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When given the symmetry $z\\to-z$, the set of weakly non-linear interacting waves display a Kolmogorov-Zakharov (KZ) spectrum $n_k\\sim k^{-4}$ in wave vector space. The wave system was studied experimentally with two inmiscible fluids of almost equal densities (water and silicon oil) where the capillary surface waves are excited by a low frequency random f"},"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":"0901.3507","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2009-01-22T20:17:24Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"a5d17c5536677e3c43b64948942ca9638a814a0a6aa7142bc68e61b66c2b4bf0","abstract_canon_sha256":"d18c9d5db67190ed02f629d0240d9d12d0f32b83db8c4be7947378a9539efe2e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:14:56.227561Z","signature_b64":"vCjJsgkeFvTVG4M7Scl3PB5aB8LfvKBoQTYWphrlPFkojFqM/mm+hueKyqcQxYp5zIrqnKWYAVyR0nJkb+7AAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"373bcca2bb05db72cd0630d2aa4481e09638b1616bdcf0501cf97b688a6e2852","last_reissued_at":"2026-05-18T02:14:56.226878Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:14:56.226878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetry Induced 4-Wave Capillary Wave Turbulence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.soft","authors_text":"Claudio Falc\\'on, Gustavo D\\\"uring","submitted_at":"2009-01-22T20:17:24Z","abstract_excerpt":"We report theoretical and experimental results on 4-wave capillary wave turbulence. 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