{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TMYMXTSU63C3W42YHQDWWB2TAQ","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":"84d607a91042cb02aa5c5ab5d99efcd423342b3642a398914d8a8ac941619771","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-24T05:37:11Z","title_canon_sha256":"219fa7708cf41b0d8cd2455e43b3ccf53d0e29106f812c2f4771bbb611c538de"},"schema_version":"1.0","source":{"id":"2605.24876","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.24876","created_at":"2026-05-26T01:04:03Z"},{"alias_kind":"arxiv_version","alias_value":"2605.24876v1","created_at":"2026-05-26T01:04:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.24876","created_at":"2026-05-26T01:04:03Z"},{"alias_kind":"pith_short_12","alias_value":"TMYMXTSU63C3","created_at":"2026-05-26T01:04:03Z"},{"alias_kind":"pith_short_16","alias_value":"TMYMXTSU63C3W42Y","created_at":"2026-05-26T01:04:03Z"},{"alias_kind":"pith_short_8","alias_value":"TMYMXTSU","created_at":"2026-05-26T01:04:03Z"}],"graph_snapshots":[{"event_id":"sha256:610dbfb2acd4a649790c767eea34bdb948f5b691b25aa98263c9ef7fe331d47f","target":"graph","created_at":"2026-05-26T01:04:03Z","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/2605.24876/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a novel neural operator architecture designed to approximate solutions of linear elliptic partial differential equations with high-contrast, spatially varying coefficients. The network, termed the Iterated V-shaped Net (IV-Net), realizes a mapping from the input coefficients and righthand side to the corresponding solution field. The architecture of IV-Net is informed by, and closely resembles, a V-cycle multigrid solver. The IV-Net model is parameterized via convolutional layers defined in the physical domain. For coercive problems with highly heterogeneous coefficients, the prop","authors_text":"George Biros, Shan Zhong","cross_cats":["cs.LG","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-24T05:37:11Z","title":"IV-Net: A neural network for elliptic PDEs with random and highly varying coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24876","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":"sha256:01b3acfc66a916938f5cc197b5dca1bb4b8664a0418078dba41e3ad2a82de715","target":"record","created_at":"2026-05-26T01:04:03Z","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":"84d607a91042cb02aa5c5ab5d99efcd423342b3642a398914d8a8ac941619771","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-24T05:37:11Z","title_canon_sha256":"219fa7708cf41b0d8cd2455e43b3ccf53d0e29106f812c2f4771bbb611c538de"},"schema_version":"1.0","source":{"id":"2605.24876","kind":"arxiv","version":1}},"canonical_sha256":"9b30cbce54f6c5bb73583c076b0753040cd54f56b55b38d60a7313effb345310","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b30cbce54f6c5bb73583c076b0753040cd54f56b55b38d60a7313effb345310","first_computed_at":"2026-05-26T01:04:03.039150Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T01:04:03.039150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J5I9jEKKKqIfVCrUnwakQ70Q5aukgOGQcCkLmXaABsLrWgGjVnKgw8R2sIgnOgGZt0odgEarSZMkkPclrAWxBw==","signature_status":"signed_v1","signed_at":"2026-05-26T01:04:03.039967Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.24876","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01b3acfc66a916938f5cc197b5dca1bb4b8664a0418078dba41e3ad2a82de715","sha256:610dbfb2acd4a649790c767eea34bdb948f5b691b25aa98263c9ef7fe331d47f"],"state_sha256":"66faa43dac9683a4345cefc3bb74f9b5db4d686bab51b16636b32e3e9c32b0c7"}