{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:WK7OOFKXHWJRQS7UHPEXZBOHZL","short_pith_number":"pith:WK7OOFKX","canonical_record":{"source":{"id":"2403.16380","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2024-03-25T02:53:32Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"afbb7542f0e6f4b84b2a6e81adaffe85521ade4bd439c53475aef58f74fceb6e","abstract_canon_sha256":"261d3dbcd87cd88d17ba06ac8e4e9a1910dc33bcdacafaa4161a82c3c673078c"},"schema_version":"1.0"},"canonical_sha256":"b2bee715573d93184bf43bc97c85c7cad77035332e1219e32d20d0f35acea332","source":{"kind":"arxiv","id":"2403.16380","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.16380","created_at":"2026-07-05T08:00:14Z"},{"alias_kind":"arxiv_version","alias_value":"2403.16380v1","created_at":"2026-07-05T08:00:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.16380","created_at":"2026-07-05T08:00:14Z"},{"alias_kind":"pith_short_12","alias_value":"WK7OOFKXHWJR","created_at":"2026-07-05T08:00:14Z"},{"alias_kind":"pith_short_16","alias_value":"WK7OOFKXHWJRQS7U","created_at":"2026-07-05T08:00:14Z"},{"alias_kind":"pith_short_8","alias_value":"WK7OOFKX","created_at":"2026-07-05T08:00:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:WK7OOFKXHWJRQS7UHPEXZBOHZL","target":"record","payload":{"canonical_record":{"source":{"id":"2403.16380","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2024-03-25T02:53:32Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"afbb7542f0e6f4b84b2a6e81adaffe85521ade4bd439c53475aef58f74fceb6e","abstract_canon_sha256":"261d3dbcd87cd88d17ba06ac8e4e9a1910dc33bcdacafaa4161a82c3c673078c"},"schema_version":"1.0"},"canonical_sha256":"b2bee715573d93184bf43bc97c85c7cad77035332e1219e32d20d0f35acea332","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:00:14.878743Z","signature_b64":"zvR1pI7/37NVkurUR5ttoREZ5xyhGpeWQO80IBIG0hZRu0/CMZpN6eR9Ul2ldUt9pf8v9oSt978ZY66/BfJ/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2bee715573d93184bf43bc97c85c7cad77035332e1219e32d20d0f35acea332","last_reissued_at":"2026-07-05T08:00:14.878262Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:00:14.878262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.16380","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":"2026-07-05T08:00:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+cM3QLVyFAggSN5JJ/GtFskvyLhb8GSRuRdTv44MuHYlPkwHU43aBAQ9y33kxBwVvucRX+dK6E8NHoP6XzgLCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T08:27:41.123522Z"},"content_sha256":"813b4ffb358871b5da277da0a32b89eb26d1a2db55c2ce1fe873d917ebba9593","schema_version":"1.0","event_id":"sha256:813b4ffb358871b5da277da0a32b89eb26d1a2db55c2ce1fe873d917ebba9593"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:WK7OOFKXHWJRQS7UHPEXZBOHZL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tensor Neural Network Based Machine Learning Method for Elliptic Multiscale Problems","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Haochen Liu, Hehu Xie, Zhongshuo Lin","submitted_at":"2024-03-25T02:53:32Z","abstract_excerpt":"In this paper, we introduce a type of tensor neural network based machine learning method to solve elliptic multiscale problems. Based on the special structure, we can do the direct and highly accurate high dimensional integrations for the tensor neural network functions without Monte Carlo process. Here, with the help of homogenization techniques, the multiscale problem is first transformed to the high dimensional limit problem with reasonable accuracy. Then, based on the tensor neural network, we design a type of machine learning method to solve the derived high dimensional limit problem. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.16380","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/2403.16380/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":"2026-07-05T08:00:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XAdB+Qka+u/jIZ9B/m2VIMakRIci0+RDt56zAmy14H6sEdzJN7vtZ58gbhD5l1gYljJKpviOOEt2dwtZW1cLBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T08:27:41.123901Z"},"content_sha256":"119ffd88c62d32e3eb517084d1c047d1f2ba830cbdadb378204d4a6ee287891d","schema_version":"1.0","event_id":"sha256:119ffd88c62d32e3eb517084d1c047d1f2ba830cbdadb378204d4a6ee287891d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WK7OOFKXHWJRQS7UHPEXZBOHZL/bundle.json","state_url":"https://pith.science/pith/WK7OOFKXHWJRQS7UHPEXZBOHZL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WK7OOFKXHWJRQS7UHPEXZBOHZL/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":"2026-07-07T08:27:41Z","links":{"resolver":"https://pith.science/pith/WK7OOFKXHWJRQS7UHPEXZBOHZL","bundle":"https://pith.science/pith/WK7OOFKXHWJRQS7UHPEXZBOHZL/bundle.json","state":"https://pith.science/pith/WK7OOFKXHWJRQS7UHPEXZBOHZL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WK7OOFKXHWJRQS7UHPEXZBOHZL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:WK7OOFKXHWJRQS7UHPEXZBOHZL","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":"261d3dbcd87cd88d17ba06ac8e4e9a1910dc33bcdacafaa4161a82c3c673078c","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2024-03-25T02:53:32Z","title_canon_sha256":"afbb7542f0e6f4b84b2a6e81adaffe85521ade4bd439c53475aef58f74fceb6e"},"schema_version":"1.0","source":{"id":"2403.16380","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.16380","created_at":"2026-07-05T08:00:14Z"},{"alias_kind":"arxiv_version","alias_value":"2403.16380v1","created_at":"2026-07-05T08:00:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.16380","created_at":"2026-07-05T08:00:14Z"},{"alias_kind":"pith_short_12","alias_value":"WK7OOFKXHWJR","created_at":"2026-07-05T08:00:14Z"},{"alias_kind":"pith_short_16","alias_value":"WK7OOFKXHWJRQS7U","created_at":"2026-07-05T08:00:14Z"},{"alias_kind":"pith_short_8","alias_value":"WK7OOFKX","created_at":"2026-07-05T08:00:14Z"}],"graph_snapshots":[{"event_id":"sha256:119ffd88c62d32e3eb517084d1c047d1f2ba830cbdadb378204d4a6ee287891d","target":"graph","created_at":"2026-07-05T08:00:14Z","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/2403.16380/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we introduce a type of tensor neural network based machine learning method to solve elliptic multiscale problems. Based on the special structure, we can do the direct and highly accurate high dimensional integrations for the tensor neural network functions without Monte Carlo process. Here, with the help of homogenization techniques, the multiscale problem is first transformed to the high dimensional limit problem with reasonable accuracy. Then, based on the tensor neural network, we design a type of machine learning method to solve the derived high dimensional limit problem. Th","authors_text":"Haochen Liu, Hehu Xie, Zhongshuo Lin","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2024-03-25T02:53:32Z","title":"Tensor Neural Network Based Machine Learning Method for Elliptic Multiscale Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.16380","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":"sha256:813b4ffb358871b5da277da0a32b89eb26d1a2db55c2ce1fe873d917ebba9593","target":"record","created_at":"2026-07-05T08:00:14Z","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":"261d3dbcd87cd88d17ba06ac8e4e9a1910dc33bcdacafaa4161a82c3c673078c","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2024-03-25T02:53:32Z","title_canon_sha256":"afbb7542f0e6f4b84b2a6e81adaffe85521ade4bd439c53475aef58f74fceb6e"},"schema_version":"1.0","source":{"id":"2403.16380","kind":"arxiv","version":1}},"canonical_sha256":"b2bee715573d93184bf43bc97c85c7cad77035332e1219e32d20d0f35acea332","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2bee715573d93184bf43bc97c85c7cad77035332e1219e32d20d0f35acea332","first_computed_at":"2026-07-05T08:00:14.878262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:00:14.878262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zvR1pI7/37NVkurUR5ttoREZ5xyhGpeWQO80IBIG0hZRu0/CMZpN6eR9Ul2ldUt9pf8v9oSt978ZY66/BfJ/Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:00:14.878743Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.16380","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:813b4ffb358871b5da277da0a32b89eb26d1a2db55c2ce1fe873d917ebba9593","sha256:119ffd88c62d32e3eb517084d1c047d1f2ba830cbdadb378204d4a6ee287891d"],"state_sha256":"c068af48c1e6af9fdfdff22804be474a1a448acfd1681b5936401d7f6858d74b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fE7N7ZYwkrGE5+YLxS4DqfyW3ll+ZSx+hEBgWgcUR+Csh7E+aYE7hxDE1apMhsGXOXjQmgqQUqqnAHA6gQqnBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T08:27:41.125852Z","bundle_sha256":"8b1fc4eac5c2d57ceeb36a83ca34d55a12cbd42f955a3e9cbf8b0157fab9454f"}}