{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1998:KAKKMXO2227RCXL4ZZVBSK6AKW","short_pith_number":"pith:KAKKMXO2","schema_version":"1.0","canonical_sha256":"5014a65ddad6bf115d7cce6a192bc055b453d227dd54dd0d7115b0165ef5f5ad","source":{"kind":"arxiv","id":"math/9804161","version":1},"attestation_state":"computed","paper":{"title":"On a class of linearizable Monge-Amp\\`ere equations","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel J. Arrigo, James M. Hill","submitted_at":"1998-04-01T00:00:00Z","abstract_excerpt":"Monge-Amp\\`ere equations of the form, $u_{xx}u_{yy}-u_{xy}^2=F(u,u_x,u_y)$ arise in many areas of fluid and solid mechanics. Here it is shown that in the special case $F=u_y^4f(u, u_x/u_y)$, where $f$ denotes an arbitrary function, the Monge-Amp\\`ere equation can be linearized by using a sequence of Amp\\`ere, point, Legendre and rotation transformations. This linearization is a generalization of three examples from finite elasticity, involving plane strain and plane stress deformations of the incompressible perfectly elastic Varga material and also relates to a previous linearization of this e"},"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":"math/9804161","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"1998-04-01T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"edce133b66919c5a4283f0ec2410797d1131139f973da526af90fc2fa8864271","abstract_canon_sha256":"35ba78efd7568e2cda85a0bd5ccae3fabc144455b9ba35829eb88437f9bcb7a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:22.878092Z","signature_b64":"sXvOHYACkVMBCr2IDPPoLr2jMXzp+lbfs7yajXVVVPEe8Wn2P+aE0OzNcTqPfA3KBPMcAFZKQA2eKt2gXPHnAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5014a65ddad6bf115d7cce6a192bc055b453d227dd54dd0d7115b0165ef5f5ad","last_reissued_at":"2026-05-18T01:38:22.877401Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:22.877401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a class of linearizable Monge-Amp\\`ere equations","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel J. Arrigo, James M. Hill","submitted_at":"1998-04-01T00:00:00Z","abstract_excerpt":"Monge-Amp\\`ere equations of the form, $u_{xx}u_{yy}-u_{xy}^2=F(u,u_x,u_y)$ arise in many areas of fluid and solid mechanics. Here it is shown that in the special case $F=u_y^4f(u, u_x/u_y)$, where $f$ denotes an arbitrary function, the Monge-Amp\\`ere equation can be linearized by using a sequence of Amp\\`ere, point, Legendre and rotation transformations. This linearization is a generalization of three examples from finite elasticity, involving plane strain and plane stress deformations of the incompressible perfectly elastic Varga material and also relates to a previous linearization of this e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9804161","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":"math/9804161","created_at":"2026-05-18T01:38:22.877508+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9804161v1","created_at":"2026-05-18T01:38:22.877508+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9804161","created_at":"2026-05-18T01:38:22.877508+00:00"},{"alias_kind":"pith_short_12","alias_value":"KAKKMXO2227R","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_16","alias_value":"KAKKMXO2227RCXL4","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_8","alias_value":"KAKKMXO2","created_at":"2026-05-18T12:25:49.038998+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/KAKKMXO2227RCXL4ZZVBSK6AKW","json":"https://pith.science/pith/KAKKMXO2227RCXL4ZZVBSK6AKW.json","graph_json":"https://pith.science/api/pith-number/KAKKMXO2227RCXL4ZZVBSK6AKW/graph.json","events_json":"https://pith.science/api/pith-number/KAKKMXO2227RCXL4ZZVBSK6AKW/events.json","paper":"https://pith.science/paper/KAKKMXO2"},"agent_actions":{"view_html":"https://pith.science/pith/KAKKMXO2227RCXL4ZZVBSK6AKW","download_json":"https://pith.science/pith/KAKKMXO2227RCXL4ZZVBSK6AKW.json","view_paper":"https://pith.science/paper/KAKKMXO2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9804161&json=true","fetch_graph":"https://pith.science/api/pith-number/KAKKMXO2227RCXL4ZZVBSK6AKW/graph.json","fetch_events":"https://pith.science/api/pith-number/KAKKMXO2227RCXL4ZZVBSK6AKW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KAKKMXO2227RCXL4ZZVBSK6AKW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KAKKMXO2227RCXL4ZZVBSK6AKW/action/storage_attestation","attest_author":"https://pith.science/pith/KAKKMXO2227RCXL4ZZVBSK6AKW/action/author_attestation","sign_citation":"https://pith.science/pith/KAKKMXO2227RCXL4ZZVBSK6AKW/action/citation_signature","submit_replication":"https://pith.science/pith/KAKKMXO2227RCXL4ZZVBSK6AKW/action/replication_record"}},"created_at":"2026-05-18T01:38:22.877508+00:00","updated_at":"2026-05-18T01:38:22.877508+00:00"}