{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:MMYRWZZSKPIEJ6TZGVZD6EQZEG","short_pith_number":"pith:MMYRWZZS","canonical_record":{"source":{"id":"2502.05463","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-02-08T06:08:45Z","cross_cats_sorted":["cs.LG","cs.NA"],"title_canon_sha256":"d7b8a0617be8c6882ae69365cacf483e1ed4b08abf0fc9983f0d4c7b3b72f4e8","abstract_canon_sha256":"a5332c6657d4cb1048c71ce848144e6b3cc9d2479140cb51b90ad93ec8c508d9"},"schema_version":"1.0"},"canonical_sha256":"63311b673253d044fa7935723f12192197b64de8f90e2a283252dc5859a34867","source":{"kind":"arxiv","id":"2502.05463","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.05463","created_at":"2026-07-05T10:58:46Z"},{"alias_kind":"arxiv_version","alias_value":"2502.05463v2","created_at":"2026-07-05T10:58:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.05463","created_at":"2026-07-05T10:58:46Z"},{"alias_kind":"pith_short_12","alias_value":"MMYRWZZSKPIE","created_at":"2026-07-05T10:58:46Z"},{"alias_kind":"pith_short_16","alias_value":"MMYRWZZSKPIEJ6TZ","created_at":"2026-07-05T10:58:46Z"},{"alias_kind":"pith_short_8","alias_value":"MMYRWZZS","created_at":"2026-07-05T10:58:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:MMYRWZZSKPIEJ6TZGVZD6EQZEG","target":"record","payload":{"canonical_record":{"source":{"id":"2502.05463","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-02-08T06:08:45Z","cross_cats_sorted":["cs.LG","cs.NA"],"title_canon_sha256":"d7b8a0617be8c6882ae69365cacf483e1ed4b08abf0fc9983f0d4c7b3b72f4e8","abstract_canon_sha256":"a5332c6657d4cb1048c71ce848144e6b3cc9d2479140cb51b90ad93ec8c508d9"},"schema_version":"1.0"},"canonical_sha256":"63311b673253d044fa7935723f12192197b64de8f90e2a283252dc5859a34867","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:58:46.908799Z","signature_b64":"csuhbd5weaiv4Cg+2jeTsZwROef6zEp8OpYjICS08kMNBbVMgEwSWSmN4mRuzjFnmhU8YbsbG0bouw76CcimDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63311b673253d044fa7935723f12192197b64de8f90e2a283252dc5859a34867","last_reissued_at":"2026-07-05T10:58:46.908242Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:58:46.908242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.05463","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":"2026-07-05T10:58:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8YXmQ97tu2OvGSyiSsnQ56n0lWE+BQRVd2to4SQ9M8Ajt1MbChv1fXXuaF2wSs4qpvkFe6yehVsSb6aQ48ObDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T00:50:25.467662Z"},"content_sha256":"becee8479fcffe6cde87a87c62c0faf67fd03ef0ed2ee0e37c5838091f176fb3","schema_version":"1.0","event_id":"sha256:becee8479fcffe6cde87a87c62c0faf67fd03ef0ed2ee0e37c5838091f176fb3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:MMYRWZZSKPIEJ6TZGVZD6EQZEG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning Memory and Material Dependent Constitutive Laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA"],"primary_cat":"math.NA","authors_text":"Andrew Stuart, George Stepaniants, Kaushik Bhattacharya, Lianghao Cao, Margaret Trautner","submitted_at":"2025-02-08T06:08:45Z","abstract_excerpt":"We propose and study a neural operator framework for learning memory- and material microstructure-dependent constitutive laws for heterogeneous materials. We work in the two-scale setting where homogenization theory provides a systematic approach to deriving macroscale constitutive laws, obviating the need to resolve complex microstructure repeatedly. However, the unit cell problems defining these constitutive models are typically not amenable to explicit evaluation. It is therefore of interest to learn constitutive models from data generated by the unit cell problem. Our proposed framework mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.05463","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/2502.05463/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":"2026-07-05T10:58:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ylf3baBtsIXyD2tjj4p+TUyjlYiLQdDkuSgPutcGEwYPxCEFNnAMXOjF+QzwJvRMkhVNfydQprNe6y6LkTjQAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T00:50:25.468672Z"},"content_sha256":"af1a3a8177b4b94d20ab2c2f254acbf5ccca5f783f001810ff969fa565d2ce93","schema_version":"1.0","event_id":"sha256:af1a3a8177b4b94d20ab2c2f254acbf5ccca5f783f001810ff969fa565d2ce93"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MMYRWZZSKPIEJ6TZGVZD6EQZEG/bundle.json","state_url":"https://pith.science/pith/MMYRWZZSKPIEJ6TZGVZD6EQZEG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MMYRWZZSKPIEJ6TZGVZD6EQZEG/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":"2026-08-18T00:50:25Z","links":{"resolver":"https://pith.science/pith/MMYRWZZSKPIEJ6TZGVZD6EQZEG","bundle":"https://pith.science/pith/MMYRWZZSKPIEJ6TZGVZD6EQZEG/bundle.json","state":"https://pith.science/pith/MMYRWZZSKPIEJ6TZGVZD6EQZEG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MMYRWZZSKPIEJ6TZGVZD6EQZEG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:MMYRWZZSKPIEJ6TZGVZD6EQZEG","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":"a5332c6657d4cb1048c71ce848144e6b3cc9d2479140cb51b90ad93ec8c508d9","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-02-08T06:08:45Z","title_canon_sha256":"d7b8a0617be8c6882ae69365cacf483e1ed4b08abf0fc9983f0d4c7b3b72f4e8"},"schema_version":"1.0","source":{"id":"2502.05463","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.05463","created_at":"2026-07-05T10:58:46Z"},{"alias_kind":"arxiv_version","alias_value":"2502.05463v2","created_at":"2026-07-05T10:58:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.05463","created_at":"2026-07-05T10:58:46Z"},{"alias_kind":"pith_short_12","alias_value":"MMYRWZZSKPIE","created_at":"2026-07-05T10:58:46Z"},{"alias_kind":"pith_short_16","alias_value":"MMYRWZZSKPIEJ6TZ","created_at":"2026-07-05T10:58:46Z"},{"alias_kind":"pith_short_8","alias_value":"MMYRWZZS","created_at":"2026-07-05T10:58:46Z"}],"graph_snapshots":[{"event_id":"sha256:af1a3a8177b4b94d20ab2c2f254acbf5ccca5f783f001810ff969fa565d2ce93","target":"graph","created_at":"2026-07-05T10:58:46Z","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/2502.05463/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose and study a neural operator framework for learning memory- and material microstructure-dependent constitutive laws for heterogeneous materials. We work in the two-scale setting where homogenization theory provides a systematic approach to deriving macroscale constitutive laws, obviating the need to resolve complex microstructure repeatedly. However, the unit cell problems defining these constitutive models are typically not amenable to explicit evaluation. It is therefore of interest to learn constitutive models from data generated by the unit cell problem. Our proposed framework mo","authors_text":"Andrew Stuart, George Stepaniants, Kaushik Bhattacharya, Lianghao Cao, Margaret Trautner","cross_cats":["cs.LG","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-02-08T06:08:45Z","title":"Learning Memory and Material Dependent Constitutive Laws"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.05463","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:becee8479fcffe6cde87a87c62c0faf67fd03ef0ed2ee0e37c5838091f176fb3","target":"record","created_at":"2026-07-05T10:58:46Z","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":"a5332c6657d4cb1048c71ce848144e6b3cc9d2479140cb51b90ad93ec8c508d9","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-02-08T06:08:45Z","title_canon_sha256":"d7b8a0617be8c6882ae69365cacf483e1ed4b08abf0fc9983f0d4c7b3b72f4e8"},"schema_version":"1.0","source":{"id":"2502.05463","kind":"arxiv","version":2}},"canonical_sha256":"63311b673253d044fa7935723f12192197b64de8f90e2a283252dc5859a34867","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63311b673253d044fa7935723f12192197b64de8f90e2a283252dc5859a34867","first_computed_at":"2026-07-05T10:58:46.908242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:58:46.908242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"csuhbd5weaiv4Cg+2jeTsZwROef6zEp8OpYjICS08kMNBbVMgEwSWSmN4mRuzjFnmhU8YbsbG0bouw76CcimDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:58:46.908799Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.05463","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:becee8479fcffe6cde87a87c62c0faf67fd03ef0ed2ee0e37c5838091f176fb3","sha256:af1a3a8177b4b94d20ab2c2f254acbf5ccca5f783f001810ff969fa565d2ce93"],"state_sha256":"d4519e46268a32d2805aaeb4c02b16ccfd0368c40b492d9977c171544d689fc6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SrIud0XWcHJ8GJUwUpPfraD0xt1bbwKvGP3cRYPNaXa8Rq9V/0mYfzRuFXfBnVkSfZJh/qHD+YHUvUMGmwo/DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T00:50:25.537993Z","bundle_sha256":"857be5d78593b4b454adfd9fc5823ee75d36260c64c5e8f06b8d76e0225f25ce"}}