{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:XP5JPXSRZOKOP36QSNXOIDW2GN","short_pith_number":"pith:XP5JPXSR","schema_version":"1.0","canonical_sha256":"bbfa97de51cb94e7efd0936ee40eda3354c68fe736f3457c0f7096ccbcf39112","source":{"kind":"arxiv","id":"2209.14977","version":4},"attestation_state":"computed","paper":{"title":"Transformer Meets Boundary Value Inverse Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.LG","authors_text":"Long Chen, Ruchi Guo, Shuhao Cao","submitted_at":"2022-09-29T17:45:25Z","abstract_excerpt":"A Transformer-based deep direct sampling method is proposed for electrical impedance tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned inverse operator between carefully designed data and the reconstructed images. An effort is made to give a specific example to a fundamental question: whether and how one can benefit from the theoretical structure of a mathematical problem to develop task-oriented and structure-conforming deep neural networks? Specifically, inspired by direct sampling methods fo"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2209.14977","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-09-29T17:45:25Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"ce19cf3d3ff521561b97e8ecbdbac2f4279fcd7822f2cd6e9e4899ffe056ff7d","abstract_canon_sha256":"830eb144686d76a592f4cb71c01cd53c6925cb709ab3f27c690ccedf02aa9c82"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:48:25.651367Z","signature_b64":"hmo00oPwtUHZEnhXKeqlA7XsjWq2upk9QagvzgFh69EinEnZBc8XP8QxqToGspY1tjuHQo0lsv6z/kQlCROGDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbfa97de51cb94e7efd0936ee40eda3354c68fe736f3457c0f7096ccbcf39112","last_reissued_at":"2026-07-05T05:48:25.650842Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:48:25.650842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transformer Meets Boundary Value Inverse Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.LG","authors_text":"Long Chen, Ruchi Guo, Shuhao Cao","submitted_at":"2022-09-29T17:45:25Z","abstract_excerpt":"A Transformer-based deep direct sampling method is proposed for electrical impedance tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned inverse operator between carefully designed data and the reconstructed images. An effort is made to give a specific example to a fundamental question: whether and how one can benefit from the theoretical structure of a mathematical problem to develop task-oriented and structure-conforming deep neural networks? Specifically, inspired by direct sampling methods fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.14977","kind":"arxiv","version":4},"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/2209.14977/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2209.14977","created_at":"2026-07-05T05:48:25.650900+00:00"},{"alias_kind":"arxiv_version","alias_value":"2209.14977v4","created_at":"2026-07-05T05:48:25.650900+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.14977","created_at":"2026-07-05T05:48:25.650900+00:00"},{"alias_kind":"pith_short_12","alias_value":"XP5JPXSRZOKO","created_at":"2026-07-05T05:48:25.650900+00:00"},{"alias_kind":"pith_short_16","alias_value":"XP5JPXSRZOKOP36Q","created_at":"2026-07-05T05:48:25.650900+00:00"},{"alias_kind":"pith_short_8","alias_value":"XP5JPXSR","created_at":"2026-07-05T05:48:25.650900+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.14475","citing_title":"Point Cloud Neural Operator for Parametric PDEs on Complex and Variable Geometries","ref_index":99,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XP5JPXSRZOKOP36QSNXOIDW2GN","json":"https://pith.science/pith/XP5JPXSRZOKOP36QSNXOIDW2GN.json","graph_json":"https://pith.science/api/pith-number/XP5JPXSRZOKOP36QSNXOIDW2GN/graph.json","events_json":"https://pith.science/api/pith-number/XP5JPXSRZOKOP36QSNXOIDW2GN/events.json","paper":"https://pith.science/paper/XP5JPXSR"},"agent_actions":{"view_html":"https://pith.science/pith/XP5JPXSRZOKOP36QSNXOIDW2GN","download_json":"https://pith.science/pith/XP5JPXSRZOKOP36QSNXOIDW2GN.json","view_paper":"https://pith.science/paper/XP5JPXSR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2209.14977&json=true","fetch_graph":"https://pith.science/api/pith-number/XP5JPXSRZOKOP36QSNXOIDW2GN/graph.json","fetch_events":"https://pith.science/api/pith-number/XP5JPXSRZOKOP36QSNXOIDW2GN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XP5JPXSRZOKOP36QSNXOIDW2GN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XP5JPXSRZOKOP36QSNXOIDW2GN/action/storage_attestation","attest_author":"https://pith.science/pith/XP5JPXSRZOKOP36QSNXOIDW2GN/action/author_attestation","sign_citation":"https://pith.science/pith/XP5JPXSRZOKOP36QSNXOIDW2GN/action/citation_signature","submit_replication":"https://pith.science/pith/XP5JPXSRZOKOP36QSNXOIDW2GN/action/replication_record"}},"created_at":"2026-07-05T05:48:25.650900+00:00","updated_at":"2026-07-05T05:48:25.650900+00:00"}