{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XJDT7AH5HZVT7QTHVEPR7YO2MH","short_pith_number":"pith:XJDT7AH5","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"},"canonical_sha256":"ba473f80fd3e6b3fc267a91f1fe1da61e1648289406e03b786d8ea1c807f86bc","source":{"kind":"arxiv","id":"1801.02207","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.02207","created_at":"2026-05-17T23:55:59Z"},{"alias_kind":"arxiv_version","alias_value":"1801.02207v1","created_at":"2026-05-17T23:55:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.02207","created_at":"2026-05-17T23:55:59Z"},{"alias_kind":"pith_short_12","alias_value":"XJDT7AH5HZVT","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XJDT7AH5HZVT7QTH","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XJDT7AH5","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XJDT7AH5HZVT7QTHVEPR7YO2MH","target":"record","payload":{"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"},"canonical_sha256":"ba473f80fd3e6b3fc267a91f1fe1da61e1648289406e03b786d8ea1c807f86bc","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"},"source_kind":"arxiv","source_id":"1801.02207","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:55:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TjAtzPnKeRYmcIJH6oA6L11zgTsra7wcxQWy5XmoYQIOJB0JBdFCFWm1zHZ4BP6cyZWvQ4E12VNMCG4RAAeNBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T11:13:57.323664Z"},"content_sha256":"23b705896adae1321656050eeae3406106ad6f135a23e5e2a20dc3b9351c15a0","schema_version":"1.0","event_id":"sha256:23b705896adae1321656050eeae3406106ad6f135a23e5e2a20dc3b9351c15a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XJDT7AH5HZVT7QTHVEPR7YO2MH","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:55:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8DRl7h74F8hatVohqQ2ELzRKOS8bFBuyRldyLRp4VUi3Xk0bYc7oIHTHEO4YPnirLBPC/lGhGvOjleKPpkzPDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T11:13:57.324003Z"},"content_sha256":"4aae1f8764b24fdc7640159fe44906e193dc11ca7fa3200158586c8f99052dd0","schema_version":"1.0","event_id":"sha256:4aae1f8764b24fdc7640159fe44906e193dc11ca7fa3200158586c8f99052dd0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XJDT7AH5HZVT7QTHVEPR7YO2MH/bundle.json","state_url":"https://pith.science/pith/XJDT7AH5HZVT7QTHVEPR7YO2MH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XJDT7AH5HZVT7QTHVEPR7YO2MH/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":"2026-06-03T11:13:57Z","links":{"resolver":"https://pith.science/pith/XJDT7AH5HZVT7QTHVEPR7YO2MH","bundle":"https://pith.science/pith/XJDT7AH5HZVT7QTHVEPR7YO2MH/bundle.json","state":"https://pith.science/pith/XJDT7AH5HZVT7QTHVEPR7YO2MH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XJDT7AH5HZVT7QTHVEPR7YO2MH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XJDT7AH5HZVT7QTHVEPR7YO2MH","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":"6a3256709a857ae21502165426e68eccea8b3a1dfe298066330708524686a9cf","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-07T16:29:43Z","title_canon_sha256":"da558587a6b223e27fb9a3cb20254cda03bd1479edfc192efb84f55599247809"},"schema_version":"1.0","source":{"id":"1801.02207","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.02207","created_at":"2026-05-17T23:55:59Z"},{"alias_kind":"arxiv_version","alias_value":"1801.02207v1","created_at":"2026-05-17T23:55:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.02207","created_at":"2026-05-17T23:55:59Z"},{"alias_kind":"pith_short_12","alias_value":"XJDT7AH5HZVT","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XJDT7AH5HZVT7QTH","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XJDT7AH5","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:4aae1f8764b24fdc7640159fe44906e193dc11ca7fa3200158586c8f99052dd0","target":"graph","created_at":"2026-05-17T23:55:59Z","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 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","authors_text":"Asaf Shachar, Cy Maor","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-07T16:29:43Z","title":"On the role of curvature in the elastic energy of non-Euclidean thin bodies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02207","kind":"arxiv","version":1},"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":"sha256:23b705896adae1321656050eeae3406106ad6f135a23e5e2a20dc3b9351c15a0","target":"record","created_at":"2026-05-17T23:55:59Z","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":"6a3256709a857ae21502165426e68eccea8b3a1dfe298066330708524686a9cf","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-07T16:29:43Z","title_canon_sha256":"da558587a6b223e27fb9a3cb20254cda03bd1479edfc192efb84f55599247809"},"schema_version":"1.0","source":{"id":"1801.02207","kind":"arxiv","version":1}},"canonical_sha256":"ba473f80fd3e6b3fc267a91f1fe1da61e1648289406e03b786d8ea1c807f86bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba473f80fd3e6b3fc267a91f1fe1da61e1648289406e03b786d8ea1c807f86bc","first_computed_at":"2026-05-17T23:55:59.653358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:59.653358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MRGL/UGNnHzCfft7u03B2BkKtC81rkInPNjptE8wXWB1nphbLxCZ+kndPdh4KQPGe2uB8Okd6Dta9jNT4m93Dg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:59.654028Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.02207","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23b705896adae1321656050eeae3406106ad6f135a23e5e2a20dc3b9351c15a0","sha256:4aae1f8764b24fdc7640159fe44906e193dc11ca7fa3200158586c8f99052dd0"],"state_sha256":"388fd0b2d0e9d37183f91e7b18f50264dcd1c4258943e0004f90120a9c42c1a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kX7PwevEKN6OGV8QMyz8ELDshPxgA881YMk+aJ/9OG6mKiJyDfnl1+ShcquboMz07EQuxgaJiSLKDhz3XeCCCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T11:13:57.325940Z","bundle_sha256":"b6a23038c80f67644b967bd84afbc123aa55c37562b3c5310e25069de76d1008"}}