{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:TARHRNY5WXTIKDZ3M4NYSJELKJ","short_pith_number":"pith:TARHRNY5","canonical_record":{"source":{"id":"2306.02687","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2023-06-05T08:27:50Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"a4e39af80091294b3e023b16e4c35c9c17ddc8f65b92264d1c5f163e2a0d84a4","abstract_canon_sha256":"abc5978012ef3ab623cb3a96910cc5d8b4a7a3edea3183d073e6df018b97d262"},"schema_version":"1.0"},"canonical_sha256":"982278b71db5e6850f3b671b89248b527d81981275a438d123c937ee56870e6d","source":{"kind":"arxiv","id":"2306.02687","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.02687","created_at":"2026-07-05T06:30:07Z"},{"alias_kind":"arxiv_version","alias_value":"2306.02687v2","created_at":"2026-07-05T06:30:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.02687","created_at":"2026-07-05T06:30:07Z"},{"alias_kind":"pith_short_12","alias_value":"TARHRNY5WXTI","created_at":"2026-07-05T06:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"TARHRNY5WXTIKDZ3","created_at":"2026-07-05T06:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"TARHRNY5","created_at":"2026-07-05T06:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:TARHRNY5WXTIKDZ3M4NYSJELKJ","target":"record","payload":{"canonical_record":{"source":{"id":"2306.02687","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2023-06-05T08:27:50Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"a4e39af80091294b3e023b16e4c35c9c17ddc8f65b92264d1c5f163e2a0d84a4","abstract_canon_sha256":"abc5978012ef3ab623cb3a96910cc5d8b4a7a3edea3183d073e6df018b97d262"},"schema_version":"1.0"},"canonical_sha256":"982278b71db5e6850f3b671b89248b527d81981275a438d123c937ee56870e6d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:30:07.360829Z","signature_b64":"AjjHq9jwCKlNNAaIAt+u/E3pD3uBswUw/TD1SL1pz3/vOaMH9xh5EIsJKeNxfOJ5u9wHyRJa6ArwkpEuCWH8Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"982278b71db5e6850f3b671b89248b527d81981275a438d123c937ee56870e6d","last_reissued_at":"2026-07-05T06:30:07.360348Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:30:07.360348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2306.02687","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":"2026-07-05T06:30:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jWpozbfjd8gqS/jdMQQ58yxxppaQm5r7yr2KFvODZVbl76eQyLS+EBj+o+wOV+G64p7LS5XhleiDZiqUOn2qDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T14:53:32.223502Z"},"content_sha256":"c0f36abfb3d73fe5c21ae6ac91daae7ebd7e8cc5cda6574f24fa59392ddef40b","schema_version":"1.0","event_id":"sha256:c0f36abfb3d73fe5c21ae6ac91daae7ebd7e8cc5cda6574f24fa59392ddef40b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:TARHRNY5WXTIKDZ3M4NYSJELKJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monolithic Hyper ROM FE$^2$ Method with Clustered Training at Finite Deformations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Bjoern Kiefer, Geralf H\\\"utter, Nils Lange","submitted_at":"2023-06-05T08:27:50Z","abstract_excerpt":"The usage of numerical homogenization to obtain structure-property relations using the finite element method at both the micro and macroscale has gained much interest in the research community. However the computational cost of this so called FE$^2$ method is so high that algorithmic modifications and reduction methods are essential. Currently the authors proposed a monolithic algorithm. Now this algorithm is combined with ROM and ECM hyper integration, applied at finite deformations and complemented by a clustered training strategy, which lowers the training effort and the number of necessary"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.02687","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/2306.02687/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":"2026-07-05T06:30:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rCr9spV6/U9jNcmAIG/g9hsOYSHJISfBgXeBknQ90xriVinMcnMQeAWQcHG8Ri0MqP1tM3ONbMALq8r3ZuU4Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T14:53:32.224343Z"},"content_sha256":"8cd6bb69ca0a0149749f0571839bbc0ee517afb8800ab55a960ad38721703cf6","schema_version":"1.0","event_id":"sha256:8cd6bb69ca0a0149749f0571839bbc0ee517afb8800ab55a960ad38721703cf6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TARHRNY5WXTIKDZ3M4NYSJELKJ/bundle.json","state_url":"https://pith.science/pith/TARHRNY5WXTIKDZ3M4NYSJELKJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TARHRNY5WXTIKDZ3M4NYSJELKJ/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":"2026-08-21T14:53:32Z","links":{"resolver":"https://pith.science/pith/TARHRNY5WXTIKDZ3M4NYSJELKJ","bundle":"https://pith.science/pith/TARHRNY5WXTIKDZ3M4NYSJELKJ/bundle.json","state":"https://pith.science/pith/TARHRNY5WXTIKDZ3M4NYSJELKJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TARHRNY5WXTIKDZ3M4NYSJELKJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:TARHRNY5WXTIKDZ3M4NYSJELKJ","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":"abc5978012ef3ab623cb3a96910cc5d8b4a7a3edea3183d073e6df018b97d262","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2023-06-05T08:27:50Z","title_canon_sha256":"a4e39af80091294b3e023b16e4c35c9c17ddc8f65b92264d1c5f163e2a0d84a4"},"schema_version":"1.0","source":{"id":"2306.02687","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.02687","created_at":"2026-07-05T06:30:07Z"},{"alias_kind":"arxiv_version","alias_value":"2306.02687v2","created_at":"2026-07-05T06:30:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.02687","created_at":"2026-07-05T06:30:07Z"},{"alias_kind":"pith_short_12","alias_value":"TARHRNY5WXTI","created_at":"2026-07-05T06:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"TARHRNY5WXTIKDZ3","created_at":"2026-07-05T06:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"TARHRNY5","created_at":"2026-07-05T06:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:8cd6bb69ca0a0149749f0571839bbc0ee517afb8800ab55a960ad38721703cf6","target":"graph","created_at":"2026-07-05T06:30:07Z","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/2306.02687/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The usage of numerical homogenization to obtain structure-property relations using the finite element method at both the micro and macroscale has gained much interest in the research community. However the computational cost of this so called FE$^2$ method is so high that algorithmic modifications and reduction methods are essential. Currently the authors proposed a monolithic algorithm. Now this algorithm is combined with ROM and ECM hyper integration, applied at finite deformations and complemented by a clustered training strategy, which lowers the training effort and the number of necessary","authors_text":"Bjoern Kiefer, Geralf H\\\"utter, Nils Lange","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2023-06-05T08:27:50Z","title":"Monolithic Hyper ROM FE$^2$ Method with Clustered Training at Finite Deformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.02687","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:c0f36abfb3d73fe5c21ae6ac91daae7ebd7e8cc5cda6574f24fa59392ddef40b","target":"record","created_at":"2026-07-05T06:30:07Z","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":"abc5978012ef3ab623cb3a96910cc5d8b4a7a3edea3183d073e6df018b97d262","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2023-06-05T08:27:50Z","title_canon_sha256":"a4e39af80091294b3e023b16e4c35c9c17ddc8f65b92264d1c5f163e2a0d84a4"},"schema_version":"1.0","source":{"id":"2306.02687","kind":"arxiv","version":2}},"canonical_sha256":"982278b71db5e6850f3b671b89248b527d81981275a438d123c937ee56870e6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"982278b71db5e6850f3b671b89248b527d81981275a438d123c937ee56870e6d","first_computed_at":"2026-07-05T06:30:07.360348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:30:07.360348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AjjHq9jwCKlNNAaIAt+u/E3pD3uBswUw/TD1SL1pz3/vOaMH9xh5EIsJKeNxfOJ5u9wHyRJa6ArwkpEuCWH8Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:30:07.360829Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.02687","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0f36abfb3d73fe5c21ae6ac91daae7ebd7e8cc5cda6574f24fa59392ddef40b","sha256:8cd6bb69ca0a0149749f0571839bbc0ee517afb8800ab55a960ad38721703cf6"],"state_sha256":"a6b2b7d4d5b66f25db44938f6978d5c2cb1f8f452ce1ad10bc2a70e19ae3d5dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bYb7AG36YWGKLCLiQxFYDzW6geA98+ehr/mbwlFrMBj0KpMTF8yhax0aQlVsYQUO0nT42EvMN9t9MwbrExqtBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T14:53:32.228188Z","bundle_sha256":"4a67161bbe185607d5382237b21013553b48388b18961aaae288930898457615"}}