{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:NBKHMKFGIPUNMOFN3PNU4XBNTA","short_pith_number":"pith:NBKHMKFG","canonical_record":{"source":{"id":"1009.5000","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-09-25T09:36:35Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"baa06014426dd158299ca43bd5e8ad2a07481f7acf8f38be69788ec9d6edda13","abstract_canon_sha256":"5cb66bb89a13f4692f850826db7dc4d3e51b3bad023aa785369c9b6657ce7ef9"},"schema_version":"1.0"},"canonical_sha256":"68547628a643e8d638addbdb4e5c2d98122c6b4b7ec24bab23ac561ee2e39570","source":{"kind":"arxiv","id":"1009.5000","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5000","created_at":"2026-05-18T04:40:19Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5000v1","created_at":"2026-05-18T04:40:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5000","created_at":"2026-05-18T04:40:19Z"},{"alias_kind":"pith_short_12","alias_value":"NBKHMKFGIPUN","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"NBKHMKFGIPUNMOFN","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"NBKHMKFG","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:NBKHMKFGIPUNMOFN3PNU4XBNTA","target":"record","payload":{"canonical_record":{"source":{"id":"1009.5000","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-09-25T09:36:35Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"baa06014426dd158299ca43bd5e8ad2a07481f7acf8f38be69788ec9d6edda13","abstract_canon_sha256":"5cb66bb89a13f4692f850826db7dc4d3e51b3bad023aa785369c9b6657ce7ef9"},"schema_version":"1.0"},"canonical_sha256":"68547628a643e8d638addbdb4e5c2d98122c6b4b7ec24bab23ac561ee2e39570","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:19.453049Z","signature_b64":"TednCWsrcqSouvwVN5pQMUszJV4MMwrnveSbu1oOuQGs+zNimKosy8JKM1g2nMD6oQZRqaNh+5xe3BcAUUP6DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68547628a643e8d638addbdb4e5c2d98122c6b4b7ec24bab23ac561ee2e39570","last_reissued_at":"2026-05-18T04:40:19.452448Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:19.452448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.5000","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":"2026-05-18T04:40:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i0w4SJNAzB7SP8UWJY5CgqHJUdcE566/rZSNwDZcCFgctFwnkWIqBNHjfV0AgQ0Kec89i4klLjMy4cw8NSZ7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T18:31:11.647021Z"},"content_sha256":"fda8a93ed6380c93c8447a14083e67d8317b51c5bbf345c7e8bed349eb4c7bdf","schema_version":"1.0","event_id":"sha256:fda8a93ed6380c93c8447a14083e67d8317b51c5bbf345c7e8bed349eb4c7bdf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:NBKHMKFGIPUNMOFN3PNU4XBNTA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Models of Laminated Piezoelectric Beams Including Effect of Transverse Interactions Between Different Layers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"C. Maurini, F. dell'Isola, J. Pouget","submitted_at":"2010-09-25T09:36:35Z","abstract_excerpt":"The present work attempts to present a consistent and efficient approach to piezoelectric laminated beams. The influence of hypotheses on three-dimensional sectional deformations and stress distributions on the estimate of the beam electromechanical properties is analyzed. By exploiting a mixed variational formulation and Lagrange multipliers method, an Euler- Bernoulli-like beam model which accounts for transverse interactions between different is presented. The fully coupled electromechanical nature of the system is described by including both mechanical and electrical kinematical descriptor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5000","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":"2026-05-18T04:40:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4tYiwNhM3jDtlLPvk8fYPNBezsMDONKqaxPUlW1md4Ww6t4AiD7oey6AKgbRUnQDyS1y3ibLUwmKgoUqIYqXDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T18:31:11.647372Z"},"content_sha256":"9b825cd128acb58768cca363e32e6d2c85af16447c5fb1e39fedc978ca7304ba","schema_version":"1.0","event_id":"sha256:9b825cd128acb58768cca363e32e6d2c85af16447c5fb1e39fedc978ca7304ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NBKHMKFGIPUNMOFN3PNU4XBNTA/bundle.json","state_url":"https://pith.science/pith/NBKHMKFGIPUNMOFN3PNU4XBNTA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NBKHMKFGIPUNMOFN3PNU4XBNTA/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":"2026-06-26T18:31:11Z","links":{"resolver":"https://pith.science/pith/NBKHMKFGIPUNMOFN3PNU4XBNTA","bundle":"https://pith.science/pith/NBKHMKFGIPUNMOFN3PNU4XBNTA/bundle.json","state":"https://pith.science/pith/NBKHMKFGIPUNMOFN3PNU4XBNTA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NBKHMKFGIPUNMOFN3PNU4XBNTA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:NBKHMKFGIPUNMOFN3PNU4XBNTA","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":"5cb66bb89a13f4692f850826db7dc4d3e51b3bad023aa785369c9b6657ce7ef9","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-09-25T09:36:35Z","title_canon_sha256":"baa06014426dd158299ca43bd5e8ad2a07481f7acf8f38be69788ec9d6edda13"},"schema_version":"1.0","source":{"id":"1009.5000","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5000","created_at":"2026-05-18T04:40:19Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5000v1","created_at":"2026-05-18T04:40:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5000","created_at":"2026-05-18T04:40:19Z"},{"alias_kind":"pith_short_12","alias_value":"NBKHMKFGIPUN","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"NBKHMKFGIPUNMOFN","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"NBKHMKFG","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:9b825cd128acb58768cca363e32e6d2c85af16447c5fb1e39fedc978ca7304ba","target":"graph","created_at":"2026-05-18T04:40:19Z","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":"The present work attempts to present a consistent and efficient approach to piezoelectric laminated beams. The influence of hypotheses on three-dimensional sectional deformations and stress distributions on the estimate of the beam electromechanical properties is analyzed. By exploiting a mixed variational formulation and Lagrange multipliers method, an Euler- Bernoulli-like beam model which accounts for transverse interactions between different is presented. The fully coupled electromechanical nature of the system is described by including both mechanical and electrical kinematical descriptor","authors_text":"C. Maurini, F. dell'Isola, J. Pouget","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-09-25T09:36:35Z","title":"Models of Laminated Piezoelectric Beams Including Effect of Transverse Interactions Between Different Layers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5000","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:fda8a93ed6380c93c8447a14083e67d8317b51c5bbf345c7e8bed349eb4c7bdf","target":"record","created_at":"2026-05-18T04:40:19Z","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":"5cb66bb89a13f4692f850826db7dc4d3e51b3bad023aa785369c9b6657ce7ef9","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-09-25T09:36:35Z","title_canon_sha256":"baa06014426dd158299ca43bd5e8ad2a07481f7acf8f38be69788ec9d6edda13"},"schema_version":"1.0","source":{"id":"1009.5000","kind":"arxiv","version":1}},"canonical_sha256":"68547628a643e8d638addbdb4e5c2d98122c6b4b7ec24bab23ac561ee2e39570","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68547628a643e8d638addbdb4e5c2d98122c6b4b7ec24bab23ac561ee2e39570","first_computed_at":"2026-05-18T04:40:19.452448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:19.452448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TednCWsrcqSouvwVN5pQMUszJV4MMwrnveSbu1oOuQGs+zNimKosy8JKM1g2nMD6oQZRqaNh+5xe3BcAUUP6DA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:19.453049Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.5000","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fda8a93ed6380c93c8447a14083e67d8317b51c5bbf345c7e8bed349eb4c7bdf","sha256:9b825cd128acb58768cca363e32e6d2c85af16447c5fb1e39fedc978ca7304ba"],"state_sha256":"dc538b75d9252483d0fc1548daffeca3362a019bdd8710a9acae3910d2450014"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"50CAhUw8o+KXShNmyJXrDjzHzIy66qKGIf5Vxv3WsHWvfswo/ixnu7MR/NnKUu71ImB9Y4k3ThpDtuX7wwiMAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T18:31:11.649191Z","bundle_sha256":"3ce982b3c410176667360e8874d0d33f02f3c81d1606c354b90584bf9957939d"}}