{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:7S7GHLXEFYNQJN2BYNNKYPM5MT","short_pith_number":"pith:7S7GHLXE","schema_version":"1.0","canonical_sha256":"fcbe63aee42e1b04b741c35aac3d9d64e8e375f581bec85a824764950088c739","source":{"kind":"arxiv","id":"1505.02203","version":3},"attestation_state":"computed","paper":{"title":"Geometry of logarithmic strain measures in solid mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bernhard Eidel, Patrizio Neff, Robert J. Martin","submitted_at":"2015-05-08T22:38:46Z","abstract_excerpt":"We consider the two logarithmic strain measures\\[\\omega_{\\rm iso}=\\|\\mathrm{dev}_n\\log U\\|=\\|\\mathrm{dev}_n\\log \\sqrt{F^TF}\\|\\quad\\text{ and }\\quad \\omega_{\\rm vol}=|\\mathrm{tr}(\\log U)|=|\\mathrm{tr}(\\log\\sqrt{F^TF})|\\,,\\]which are isotropic invariants of the Hencky strain tensor $\\log U$, and show that they can be uniquely characterized by purely geometric methods based on the geodesic distance on the general linear group $\\mathrm{GL}(n)$. Here, $F$ is the deformation gradient, $U=\\sqrt{F^TF}$ is the right Biot-stretch tensor, $\\log$ denotes the principal matrix logarithm, $\\|.\\|$ is the Frob"},"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":"1505.02203","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-08T22:38:46Z","cross_cats_sorted":[],"title_canon_sha256":"11b82a9db4705d3476f977ed690f62d0bc5721198e3bf7666f915aa5f24760b0","abstract_canon_sha256":"295acfa67906d55fc383c0e32b9ca20731246328515c5e6abf9865f888ed611d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:53.926602Z","signature_b64":"lLJOt3nPr+dtrCqs8fFXomEdJuxiKrMXCvAbGaeGjZHEu3XFP2KpURqliVf9WCKGV6vzB+NTK5rRYqf2QM1FAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcbe63aee42e1b04b741c35aac3d9d64e8e375f581bec85a824764950088c739","last_reissued_at":"2026-05-18T01:00:53.925900Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:53.925900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometry of logarithmic strain measures in solid mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bernhard Eidel, Patrizio Neff, Robert J. Martin","submitted_at":"2015-05-08T22:38:46Z","abstract_excerpt":"We consider the two logarithmic strain measures\\[\\omega_{\\rm iso}=\\|\\mathrm{dev}_n\\log U\\|=\\|\\mathrm{dev}_n\\log \\sqrt{F^TF}\\|\\quad\\text{ and }\\quad \\omega_{\\rm vol}=|\\mathrm{tr}(\\log U)|=|\\mathrm{tr}(\\log\\sqrt{F^TF})|\\,,\\]which are isotropic invariants of the Hencky strain tensor $\\log U$, and show that they can be uniquely characterized by purely geometric methods based on the geodesic distance on the general linear group $\\mathrm{GL}(n)$. Here, $F$ is the deformation gradient, $U=\\sqrt{F^TF}$ is the right Biot-stretch tensor, $\\log$ denotes the principal matrix logarithm, $\\|.\\|$ is the Frob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02203","kind":"arxiv","version":3},"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":"1505.02203","created_at":"2026-05-18T01:00:53.926022+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.02203v3","created_at":"2026-05-18T01:00:53.926022+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02203","created_at":"2026-05-18T01:00:53.926022+00:00"},{"alias_kind":"pith_short_12","alias_value":"7S7GHLXEFYNQ","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"7S7GHLXEFYNQJN2B","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"7S7GHLXE","created_at":"2026-05-18T12:29:10.953037+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/7S7GHLXEFYNQJN2BYNNKYPM5MT","json":"https://pith.science/pith/7S7GHLXEFYNQJN2BYNNKYPM5MT.json","graph_json":"https://pith.science/api/pith-number/7S7GHLXEFYNQJN2BYNNKYPM5MT/graph.json","events_json":"https://pith.science/api/pith-number/7S7GHLXEFYNQJN2BYNNKYPM5MT/events.json","paper":"https://pith.science/paper/7S7GHLXE"},"agent_actions":{"view_html":"https://pith.science/pith/7S7GHLXEFYNQJN2BYNNKYPM5MT","download_json":"https://pith.science/pith/7S7GHLXEFYNQJN2BYNNKYPM5MT.json","view_paper":"https://pith.science/paper/7S7GHLXE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.02203&json=true","fetch_graph":"https://pith.science/api/pith-number/7S7GHLXEFYNQJN2BYNNKYPM5MT/graph.json","fetch_events":"https://pith.science/api/pith-number/7S7GHLXEFYNQJN2BYNNKYPM5MT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7S7GHLXEFYNQJN2BYNNKYPM5MT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7S7GHLXEFYNQJN2BYNNKYPM5MT/action/storage_attestation","attest_author":"https://pith.science/pith/7S7GHLXEFYNQJN2BYNNKYPM5MT/action/author_attestation","sign_citation":"https://pith.science/pith/7S7GHLXEFYNQJN2BYNNKYPM5MT/action/citation_signature","submit_replication":"https://pith.science/pith/7S7GHLXEFYNQJN2BYNNKYPM5MT/action/replication_record"}},"created_at":"2026-05-18T01:00:53.926022+00:00","updated_at":"2026-05-18T01:00:53.926022+00:00"}