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In Theorem 3.8 we reformulate the projective metrizability problem for a spray in terms of a first-order partial differential operator $P_1$ and a set of algebraic conditions on semi-basic 1-forms. We discuss the formal integrability of $P_1$ using two sufficient conditions provided by Cartan-K\\\"ahler theorem. We prove in Theorem 4.2 that the symbol of $P_1$ is involutive and hence one of the two condition"},"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":"1105.2142","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DG","submitted_at":"2011-05-11T09:48:34Z","cross_cats_sorted":[],"title_canon_sha256":"a7fcff33ee4b0b722b5c6a10907bf2bcf566f57a47a4936d387fa03160cc35ee","abstract_canon_sha256":"b1dca60e2fec32b9f31a99e2a3ae4d7b4732a01070bb43168f62508e8ce1bb1e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:43.520921Z","signature_b64":"skxyRCPHz9YdjRBm2I6r/uESKigfGwNbupxsValqF2WaWCbKUi4MwOInuxM9bDfYCpl235mWpDFPH3TfmDpJBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2bbde3e77c46bfd8553b39748b43aad5d377915f3790e76e51bda8b27c1f1e27","last_reissued_at":"2026-05-18T04:06:43.520434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:43.520434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Projective Metrizability and Formal Integrability","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ioan Bucataru, Zolt\\'an Muzsnay","submitted_at":"2011-05-11T09:48:34Z","abstract_excerpt":"The projective metrizability problem can be formulated as follows: under what conditions the geodesics of a given spray coincide with the geodesics of some Finsler space, as oriented curves. 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