{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:3AQN2QHLSLBITTOM5REBN5YP2A","short_pith_number":"pith:3AQN2QHL","schema_version":"1.0","canonical_sha256":"d820dd40eb92c289cdccec4816f70fd03bdad95db4c9a7738cac41a3461d1814","source":{"kind":"arxiv","id":"1607.02311","version":1},"attestation_state":"computed","paper":{"title":"Second-order structured deformations: relaxation, integral representation and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Ana Cristina Barroso, David R. Owen, Jos\\'e Matias, Marco Morandotti","submitted_at":"2016-07-08T11:03:09Z","abstract_excerpt":"Second-order structured deformations of continua provide an extension of the multiscale geometry of first-order structured deformations by taking into account the effects of submacroscopic bending and curving. We derive here an integral representation for a relaxed energy functional in the setting of second-order structured deformations. Our derivation covers inhomogeneous initial energy densities (i.e., with explicit dependence on the position); finally, we provide explicit formulas for bulk relaxed energies as well as anticipated applications."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1607.02311","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-07-08T11:03:09Z","cross_cats_sorted":[],"title_canon_sha256":"ab910cbb605098ea69ccc848f5bdc0548a475115e18f2b5e028622b7f4b48955","abstract_canon_sha256":"cbdb3416a680a4857a12b230f0e0aced0452fe6a7768da0accbb80bdcaf0aa18"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:00.716012Z","signature_b64":"9/DXESe7UUjv41q5f0lVa5B0AQMI+8wtTuK7n4mVF+4Z9Bq2VAr1xVt31uDSGljtU7pmLWf1RCr3SdruwGpHBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d820dd40eb92c289cdccec4816f70fd03bdad95db4c9a7738cac41a3461d1814","last_reissued_at":"2026-05-18T00:44:00.715264Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:00.715264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Second-order structured deformations: relaxation, integral representation and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Ana Cristina Barroso, David R. Owen, Jos\\'e Matias, Marco Morandotti","submitted_at":"2016-07-08T11:03:09Z","abstract_excerpt":"Second-order structured deformations of continua provide an extension of the multiscale geometry of first-order structured deformations by taking into account the effects of submacroscopic bending and curving. We derive here an integral representation for a relaxed energy functional in the setting of second-order structured deformations. Our derivation covers inhomogeneous initial energy densities (i.e., with explicit dependence on the position); finally, we provide explicit formulas for bulk relaxed energies as well as anticipated applications."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02311","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1607.02311","created_at":"2026-05-18T00:44:00.715388+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.02311v1","created_at":"2026-05-18T00:44:00.715388+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02311","created_at":"2026-05-18T00:44:00.715388+00:00"},{"alias_kind":"pith_short_12","alias_value":"3AQN2QHLSLBI","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"3AQN2QHLSLBITTOM","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"3AQN2QHL","created_at":"2026-05-18T12:29:55.572404+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3AQN2QHLSLBITTOM5REBN5YP2A","json":"https://pith.science/pith/3AQN2QHLSLBITTOM5REBN5YP2A.json","graph_json":"https://pith.science/api/pith-number/3AQN2QHLSLBITTOM5REBN5YP2A/graph.json","events_json":"https://pith.science/api/pith-number/3AQN2QHLSLBITTOM5REBN5YP2A/events.json","paper":"https://pith.science/paper/3AQN2QHL"},"agent_actions":{"view_html":"https://pith.science/pith/3AQN2QHLSLBITTOM5REBN5YP2A","download_json":"https://pith.science/pith/3AQN2QHLSLBITTOM5REBN5YP2A.json","view_paper":"https://pith.science/paper/3AQN2QHL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.02311&json=true","fetch_graph":"https://pith.science/api/pith-number/3AQN2QHLSLBITTOM5REBN5YP2A/graph.json","fetch_events":"https://pith.science/api/pith-number/3AQN2QHLSLBITTOM5REBN5YP2A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3AQN2QHLSLBITTOM5REBN5YP2A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3AQN2QHLSLBITTOM5REBN5YP2A/action/storage_attestation","attest_author":"https://pith.science/pith/3AQN2QHLSLBITTOM5REBN5YP2A/action/author_attestation","sign_citation":"https://pith.science/pith/3AQN2QHLSLBITTOM5REBN5YP2A/action/citation_signature","submit_replication":"https://pith.science/pith/3AQN2QHLSLBITTOM5REBN5YP2A/action/replication_record"}},"created_at":"2026-05-18T00:44:00.715388+00:00","updated_at":"2026-05-18T00:44:00.715388+00:00"}