{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:XNCDIOI27H3Z3KFJNXW2SCOJGY","short_pith_number":"pith:XNCDIOI2","canonical_record":{"source":{"id":"1002.2252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-02-11T01:08:25Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f0370bb83bc69f30c40bf8a482d20b0ba5f42fd1bea671d218421de42ba6e9f4","abstract_canon_sha256":"68ecd2a353f19ece601524adf8534d44a10575c0264f15ceb28aaad73935e577"},"schema_version":"1.0"},"canonical_sha256":"bb4434391af9f79da8a96deda909c9360b6a2e99343dc9f82d0352ef9ec62670","source":{"kind":"arxiv","id":"1002.2252","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.2252","created_at":"2026-05-18T02:09:09Z"},{"alias_kind":"arxiv_version","alias_value":"1002.2252v1","created_at":"2026-05-18T02:09:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.2252","created_at":"2026-05-18T02:09:09Z"},{"alias_kind":"pith_short_12","alias_value":"XNCDIOI27H3Z","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XNCDIOI27H3Z3KFJ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XNCDIOI2","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:XNCDIOI27H3Z3KFJNXW2SCOJGY","target":"record","payload":{"canonical_record":{"source":{"id":"1002.2252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-02-11T01:08:25Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f0370bb83bc69f30c40bf8a482d20b0ba5f42fd1bea671d218421de42ba6e9f4","abstract_canon_sha256":"68ecd2a353f19ece601524adf8534d44a10575c0264f15ceb28aaad73935e577"},"schema_version":"1.0"},"canonical_sha256":"bb4434391af9f79da8a96deda909c9360b6a2e99343dc9f82d0352ef9ec62670","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:09.646098Z","signature_b64":"6pdrivU9xO+umRnvAZzUZeGyMSz9+wZJj6b7rxN7v1WTk8bTnVGMvhb+nKVH+7bfwHMsRJThcz2Hy9+pZqMDAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb4434391af9f79da8a96deda909c9360b6a2e99343dc9f82d0352ef9ec62670","last_reissued_at":"2026-05-18T02:09:09.645294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:09.645294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.2252","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":"2026-05-18T02:09:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X0nOTSibUfZOFo7NF88zlNJxcku7AFikaBs4MORq+OW7rFL3hk+J7S8fL9veMXqF/KCzITl5AX2nVv9YMFIKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:22:02.241168Z"},"content_sha256":"692303512df76ed29a2b18270fa434fab1468585fbda2f17b8a8907223a0fa7d","schema_version":"1.0","event_id":"sha256:692303512df76ed29a2b18270fa434fab1468585fbda2f17b8a8907223a0fa7d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:XNCDIOI27H3Z3KFJNXW2SCOJGY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The von Karman equations for plates with residual strain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"L. Mahadevan, Marta Lewicka, Reza Pakzad","submitted_at":"2010-02-11T01:08:25Z","abstract_excerpt":"We provide a derivation of the Foppl-von Karman equations for the shape of and stresses in an elastic plate with residual strains. These might arise from a range of causes: inhomogeneous growth, plastic deformation, swelling or shrinkage driven by solvent absorption. Our analysis gives rigorous bounds on the convergence of the three dimensional equations of elasticity to the low-dimensional description embodied in the plate-like description of laminae and thus justifies a recent formulation of the problem to the shape of growing leaves. It also formalizes a procedure that can be used to derive"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.2252","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":"2026-05-18T02:09:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k6p5A8f+O2Kz6VdhIYV57AUJ9kUZJT1E/mtLkSYfv3spHD+cxFDN3Gt9rQOOoezyFTWfkZWBTQH6HN2h1bm9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:22:02.241859Z"},"content_sha256":"2aa9f6459f8ce2de8f7e965a0a64be4a844c9934aeae7b72a3565c1dfe63f66c","schema_version":"1.0","event_id":"sha256:2aa9f6459f8ce2de8f7e965a0a64be4a844c9934aeae7b72a3565c1dfe63f66c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XNCDIOI27H3Z3KFJNXW2SCOJGY/bundle.json","state_url":"https://pith.science/pith/XNCDIOI27H3Z3KFJNXW2SCOJGY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XNCDIOI27H3Z3KFJNXW2SCOJGY/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":"2026-05-25T21:22:02Z","links":{"resolver":"https://pith.science/pith/XNCDIOI27H3Z3KFJNXW2SCOJGY","bundle":"https://pith.science/pith/XNCDIOI27H3Z3KFJNXW2SCOJGY/bundle.json","state":"https://pith.science/pith/XNCDIOI27H3Z3KFJNXW2SCOJGY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XNCDIOI27H3Z3KFJNXW2SCOJGY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XNCDIOI27H3Z3KFJNXW2SCOJGY","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":"68ecd2a353f19ece601524adf8534d44a10575c0264f15ceb28aaad73935e577","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-02-11T01:08:25Z","title_canon_sha256":"f0370bb83bc69f30c40bf8a482d20b0ba5f42fd1bea671d218421de42ba6e9f4"},"schema_version":"1.0","source":{"id":"1002.2252","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.2252","created_at":"2026-05-18T02:09:09Z"},{"alias_kind":"arxiv_version","alias_value":"1002.2252v1","created_at":"2026-05-18T02:09:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.2252","created_at":"2026-05-18T02:09:09Z"},{"alias_kind":"pith_short_12","alias_value":"XNCDIOI27H3Z","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XNCDIOI27H3Z3KFJ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XNCDIOI2","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:2aa9f6459f8ce2de8f7e965a0a64be4a844c9934aeae7b72a3565c1dfe63f66c","target":"graph","created_at":"2026-05-18T02:09:09Z","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 provide a derivation of the Foppl-von Karman equations for the shape of and stresses in an elastic plate with residual strains. These might arise from a range of causes: inhomogeneous growth, plastic deformation, swelling or shrinkage driven by solvent absorption. Our analysis gives rigorous bounds on the convergence of the three dimensional equations of elasticity to the low-dimensional description embodied in the plate-like description of laminae and thus justifies a recent formulation of the problem to the shape of growing leaves. It also formalizes a procedure that can be used to derive","authors_text":"L. Mahadevan, Marta Lewicka, Reza Pakzad","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-02-11T01:08:25Z","title":"The von Karman equations for plates with residual strain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.2252","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":"sha256:692303512df76ed29a2b18270fa434fab1468585fbda2f17b8a8907223a0fa7d","target":"record","created_at":"2026-05-18T02:09:09Z","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":"68ecd2a353f19ece601524adf8534d44a10575c0264f15ceb28aaad73935e577","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-02-11T01:08:25Z","title_canon_sha256":"f0370bb83bc69f30c40bf8a482d20b0ba5f42fd1bea671d218421de42ba6e9f4"},"schema_version":"1.0","source":{"id":"1002.2252","kind":"arxiv","version":1}},"canonical_sha256":"bb4434391af9f79da8a96deda909c9360b6a2e99343dc9f82d0352ef9ec62670","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb4434391af9f79da8a96deda909c9360b6a2e99343dc9f82d0352ef9ec62670","first_computed_at":"2026-05-18T02:09:09.645294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:09:09.645294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6pdrivU9xO+umRnvAZzUZeGyMSz9+wZJj6b7rxN7v1WTk8bTnVGMvhb+nKVH+7bfwHMsRJThcz2Hy9+pZqMDAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:09:09.646098Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.2252","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:692303512df76ed29a2b18270fa434fab1468585fbda2f17b8a8907223a0fa7d","sha256:2aa9f6459f8ce2de8f7e965a0a64be4a844c9934aeae7b72a3565c1dfe63f66c"],"state_sha256":"9005cb6e9f0581f4ce060f7a9434c2a79a04d5ea7f163c90afb0a9ce6b76ae6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZQMk9A8nuOjgbSTBc5UvXV9Mauu3/k3XqfjDftMqCmCU9aLoMqi4GVm2oYsYY5vRbH4QoH0ksky+aYjYfWQ+Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T21:22:02.244616Z","bundle_sha256":"c9438ec1a0e5ce4252c44d66c2c4afb12a1614cf178577eae5249fa5c2a1b8ae"}}