{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:JBNPIO5SQ5FST2OUTS52NG3NUB","short_pith_number":"pith:JBNPIO5S","schema_version":"1.0","canonical_sha256":"485af43bb2874b29e9d49cbba69b6da078ff563a1231e912e4bcfb438f7ccb3b","source":{"kind":"arxiv","id":"2205.14139","version":2},"attestation_state":"computed","paper":{"title":"Learning Markovian Homogenized Models in Viscoelasticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Andrew M. Stuart, Burigede Liu, Kaushik Bhattacharya, Margaret Trautner","submitted_at":"2022-05-27T17:58:35Z","abstract_excerpt":"Fully resolving dynamics of materials with rapidly-varying features involves expensive fine-scale computations which need to be conducted on macroscopic scales. The theory of homogenization provides an approach to derive effective macroscopic equations which eliminates the small scales by exploiting scale separation. An accurate homogenized model avoids the computationally-expensive task of numerically solving the underlying balance laws at a fine scale, thereby rendering a numerical solution of the balance laws more computationally tractable.\n  In complex settings, homogenization only defines"},"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":"2205.14139","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-05-27T17:58:35Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"c679050aa9ecbe7734c6a548673f8efd660a8ffc945fd91fa160d6afcbeb2c43","abstract_canon_sha256":"64a23ecccaba328d4ca2dc3e3fbaf7161e21b6b42babe41dc12eff50efa253f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:28:55.324855Z","signature_b64":"v9hS9UV/+oV+969hxr+BIKUKvRMkCtQFSe6T0IHmUiKIraWPdUl+ks+92n1SXXf/Zp4YCdq1ejcDYja316nsAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"485af43bb2874b29e9d49cbba69b6da078ff563a1231e912e4bcfb438f7ccb3b","last_reissued_at":"2026-07-05T04:28:55.324419Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:28:55.324419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Learning Markovian Homogenized Models in Viscoelasticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Andrew M. Stuart, Burigede Liu, Kaushik Bhattacharya, Margaret Trautner","submitted_at":"2022-05-27T17:58:35Z","abstract_excerpt":"Fully resolving dynamics of materials with rapidly-varying features involves expensive fine-scale computations which need to be conducted on macroscopic scales. The theory of homogenization provides an approach to derive effective macroscopic equations which eliminates the small scales by exploiting scale separation. An accurate homogenized model avoids the computationally-expensive task of numerically solving the underlying balance laws at a fine scale, thereby rendering a numerical solution of the balance laws more computationally tractable.\n  In complex settings, homogenization only defines"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.14139","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/2205.14139/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":"2205.14139","created_at":"2026-07-05T04:28:55.324476+00:00"},{"alias_kind":"arxiv_version","alias_value":"2205.14139v2","created_at":"2026-07-05T04:28:55.324476+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.14139","created_at":"2026-07-05T04:28:55.324476+00:00"},{"alias_kind":"pith_short_12","alias_value":"JBNPIO5SQ5FS","created_at":"2026-07-05T04:28:55.324476+00:00"},{"alias_kind":"pith_short_16","alias_value":"JBNPIO5SQ5FST2OU","created_at":"2026-07-05T04:28:55.324476+00:00"},{"alias_kind":"pith_short_8","alias_value":"JBNPIO5S","created_at":"2026-07-05T04:28:55.324476+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.18806","citing_title":"Temperature-Aware Recurrent Neural Operator for Temperature-Dependent Anisotropic Plasticity in HCP Materials","ref_index":28,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JBNPIO5SQ5FST2OUTS52NG3NUB","json":"https://pith.science/pith/JBNPIO5SQ5FST2OUTS52NG3NUB.json","graph_json":"https://pith.science/api/pith-number/JBNPIO5SQ5FST2OUTS52NG3NUB/graph.json","events_json":"https://pith.science/api/pith-number/JBNPIO5SQ5FST2OUTS52NG3NUB/events.json","paper":"https://pith.science/paper/JBNPIO5S"},"agent_actions":{"view_html":"https://pith.science/pith/JBNPIO5SQ5FST2OUTS52NG3NUB","download_json":"https://pith.science/pith/JBNPIO5SQ5FST2OUTS52NG3NUB.json","view_paper":"https://pith.science/paper/JBNPIO5S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2205.14139&json=true","fetch_graph":"https://pith.science/api/pith-number/JBNPIO5SQ5FST2OUTS52NG3NUB/graph.json","fetch_events":"https://pith.science/api/pith-number/JBNPIO5SQ5FST2OUTS52NG3NUB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JBNPIO5SQ5FST2OUTS52NG3NUB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JBNPIO5SQ5FST2OUTS52NG3NUB/action/storage_attestation","attest_author":"https://pith.science/pith/JBNPIO5SQ5FST2OUTS52NG3NUB/action/author_attestation","sign_citation":"https://pith.science/pith/JBNPIO5SQ5FST2OUTS52NG3NUB/action/citation_signature","submit_replication":"https://pith.science/pith/JBNPIO5SQ5FST2OUTS52NG3NUB/action/replication_record"}},"created_at":"2026-07-05T04:28:55.324476+00:00","updated_at":"2026-07-05T04:28:55.324476+00:00"}