{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3B4DCDG6J4VSWQQ35FLINZ5W62","short_pith_number":"pith:3B4DCDG6","canonical_record":{"source":{"id":"1411.0702","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2014-11-03T21:24:36Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f491b78fbe62734802cc6f9867795ea1e494237f6992808dbd0d86edefa5bda8","abstract_canon_sha256":"7d052668728d4b2b72ad4b3fa73d8298262abe639a28947c9349fc837b234ac4"},"schema_version":"1.0"},"canonical_sha256":"d878310cde4f2b2b421be95686e7b6f697c504f88981b698ba96338cccf5b32c","source":{"kind":"arxiv","id":"1411.0702","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0702","created_at":"2026-05-18T02:38:38Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0702v1","created_at":"2026-05-18T02:38:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0702","created_at":"2026-05-18T02:38:38Z"},{"alias_kind":"pith_short_12","alias_value":"3B4DCDG6J4VS","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3B4DCDG6J4VSWQQ3","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3B4DCDG6","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3B4DCDG6J4VSWQQ35FLINZ5W62","target":"record","payload":{"canonical_record":{"source":{"id":"1411.0702","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2014-11-03T21:24:36Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f491b78fbe62734802cc6f9867795ea1e494237f6992808dbd0d86edefa5bda8","abstract_canon_sha256":"7d052668728d4b2b72ad4b3fa73d8298262abe639a28947c9349fc837b234ac4"},"schema_version":"1.0"},"canonical_sha256":"d878310cde4f2b2b421be95686e7b6f697c504f88981b698ba96338cccf5b32c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:38.409758Z","signature_b64":"vFWvso16P3HBy6c4sfvR7gvWnmmVyKBvXU6HsRk4wpR5HmPX6vN+5d/SnXhRE9SPUUFMifSgSHA8MRAmp49cBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d878310cde4f2b2b421be95686e7b6f697c504f88981b698ba96338cccf5b32c","last_reissued_at":"2026-05-18T02:38:38.409262Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:38.409262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.0702","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":"2026-05-18T02:38:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IayV+x3zv66E5LSu/htzXARNlFpqipEvWNwK5u/LcrcZ8vRQ1xA1HcldIiSMBbM/HAM6QxC7d0t1Jr9/dZ1bDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T02:49:30.141853Z"},"content_sha256":"3b59415d20c149fd93db5577eabb1dd06e754d485384a40e857e265f679cbe86","schema_version":"1.0","event_id":"sha256:3b59415d20c149fd93db5577eabb1dd06e754d485384a40e857e265f679cbe86"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3B4DCDG6J4VSWQQ35FLINZ5W62","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear bending theories for non Euclidean plates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.soft","authors_text":"Peter Hornung","submitted_at":"2014-11-03T21:24:36Z","abstract_excerpt":"Thin growing tissues (such as plant leaves) can be modelled by a bounded domain $S\\subset R^2$ endowed with a Riemannian metric $g$, which models the internal strains caused by the differential growth of the tissue. The elastic energy is given by a nonlinear isometry-constrained bending energy functional which is a natural generalization of Kirchhoff's plate functional. We introduce and discuss a natural notion of (possibly non-minimising) stationarity points. We show that rotationally symmetric immersions of the unit disk are stationary, and we give examples of metrics $g$ leading to function"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0702","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":"2026-05-18T02:38:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P8lSwysd6cAXu0UDH1chAgEvrh1oZPqaaJ+agJzaIeir6BLjDqsSpjgKciGG/PirsTqQPlw+9bycG8QdTkDvCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T02:49:30.142204Z"},"content_sha256":"31f60f805944b656ea167ed01ff5a731931f22c7ab234dccf5b8d072f1c99f8e","schema_version":"1.0","event_id":"sha256:31f60f805944b656ea167ed01ff5a731931f22c7ab234dccf5b8d072f1c99f8e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3B4DCDG6J4VSWQQ35FLINZ5W62/bundle.json","state_url":"https://pith.science/pith/3B4DCDG6J4VSWQQ35FLINZ5W62/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3B4DCDG6J4VSWQQ35FLINZ5W62/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":"2026-07-04T02:49:30Z","links":{"resolver":"https://pith.science/pith/3B4DCDG6J4VSWQQ35FLINZ5W62","bundle":"https://pith.science/pith/3B4DCDG6J4VSWQQ35FLINZ5W62/bundle.json","state":"https://pith.science/pith/3B4DCDG6J4VSWQQ35FLINZ5W62/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3B4DCDG6J4VSWQQ35FLINZ5W62/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3B4DCDG6J4VSWQQ35FLINZ5W62","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":"7d052668728d4b2b72ad4b3fa73d8298262abe639a28947c9349fc837b234ac4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2014-11-03T21:24:36Z","title_canon_sha256":"f491b78fbe62734802cc6f9867795ea1e494237f6992808dbd0d86edefa5bda8"},"schema_version":"1.0","source":{"id":"1411.0702","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0702","created_at":"2026-05-18T02:38:38Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0702v1","created_at":"2026-05-18T02:38:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0702","created_at":"2026-05-18T02:38:38Z"},{"alias_kind":"pith_short_12","alias_value":"3B4DCDG6J4VS","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3B4DCDG6J4VSWQQ3","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3B4DCDG6","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:31f60f805944b656ea167ed01ff5a731931f22c7ab234dccf5b8d072f1c99f8e","target":"graph","created_at":"2026-05-18T02:38:38Z","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":"Thin growing tissues (such as plant leaves) can be modelled by a bounded domain $S\\subset R^2$ endowed with a Riemannian metric $g$, which models the internal strains caused by the differential growth of the tissue. The elastic energy is given by a nonlinear isometry-constrained bending energy functional which is a natural generalization of Kirchhoff's plate functional. We introduce and discuss a natural notion of (possibly non-minimising) stationarity points. We show that rotationally symmetric immersions of the unit disk are stationary, and we give examples of metrics $g$ leading to function","authors_text":"Peter Hornung","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2014-11-03T21:24:36Z","title":"Nonlinear bending theories for non Euclidean plates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0702","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":"sha256:3b59415d20c149fd93db5577eabb1dd06e754d485384a40e857e265f679cbe86","target":"record","created_at":"2026-05-18T02:38:38Z","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":"7d052668728d4b2b72ad4b3fa73d8298262abe639a28947c9349fc837b234ac4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2014-11-03T21:24:36Z","title_canon_sha256":"f491b78fbe62734802cc6f9867795ea1e494237f6992808dbd0d86edefa5bda8"},"schema_version":"1.0","source":{"id":"1411.0702","kind":"arxiv","version":1}},"canonical_sha256":"d878310cde4f2b2b421be95686e7b6f697c504f88981b698ba96338cccf5b32c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d878310cde4f2b2b421be95686e7b6f697c504f88981b698ba96338cccf5b32c","first_computed_at":"2026-05-18T02:38:38.409262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:38.409262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vFWvso16P3HBy6c4sfvR7gvWnmmVyKBvXU6HsRk4wpR5HmPX6vN+5d/SnXhRE9SPUUFMifSgSHA8MRAmp49cBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:38.409758Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.0702","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b59415d20c149fd93db5577eabb1dd06e754d485384a40e857e265f679cbe86","sha256:31f60f805944b656ea167ed01ff5a731931f22c7ab234dccf5b8d072f1c99f8e"],"state_sha256":"0aecf94bc137f77903bb1e3756e7c1c7b6ea8004f525f77d5fc333cc433d66d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i5kzDlVjUqibIzz/oaCNLNCVHoxfCkep5OViW5zvFxrTM2Jn4DaTaXchQGuq+9c9pSuUpM4PfeWQcz5gn9/WDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T02:49:30.144136Z","bundle_sha256":"f3439a7442b341e323a0c8c12951727bb99e521223e2989c3bbe0f21f8fb2485"}}