{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:TNP4TNDZ6Z5PR3AH2HWP2QNSUP","short_pith_number":"pith:TNP4TNDZ","canonical_record":{"source":{"id":"1104.0661","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-04T19:40:50Z","cross_cats_sorted":[],"title_canon_sha256":"57c3e71ccb371a9c9caaff4bf74cb73bcc5e1e4fa3b420d550fd4c4f3c833acd","abstract_canon_sha256":"2b1adce9042c5fe19e93b7dfea67b2c531a0ff30f2d0afc795911ae352ad5ae3"},"schema_version":"1.0"},"canonical_sha256":"9b5fc9b479f67af8ec07d1ecfd41b2a3f86fd38b2268b6976794c4bcc005b3ec","source":{"kind":"arxiv","id":"1104.0661","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0661","created_at":"2026-05-18T04:25:03Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0661v1","created_at":"2026-05-18T04:25:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0661","created_at":"2026-05-18T04:25:03Z"},{"alias_kind":"pith_short_12","alias_value":"TNP4TNDZ6Z5P","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TNP4TNDZ6Z5PR3AH","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TNP4TNDZ","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:TNP4TNDZ6Z5PR3AH2HWP2QNSUP","target":"record","payload":{"canonical_record":{"source":{"id":"1104.0661","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-04T19:40:50Z","cross_cats_sorted":[],"title_canon_sha256":"57c3e71ccb371a9c9caaff4bf74cb73bcc5e1e4fa3b420d550fd4c4f3c833acd","abstract_canon_sha256":"2b1adce9042c5fe19e93b7dfea67b2c531a0ff30f2d0afc795911ae352ad5ae3"},"schema_version":"1.0"},"canonical_sha256":"9b5fc9b479f67af8ec07d1ecfd41b2a3f86fd38b2268b6976794c4bcc005b3ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:03.717582Z","signature_b64":"ulGnhhCS1qQRt6QnA0Ueq/WpT254375AFy9ycPuvfIKPR30Ln24sy9ihJkCzCF8hbh1WHoOvlMqKR38JJ95jCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b5fc9b479f67af8ec07d1ecfd41b2a3f86fd38b2268b6976794c4bcc005b3ec","last_reissued_at":"2026-05-18T04:25:03.716731Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:03.716731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.0661","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":"2026-05-18T04:25:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GDTV3wxUvW2/Mt7hi4e/eopbSfiCWFaG62jBtGasyflmQYqURay7cDSNmvGDSIEubWDAfribhUYGuwegKiELCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:17:56.270873Z"},"content_sha256":"12c31f87dcded639395ae36c8757bf905b61f8bf67a3781c9a8b41e371585849","schema_version":"1.0","event_id":"sha256:12c31f87dcded639395ae36c8757bf905b61f8bf67a3781c9a8b41e371585849"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:TNP4TNDZ6Z5PR3AH2HWP2QNSUP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Periodically wrinkled plate of the F\\\"oppl-von K\\'arm\\'an type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Igor Vel\\v{c}i\\'c","submitted_at":"2011-04-04T19:40:50Z","abstract_excerpt":"In this paper we derive, by means of $\\Gamma$-convergence, the periodically wrinkled plate model starting from three dimensional nonlinear elasticity. We assume that the thickness of the plate is $h^2$ and that the mid-surface of the plate is given by $(x_1,x_2) \\to (x_1,x_2,h^2\\theta(\\per))$, where $\\theta$ is $[0,1]^2$ periodic function. We also assume that the strain energy of the plate has the order $h^8=(h^2)^4$, which corresponds to the F\\\"oppl-von K\\'arm\\'an model in the case of the ordinary plate. The obtained model mixes the bending part of the energy with the stretching part."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0661","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":"2026-05-18T04:25:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S5f5W638cLWC80mA2pIqKtoPJZFabsRWrm0IZmsT955QE6lILTjwV4c3rF4ZgVa+577xq/kGDEk9y1QSJO6mCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:17:56.271629Z"},"content_sha256":"fe71e449b09ae71697c4c06d363a413523e815d1de9a0485d2ef453182889ab8","schema_version":"1.0","event_id":"sha256:fe71e449b09ae71697c4c06d363a413523e815d1de9a0485d2ef453182889ab8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TNP4TNDZ6Z5PR3AH2HWP2QNSUP/bundle.json","state_url":"https://pith.science/pith/TNP4TNDZ6Z5PR3AH2HWP2QNSUP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TNP4TNDZ6Z5PR3AH2HWP2QNSUP/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":"2026-06-09T03:17:56Z","links":{"resolver":"https://pith.science/pith/TNP4TNDZ6Z5PR3AH2HWP2QNSUP","bundle":"https://pith.science/pith/TNP4TNDZ6Z5PR3AH2HWP2QNSUP/bundle.json","state":"https://pith.science/pith/TNP4TNDZ6Z5PR3AH2HWP2QNSUP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TNP4TNDZ6Z5PR3AH2HWP2QNSUP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TNP4TNDZ6Z5PR3AH2HWP2QNSUP","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":"2b1adce9042c5fe19e93b7dfea67b2c531a0ff30f2d0afc795911ae352ad5ae3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-04T19:40:50Z","title_canon_sha256":"57c3e71ccb371a9c9caaff4bf74cb73bcc5e1e4fa3b420d550fd4c4f3c833acd"},"schema_version":"1.0","source":{"id":"1104.0661","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0661","created_at":"2026-05-18T04:25:03Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0661v1","created_at":"2026-05-18T04:25:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0661","created_at":"2026-05-18T04:25:03Z"},{"alias_kind":"pith_short_12","alias_value":"TNP4TNDZ6Z5P","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TNP4TNDZ6Z5PR3AH","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TNP4TNDZ","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:fe71e449b09ae71697c4c06d363a413523e815d1de9a0485d2ef453182889ab8","target":"graph","created_at":"2026-05-18T04:25:03Z","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":"In this paper we derive, by means of $\\Gamma$-convergence, the periodically wrinkled plate model starting from three dimensional nonlinear elasticity. We assume that the thickness of the plate is $h^2$ and that the mid-surface of the plate is given by $(x_1,x_2) \\to (x_1,x_2,h^2\\theta(\\per))$, where $\\theta$ is $[0,1]^2$ periodic function. We also assume that the strain energy of the plate has the order $h^8=(h^2)^4$, which corresponds to the F\\\"oppl-von K\\'arm\\'an model in the case of the ordinary plate. The obtained model mixes the bending part of the energy with the stretching part.","authors_text":"Igor Vel\\v{c}i\\'c","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-04T19:40:50Z","title":"Periodically wrinkled plate of the F\\\"oppl-von K\\'arm\\'an type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0661","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":"sha256:12c31f87dcded639395ae36c8757bf905b61f8bf67a3781c9a8b41e371585849","target":"record","created_at":"2026-05-18T04:25:03Z","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":"2b1adce9042c5fe19e93b7dfea67b2c531a0ff30f2d0afc795911ae352ad5ae3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-04T19:40:50Z","title_canon_sha256":"57c3e71ccb371a9c9caaff4bf74cb73bcc5e1e4fa3b420d550fd4c4f3c833acd"},"schema_version":"1.0","source":{"id":"1104.0661","kind":"arxiv","version":1}},"canonical_sha256":"9b5fc9b479f67af8ec07d1ecfd41b2a3f86fd38b2268b6976794c4bcc005b3ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b5fc9b479f67af8ec07d1ecfd41b2a3f86fd38b2268b6976794c4bcc005b3ec","first_computed_at":"2026-05-18T04:25:03.716731Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:03.716731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ulGnhhCS1qQRt6QnA0Ueq/WpT254375AFy9ycPuvfIKPR30Ln24sy9ihJkCzCF8hbh1WHoOvlMqKR38JJ95jCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:03.717582Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0661","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12c31f87dcded639395ae36c8757bf905b61f8bf67a3781c9a8b41e371585849","sha256:fe71e449b09ae71697c4c06d363a413523e815d1de9a0485d2ef453182889ab8"],"state_sha256":"67a3c8e76703d54bb9f4c3b91076950c7d6c11c50e78407b80858f90e1b1b83b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fzHoYSiV45L3dg7qQdnp1hq1OXTvmVnXHVRHe9nsDhXuupo+0ApqpBVxgYeEDastjLrEPA+zcOGevuxjv+PaDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T03:17:56.276092Z","bundle_sha256":"fd1b10bc4ddc31ed6c2f75ec7877389a516d7134c070bf56ae879d378bab3bdb"}}