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Algebraically, the problem can be reformulated as follows: for a vector space $W$ of dimension $n+2$, classify $n$-tuples of skew-symmetric 2-forms $A^{\\alpha} \\in \\Lambda^2(W)$ such that \\[ \\phi_{\\beta \\gamma}A^{\\beta}\\wedge A^{\\gamma}=0, \\] for some non-degenerate symmetric $\\phi$."},"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":"1703.06173","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-03-17T19:06:39Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"c37986283f850d03b58cf95e1512fe48784e66bae260db77cf036626db5094b2","abstract_canon_sha256":"64c100f091f6295da87f29299f2086aefa8ad07717c82d88ac9842aef6c3b2b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:56.558161Z","signature_b64":"kcxaET3aL9bEqXhUq5jQEESYcJYK3id98gMqW/RM19Ci7Xc9sQAQ33J9rCgCfuxsEWItIqZwxALbJfb1fUsACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf56a3c417625e15a8bfaefff950d3a22f79347be161d57a70fdb8ee198a5b89","last_reissued_at":"2026-05-18T00:16:56.557518Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:56.557518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Systems of conservation laws with third-order Hamiltonian structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"nlin.SI","authors_text":"E.V. 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