{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:KJO4YCBCKLUWOAU7FAK4BZZJ4Z","short_pith_number":"pith:KJO4YCBC","canonical_record":{"source":{"id":"2403.14084","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-03-21T02:30:56Z","cross_cats_sorted":["cs.LG","cs.NA"],"title_canon_sha256":"d1d4ff3a0767c52d0208b0be20c0ac986aa430a0633269949d4b4c6bf7d88b09","abstract_canon_sha256":"a1d177d3da02997d6a7626a9177bdf14b5d3ba39501a76edd98ebd414e4adb73"},"schema_version":"1.0"},"canonical_sha256":"525dcc082252e967029f2815c0e729e657b8a14b5f93421228a9e0a4427c6803","source":{"kind":"arxiv","id":"2403.14084","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.14084","created_at":"2026-07-05T08:34:15Z"},{"alias_kind":"arxiv_version","alias_value":"2403.14084v2","created_at":"2026-07-05T08:34:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.14084","created_at":"2026-07-05T08:34:15Z"},{"alias_kind":"pith_short_12","alias_value":"KJO4YCBCKLUW","created_at":"2026-07-05T08:34:15Z"},{"alias_kind":"pith_short_16","alias_value":"KJO4YCBCKLUWOAU7","created_at":"2026-07-05T08:34:15Z"},{"alias_kind":"pith_short_8","alias_value":"KJO4YCBC","created_at":"2026-07-05T08:34:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:KJO4YCBCKLUWOAU7FAK4BZZJ4Z","target":"record","payload":{"canonical_record":{"source":{"id":"2403.14084","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-03-21T02:30:56Z","cross_cats_sorted":["cs.LG","cs.NA"],"title_canon_sha256":"d1d4ff3a0767c52d0208b0be20c0ac986aa430a0633269949d4b4c6bf7d88b09","abstract_canon_sha256":"a1d177d3da02997d6a7626a9177bdf14b5d3ba39501a76edd98ebd414e4adb73"},"schema_version":"1.0"},"canonical_sha256":"525dcc082252e967029f2815c0e729e657b8a14b5f93421228a9e0a4427c6803","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:34:15.880354Z","signature_b64":"a4QrAikZlCF4DFZjuDFN+OTfmXA3Qi8txelfTAg8gu3CqaiGJEYpdJPSj5/rQRR4ASUhot0df6/h+p1ZG5IKDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"525dcc082252e967029f2815c0e729e657b8a14b5f93421228a9e0a4427c6803","last_reissued_at":"2026-07-05T08:34:15.879809Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:34:15.879809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.14084","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:34:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xg2ZbWIm9OFEJ8sPhWv5GgRRQas0bQqEGHuvyR1NORwbi2+ZEZKB+fYm+esNhgEMVK8RwyC8PEhouGeTNE53CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T02:38:39.958761Z"},"content_sha256":"7662e4f91f49d80ec7a2469a943c2cbf1d1fd906f11186e7447ccf0888bed14e","schema_version":"1.0","event_id":"sha256:7662e4f91f49d80ec7a2469a943c2cbf1d1fd906f11186e7447ccf0888bed14e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:KJO4YCBCKLUWOAU7FAK4BZZJ4Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning-based Multi-continuum Model for Multiscale Flow Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA"],"primary_cat":"math.NA","authors_text":"Fan Wang, Wing Tat Leung, Yating Wang, Zongben Xu","submitted_at":"2024-03-21T02:30:56Z","abstract_excerpt":"Multiscale problems can usually be approximated through numerical homogenization by an equation with some effective parameters that can capture the macroscopic behavior of the original system on the coarse grid to speed up the simulation. However, this approach usually assumes scale separation and that the heterogeneity of the solution can be approximated by the solution average in each coarse block. For complex multiscale problems, the computed single effective properties/continuum might be inadequate. In this paper, we propose a novel learning-based multi-continuum model to enrich the homoge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.14084","kind":"arxiv","version":2},"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/2403.14084/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":"2026-07-05T08:34:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aTmaLaVzFEVA4geylmoYuyJOLONGVWp+IbVIkGFynRklQpk3XFXeh97TIKt/v4L0ncZ3XunUmaFDaczodEa+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T02:38:39.959403Z"},"content_sha256":"38bee9d8ace3bd2616e1d7cd52bfec08459f0acf9a45e5a1472dfab662e8575d","schema_version":"1.0","event_id":"sha256:38bee9d8ace3bd2616e1d7cd52bfec08459f0acf9a45e5a1472dfab662e8575d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KJO4YCBCKLUWOAU7FAK4BZZJ4Z/bundle.json","state_url":"https://pith.science/pith/KJO4YCBCKLUWOAU7FAK4BZZJ4Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KJO4YCBCKLUWOAU7FAK4BZZJ4Z/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":"2026-07-07T02:38:39Z","links":{"resolver":"https://pith.science/pith/KJO4YCBCKLUWOAU7FAK4BZZJ4Z","bundle":"https://pith.science/pith/KJO4YCBCKLUWOAU7FAK4BZZJ4Z/bundle.json","state":"https://pith.science/pith/KJO4YCBCKLUWOAU7FAK4BZZJ4Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KJO4YCBCKLUWOAU7FAK4BZZJ4Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:KJO4YCBCKLUWOAU7FAK4BZZJ4Z","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":"a1d177d3da02997d6a7626a9177bdf14b5d3ba39501a76edd98ebd414e4adb73","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-03-21T02:30:56Z","title_canon_sha256":"d1d4ff3a0767c52d0208b0be20c0ac986aa430a0633269949d4b4c6bf7d88b09"},"schema_version":"1.0","source":{"id":"2403.14084","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.14084","created_at":"2026-07-05T08:34:15Z"},{"alias_kind":"arxiv_version","alias_value":"2403.14084v2","created_at":"2026-07-05T08:34:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.14084","created_at":"2026-07-05T08:34:15Z"},{"alias_kind":"pith_short_12","alias_value":"KJO4YCBCKLUW","created_at":"2026-07-05T08:34:15Z"},{"alias_kind":"pith_short_16","alias_value":"KJO4YCBCKLUWOAU7","created_at":"2026-07-05T08:34:15Z"},{"alias_kind":"pith_short_8","alias_value":"KJO4YCBC","created_at":"2026-07-05T08:34:15Z"}],"graph_snapshots":[{"event_id":"sha256:38bee9d8ace3bd2616e1d7cd52bfec08459f0acf9a45e5a1472dfab662e8575d","target":"graph","created_at":"2026-07-05T08:34:15Z","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/2403.14084/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Multiscale problems can usually be approximated through numerical homogenization by an equation with some effective parameters that can capture the macroscopic behavior of the original system on the coarse grid to speed up the simulation. However, this approach usually assumes scale separation and that the heterogeneity of the solution can be approximated by the solution average in each coarse block. For complex multiscale problems, the computed single effective properties/continuum might be inadequate. In this paper, we propose a novel learning-based multi-continuum model to enrich the homoge","authors_text":"Fan Wang, Wing Tat Leung, Yating Wang, Zongben Xu","cross_cats":["cs.LG","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-03-21T02:30:56Z","title":"Learning-based Multi-continuum Model for Multiscale Flow Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.14084","kind":"arxiv","version":2},"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":"sha256:7662e4f91f49d80ec7a2469a943c2cbf1d1fd906f11186e7447ccf0888bed14e","target":"record","created_at":"2026-07-05T08:34:15Z","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":"a1d177d3da02997d6a7626a9177bdf14b5d3ba39501a76edd98ebd414e4adb73","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-03-21T02:30:56Z","title_canon_sha256":"d1d4ff3a0767c52d0208b0be20c0ac986aa430a0633269949d4b4c6bf7d88b09"},"schema_version":"1.0","source":{"id":"2403.14084","kind":"arxiv","version":2}},"canonical_sha256":"525dcc082252e967029f2815c0e729e657b8a14b5f93421228a9e0a4427c6803","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"525dcc082252e967029f2815c0e729e657b8a14b5f93421228a9e0a4427c6803","first_computed_at":"2026-07-05T08:34:15.879809Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:34:15.879809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a4QrAikZlCF4DFZjuDFN+OTfmXA3Qi8txelfTAg8gu3CqaiGJEYpdJPSj5/rQRR4ASUhot0df6/h+p1ZG5IKDA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:34:15.880354Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.14084","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7662e4f91f49d80ec7a2469a943c2cbf1d1fd906f11186e7447ccf0888bed14e","sha256:38bee9d8ace3bd2616e1d7cd52bfec08459f0acf9a45e5a1472dfab662e8575d"],"state_sha256":"9f007a5f7a7921e7098144d4dda8d2811dc9a8618848a44a165ebca662cf93ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5mDF2VzZYJ+A3scFkHK3MSQt2JYK9dv4FP94jsM7sn3VgK4n4ivs2igp9kFd4SrGACLId4gXndy9OG3DlGFOBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T02:38:39.962759Z","bundle_sha256":"df658e4f3d141a7d6a872167233f8b4b4fdfef3fbb5942b3b32bf99cebbc0ae6"}}