSAY3LKN3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:2INVOHUCHWDEDI4OXQSAY3LKN3","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":"1cdf8145ea8913805b92c6210d9f170aee2977fbdf04b8dd8820482bf614be21","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-08-16T05:52:29Z","title_canon_sha256":"952324614f4f7dc4c791ec6abc240298fc4bf154b974d38a8f8ac859128c813f"},"schema_version":"1.0","source":{"id":"2408.08540","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.08540","created_at":"2026-07-05T11:16:50Z"},{"alias_kind":"arxiv_version","alias_value":"2408.08540v3","created_at":"2026-07-05T11:16:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.08540","created_at":"2026-07-05T11:16:50Z"},{"alias_kind":"pith_short_12","alias_value":"2INVOHUCHWDE","created_at":"2026-07-05T11:16:50Z"},{"alias_kind":"pith_short_16","alias_value":"2INVOHUCHWDEDI4O","created_at":"2026-07-05T11:16:50Z"},{"alias_kind":"pith_short_8","alias_value":"2INVOHUC","created_at":"2026-07-05T11:16:50Z"}],"graph_snapshots":[{"event_id":"sha256:04afdc1f26778cb8db4466e88ea337779c7c39f41e7f80ca2d3a80284590f632","target":"graph","created_at":"2026-07-05T11:16:50Z","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/2408.08540/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Deep learning-based hybrid iterative methods (DL-HIM) have emerged as a promising approach for designing fast neural solvers to tackle large-scale sparse linear systems. DL-HIM combine the smoothing effect of simple iterative methods with the spectral bias of neural networks, which allows them to effectively eliminate both high-frequency and low-frequency error components. However, their efficiency may decrease if simple iterative methods can not provide effective smoothing, making it difficult for the neural network to learn mid-frequency and high-frequency components. This paper first conduc","authors_text":"Chen Cui, Kai Jiang, Shi Shu, Yun Liu","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-08-16T05:52:29Z","title":"A Hybrid Iterative Neural Solver Based on Spectral Analysis for Parametric PDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.08540","kind":"arxiv","version":3},"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:cfa3ec2f49d61fa809365089ab7c10c9d649aa0594696b63fa9fa50077c48d4f","target":"record","created_at":"2026-07-05T11:16:50Z","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":"1cdf8145ea8913805b92c6210d9f170aee2977fbdf04b8dd8820482bf614be21","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-08-16T05:52:29Z","title_canon_sha256":"952324614f4f7dc4c791ec6abc240298fc4bf154b974d38a8f8ac859128c813f"},"schema_version":"1.0","source":{"id":"2408.08540","kind":"arxiv","version":3}},"canonical_sha256":"d21b571e823d8641a38ebc240c6d6a6eca2ae6274af810650bc491675a5c962d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d21b571e823d8641a38ebc240c6d6a6eca2ae6274af810650bc491675a5c962d","first_computed_at":"2026-07-05T11:16:50.376087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:16:50.376087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hfHMu3rDJHV+Q8bow0lVntYQHPmjFL6R0jiHpPnSlAIVscoKwLlGjiPig3yGpD9+PZ/swkcGPsT3JsHN0GmJBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:16:50.376817Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.08540","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfa3ec2f49d61fa809365089ab7c10c9d649aa0594696b63fa9fa50077c48d4f","sha256:04afdc1f26778cb8db4466e88ea337779c7c39f41e7f80ca2d3a80284590f632"],"state_sha256":"8acd21dc6aa96b292583d27052109092b76e408f7d187f6318109d29680a81b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OTRftxeOgWbynClJw0wQ0GOhahPiRp5YuUn1HGqp2z5ogP0MxOaBsdEnCXfZzl8Qcyu+peibI1i5SSHHZtZ6Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T13:11:04.708517Z","bundle_sha256":"3d7c5fc893816d643edaec9e5fa3740f0cdacf089f6c594b5b8df50629d245a4"}}