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We first show that on the torus $(\\mathbb{R}/2\\pi\\mathbb{Z})^{2}$, a non-constant eigenfunction has an even number of nodal domains. We then consider the torus $(\\mathbb{R}/2\\pi\\mathbb{Z})\\times(\\mathbb{R}/2\\rho\\pi\\mathbb{Z})\\,$, with $\\rho=\\frac{1}{\\sqrt{3}}\\,$, and construct on it an eigenfunction with three nodal domains."},"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":"1504.03944","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-15T15:29:14Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"13adf4879acb7f217dca061955d89e6a59a664bf5b5df1f8837dcb6303d87413","abstract_canon_sha256":"d266fc59f6787617239b143536fa21cb35f9ac9c5561d034daa1c1bc1d046bef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:58.020805Z","signature_b64":"T5VhWoY04Je+3u7HNmjCCatkul48ImfMQZ9/F77j2FJ7ojzi9NNSaJprAhLPqmy058J5k2EqTUgcKklybAO4DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2372ae317463743e0c10354aedbbb36448d5ec95b6e74d8aecda717022df8b17","last_reissued_at":"2026-05-18T01:36:58.020124Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:58.020124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the parity of the number of nodal domains for an eigenfunction of the Laplacian on tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Corentin L\\'ena","submitted_at":"2015-04-15T15:29:14Z","abstract_excerpt":"In this note, we discuss a question posed by T. 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