{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CZ26OAHEXBML34UIX53KJMFSOS","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":"8e1f488070437f987f4e5d3deb917d3d04aa15463ecf1ba6073b6423adc0b2e8","cross_cats_sorted":["cond-mat.soft","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-17T17:29:01Z","title_canon_sha256":"d679f4874615ed4cee354f321114e275fb7d79b736909c5a70b965e38e90e752"},"schema_version":"1.0","source":{"id":"1201.3565","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3565","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3565v2","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3565","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"pith_short_12","alias_value":"CZ26OAHEXBML","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CZ26OAHEXBML34UI","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CZ26OAHE","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:dccf8026babacb28beb2e5debfe50b90ba250529b637a14bc3944a10fe879a8f","target":"graph","created_at":"2026-05-18T02:43:17Z","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"},"paper":{"abstract_excerpt":"We derive a dimensionally-reduced limit theory for an $n$-dimensional nonlinear elastic body that is slender along $k$ dimensions. The starting point is to view an elastic body as an $n$-dimensional Riemannian manifold together with a not necessarily isometric $W^{1,2}$-immersion in $n$-dimensional Euclidean space. The equilibrium configuration is the immersion that minimizes the average discrepancy between the induced and intrinsic metrics. The dimensionally reduced limit theory views the elastic body as a $k$-dimensional Riemannian manifold along with an isometric $W^{2,2}$-immersion in $n$-","authors_text":"Jake P. Solomon, Raz Kupferman","cross_cats":["cond-mat.soft","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-17T17:29:01Z","title":"A Riemannian Approach to Reduced Plate, Shell, and Rod Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3565","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:a3e92af646a03c7778971fe022ae28c03f738267311d8ed0dce913aee1582d1e","target":"record","created_at":"2026-05-18T02:43:17Z","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":"8e1f488070437f987f4e5d3deb917d3d04aa15463ecf1ba6073b6423adc0b2e8","cross_cats_sorted":["cond-mat.soft","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-17T17:29:01Z","title_canon_sha256":"d679f4874615ed4cee354f321114e275fb7d79b736909c5a70b965e38e90e752"},"schema_version":"1.0","source":{"id":"1201.3565","kind":"arxiv","version":2}},"canonical_sha256":"1675e700e4b858bdf288bf76a4b0b274a5b7196d45eba0b02fb62fc419863ef9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1675e700e4b858bdf288bf76a4b0b274a5b7196d45eba0b02fb62fc419863ef9","first_computed_at":"2026-05-18T02:43:17.096012Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:17.096012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u6RFQnaJQqkKtVeYwWak9ol6v381D/YRC80rcBgW8JyfoCUHm6r+1wQwmRGicrQ+l5gobut6BqB1rNp90sAeBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:17.096530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3565","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3e92af646a03c7778971fe022ae28c03f738267311d8ed0dce913aee1582d1e","sha256:dccf8026babacb28beb2e5debfe50b90ba250529b637a14bc3944a10fe879a8f"],"state_sha256":"91f3ffe0b6f97723128ab8215a60cf30e1ed0e46d04024d5d7653fe369114fbf"}