{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:EPZUAHXXJSGMEQA5AR6TURJ7TC","short_pith_number":"pith:EPZUAHXX","schema_version":"1.0","canonical_sha256":"23f3401ef74c8cc2401d047d3a453f98821327f343cab08fde96f1c6042fcf30","source":{"kind":"arxiv","id":"1504.08003","version":1},"attestation_state":"computed","paper":{"title":"Integrability conditions between the first and second Cosserat deformation tensor in geometrically nonlinear micropolar models and existence of minimizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Frank Osterbrink, Johannes Lankeit, Patrizio Neff","submitted_at":"2015-04-29T20:03:35Z","abstract_excerpt":"In this note we extend integrability conditions for the symmetric stretch tensor $U$ in the polar decomposition of the deformation gradient $\\nabla\\varphi=F=R\\,U$ to the non-symmetric case. In doing so we recover integrability conditions for the first Cosserat deformation tensor. Let $F=\\bar R\\,\\bar U$ with $\\bar R:\\Omega\\subset\\mathbb{R}^3\\longrightarrow\\mathrm{SO}(3)$ and $\\bar U:\\Omega\\subset\\mathbb{R}^3\\longrightarrow \\mathrm{GL}(3)$. Then $\\mathfrak{K}:={\\bar R}^T\\mathrm{Grad}\\,{\\bar R}=\\mathrm{Anti}\\Big( \\frac{1}{\\mathrm{det} \\bar U}\\Big[\\bar U(\\mathrm{Curl} \\bar U)^T-\\frac{1}{2} \\mathrm"},"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":"1504.08003","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-04-29T20:03:35Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"524120bb12ef3afffbf52b01ea186144e6c11a287638968535ed091b8c646b62","abstract_canon_sha256":"0c942c467896f54a024f0697ebf17779e712cf74fc85553295565eb31516b3b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:23.598299Z","signature_b64":"nVKFd4l4x1QKQdos3OICKE4X6TIDpo9SUm/hVJGVpTnCwJbWZmckchSmaV7CPBODv5u9WX9LBZOy7vPxUu0cDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23f3401ef74c8cc2401d047d3a453f98821327f343cab08fde96f1c6042fcf30","last_reissued_at":"2026-05-18T02:17:23.597564Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:23.597564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integrability conditions between the first and second Cosserat deformation tensor in geometrically nonlinear micropolar models and existence of minimizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Frank Osterbrink, Johannes Lankeit, Patrizio Neff","submitted_at":"2015-04-29T20:03:35Z","abstract_excerpt":"In this note we extend integrability conditions for the symmetric stretch tensor $U$ in the polar decomposition of the deformation gradient $\\nabla\\varphi=F=R\\,U$ to the non-symmetric case. In doing so we recover integrability conditions for the first Cosserat deformation tensor. Let $F=\\bar R\\,\\bar U$ with $\\bar R:\\Omega\\subset\\mathbb{R}^3\\longrightarrow\\mathrm{SO}(3)$ and $\\bar U:\\Omega\\subset\\mathbb{R}^3\\longrightarrow \\mathrm{GL}(3)$. Then $\\mathfrak{K}:={\\bar R}^T\\mathrm{Grad}\\,{\\bar R}=\\mathrm{Anti}\\Big( \\frac{1}{\\mathrm{det} \\bar U}\\Big[\\bar U(\\mathrm{Curl} \\bar U)^T-\\frac{1}{2} \\mathrm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08003","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":"1504.08003","created_at":"2026-05-18T02:17:23.597688+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.08003v1","created_at":"2026-05-18T02:17:23.597688+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.08003","created_at":"2026-05-18T02:17:23.597688+00:00"},{"alias_kind":"pith_short_12","alias_value":"EPZUAHXXJSGM","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"EPZUAHXXJSGMEQA5","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"EPZUAHXX","created_at":"2026-05-18T12:29:19.899920+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/EPZUAHXXJSGMEQA5AR6TURJ7TC","json":"https://pith.science/pith/EPZUAHXXJSGMEQA5AR6TURJ7TC.json","graph_json":"https://pith.science/api/pith-number/EPZUAHXXJSGMEQA5AR6TURJ7TC/graph.json","events_json":"https://pith.science/api/pith-number/EPZUAHXXJSGMEQA5AR6TURJ7TC/events.json","paper":"https://pith.science/paper/EPZUAHXX"},"agent_actions":{"view_html":"https://pith.science/pith/EPZUAHXXJSGMEQA5AR6TURJ7TC","download_json":"https://pith.science/pith/EPZUAHXXJSGMEQA5AR6TURJ7TC.json","view_paper":"https://pith.science/paper/EPZUAHXX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.08003&json=true","fetch_graph":"https://pith.science/api/pith-number/EPZUAHXXJSGMEQA5AR6TURJ7TC/graph.json","fetch_events":"https://pith.science/api/pith-number/EPZUAHXXJSGMEQA5AR6TURJ7TC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EPZUAHXXJSGMEQA5AR6TURJ7TC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EPZUAHXXJSGMEQA5AR6TURJ7TC/action/storage_attestation","attest_author":"https://pith.science/pith/EPZUAHXXJSGMEQA5AR6TURJ7TC/action/author_attestation","sign_citation":"https://pith.science/pith/EPZUAHXXJSGMEQA5AR6TURJ7TC/action/citation_signature","submit_replication":"https://pith.science/pith/EPZUAHXXJSGMEQA5AR6TURJ7TC/action/replication_record"}},"created_at":"2026-05-18T02:17:23.597688+00:00","updated_at":"2026-05-18T02:17:23.597688+00:00"}