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We answer the following question: Given a pseudo-spherical surface determined by a solution $u$ of such an equation, do the coefficients of the second fundamental form of the local isometric immersion in $\\mathbb{R}^3$ depend on a jet of finite order of $u$? We show that, except for the sine-Gordon equation, where the coefficients  depend on a jet of o"},"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":"1308.6545","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-29T18:24:05Z","cross_cats_sorted":[],"title_canon_sha256":"255f3aa6612b2f7cbcd050fba5ae832d9b95ac26d197fc7d7a5843a858d15330","abstract_canon_sha256":"7fe372a776c95144362a0503181ac6a8ada4e22ce86720b00853c4a4ec3669d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:49.378552Z","signature_b64":"gnTpVjoGws2+mnkXTf6HYDFskSL9HWRkXvLNRDLH9+MDsLQ/HMK2Fk56Y8UuDgNtQ0w8MwsTnMbxdhc4Smz1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c225d602df760bb70e8a22021e664ed9cba9367af0abb4b0438dd9555d34636","last_reissued_at":"2026-05-18T01:33:49.378102Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:49.378102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Second-order equations and local isometric immersions of pseudo-spherical surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Keti Tenenblat, Nabil Kahouadji, Niky Kamran","submitted_at":"2013-08-29T18:24:05Z","abstract_excerpt":"We consider the class of differential equations that describe pseudo-spherical surfaces of the form  $u\\_t=F(u,u\\_x,u\\_{xx})$ and $u\\_{xt}=F(u, u\\_x)$ given in Chern-Tenenblat \\cite{ChernTenenblat} and Rabelo-Tenenblat \\cite{RabeloTenenblat90}.  We answer the following question: Given a pseudo-spherical surface determined by a solution $u$ of such an equation, do the coefficients of the second fundamental form of the local isometric immersion in $\\mathbb{R}^3$ depend on a jet of finite order of $u$? We show that, except for the sine-Gordon equation, where the coefficients  depend on a jet of o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6545","kind":"arxiv","version":2},"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":"1308.6545","created_at":"2026-05-18T01:33:49.378168+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.6545v2","created_at":"2026-05-18T01:33:49.378168+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6545","created_at":"2026-05-18T01:33:49.378168+00:00"},{"alias_kind":"pith_short_12","alias_value":"RQRF2YBN65QL","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"RQRF2YBN65QLW4HI","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"RQRF2YBN","created_at":"2026-05-18T12:27:59.945178+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/RQRF2YBN65QLW4HIUIQCDZTE5W","json":"https://pith.science/pith/RQRF2YBN65QLW4HIUIQCDZTE5W.json","graph_json":"https://pith.science/api/pith-number/RQRF2YBN65QLW4HIUIQCDZTE5W/graph.json","events_json":"https://pith.science/api/pith-number/RQRF2YBN65QLW4HIUIQCDZTE5W/events.json","paper":"https://pith.science/paper/RQRF2YBN"},"agent_actions":{"view_html":"https://pith.science/pith/RQRF2YBN65QLW4HIUIQCDZTE5W","download_json":"https://pith.science/pith/RQRF2YBN65QLW4HIUIQCDZTE5W.json","view_paper":"https://pith.science/paper/RQRF2YBN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.6545&json=true","fetch_graph":"https://pith.science/api/pith-number/RQRF2YBN65QLW4HIUIQCDZTE5W/graph.json","fetch_events":"https://pith.science/api/pith-number/RQRF2YBN65QLW4HIUIQCDZTE5W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RQRF2YBN65QLW4HIUIQCDZTE5W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RQRF2YBN65QLW4HIUIQCDZTE5W/action/storage_attestation","attest_author":"https://pith.science/pith/RQRF2YBN65QLW4HIUIQCDZTE5W/action/author_attestation","sign_citation":"https://pith.science/pith/RQRF2YBN65QLW4HIUIQCDZTE5W/action/citation_signature","submit_replication":"https://pith.science/pith/RQRF2YBN65QLW4HIUIQCDZTE5W/action/replication_record"}},"created_at":"2026-05-18T01:33:49.378168+00:00","updated_at":"2026-05-18T01:33:49.378168+00:00"}