{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:XJDT7AH5HZVT7QTHVEPR7YO2MH","short_pith_number":"pith:XJDT7AH5","schema_version":"1.0","canonical_sha256":"ba473f80fd3e6b3fc267a91f1fe1da61e1648289406e03b786d8ea1c807f86bc","source":{"kind":"arxiv","id":"1801.02207","version":1},"attestation_state":"computed","paper":{"title":"On the role of curvature in the elastic energy of non-Euclidean thin bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Asaf Shachar, Cy Maor","submitted_at":"2018-01-07T16:29:43Z","abstract_excerpt":"We prove a relation between the scaling $h^\\beta$ of the elastic energies of shrinking non-Euclidean bodies $S_h$ of thickness $h\\to 0$, and the curvature along their mid-surface $S$. This extends and generalizes similar results for plates [BLS16, LRR] to any dimension and co-dimension. In particular, it proves that the natural scaling for non-Euclidean rods with smooth metric is $h^4$, as claimed in [AAE+12] using a formal asymptotic expansion. The proof involves calculating the $\\Gamma$-limit for the elastic energies of small balls $B_h(p)$, scaled by $h^4$, and showing that the limit infimu"},"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":"1801.02207","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-07T16:29:43Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"da558587a6b223e27fb9a3cb20254cda03bd1479edfc192efb84f55599247809","abstract_canon_sha256":"6a3256709a857ae21502165426e68eccea8b3a1dfe298066330708524686a9cf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:59.654028Z","signature_b64":"MRGL/UGNnHzCfft7u03B2BkKtC81rkInPNjptE8wXWB1nphbLxCZ+kndPdh4KQPGe2uB8Okd6Dta9jNT4m93Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba473f80fd3e6b3fc267a91f1fe1da61e1648289406e03b786d8ea1c807f86bc","last_reissued_at":"2026-05-17T23:55:59.653358Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:59.653358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the role of curvature in the elastic energy of non-Euclidean thin bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Asaf Shachar, Cy Maor","submitted_at":"2018-01-07T16:29:43Z","abstract_excerpt":"We prove a relation between the scaling $h^\\beta$ of the elastic energies of shrinking non-Euclidean bodies $S_h$ of thickness $h\\to 0$, and the curvature along their mid-surface $S$. This extends and generalizes similar results for plates [BLS16, LRR] to any dimension and co-dimension. In particular, it proves that the natural scaling for non-Euclidean rods with smooth metric is $h^4$, as claimed in [AAE+12] using a formal asymptotic expansion. The proof involves calculating the $\\Gamma$-limit for the elastic energies of small balls $B_h(p)$, scaled by $h^4$, and showing that the limit infimu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02207","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1801.02207","created_at":"2026-05-17T23:55:59.653471+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.02207v1","created_at":"2026-05-17T23:55:59.653471+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.02207","created_at":"2026-05-17T23:55:59.653471+00:00"},{"alias_kind":"pith_short_12","alias_value":"XJDT7AH5HZVT","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"XJDT7AH5HZVT7QTH","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"XJDT7AH5","created_at":"2026-05-18T12:33:01.666342+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XJDT7AH5HZVT7QTHVEPR7YO2MH","json":"https://pith.science/pith/XJDT7AH5HZVT7QTHVEPR7YO2MH.json","graph_json":"https://pith.science/api/pith-number/XJDT7AH5HZVT7QTHVEPR7YO2MH/graph.json","events_json":"https://pith.science/api/pith-number/XJDT7AH5HZVT7QTHVEPR7YO2MH/events.json","paper":"https://pith.science/paper/XJDT7AH5"},"agent_actions":{"view_html":"https://pith.science/pith/XJDT7AH5HZVT7QTHVEPR7YO2MH","download_json":"https://pith.science/pith/XJDT7AH5HZVT7QTHVEPR7YO2MH.json","view_paper":"https://pith.science/paper/XJDT7AH5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.02207&json=true","fetch_graph":"https://pith.science/api/pith-number/XJDT7AH5HZVT7QTHVEPR7YO2MH/graph.json","fetch_events":"https://pith.science/api/pith-number/XJDT7AH5HZVT7QTHVEPR7YO2MH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XJDT7AH5HZVT7QTHVEPR7YO2MH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XJDT7AH5HZVT7QTHVEPR7YO2MH/action/storage_attestation","attest_author":"https://pith.science/pith/XJDT7AH5HZVT7QTHVEPR7YO2MH/action/author_attestation","sign_citation":"https://pith.science/pith/XJDT7AH5HZVT7QTHVEPR7YO2MH/action/citation_signature","submit_replication":"https://pith.science/pith/XJDT7AH5HZVT7QTHVEPR7YO2MH/action/replication_record"}},"created_at":"2026-05-17T23:55:59.653471+00:00","updated_at":"2026-05-17T23:55:59.653471+00:00"}