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In the zero-potential case, this removes the logarithmic loss in the support-count estimate of Li and Zhang [Duke Math. J. 171 (2022), 327--415]. In high dimensions, our support-only estimates improve Krymskii's support-dimension bound [arXiv:2401.02800], yielding exponents that exceed two for $d\\ge17$ and approac"},"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":"2608.01673","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2026-08-03T04:07:59Z","cross_cats_sorted":[],"title_canon_sha256":"b0b3459690fa9df6241f3dfda323f8427763ff32137a2eee917c38ca3dadd3f3","abstract_canon_sha256":"489457fbf61e76831c94d1c787c06245b4691301a7a349964bc9b0c8a0bdbf76"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T02:06:23.420775Z","signature_b64":"boJEjmFIBtSMjhPS/wl0hVjiW9lVKJwDsYi96GEugAX9lo59Ezok4+ESC1nhzUWlXc45jGSqRa9wwVkF2NACBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"718ef3abbe38ec16fd4d411999d0ffd762f0d7ce14f54eb19f96b63020c30055","last_reissued_at":"2026-08-04T02:06:23.419318Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T02:06:23.419318Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sparse supports of lattice eigenfunctions: quantitative growth and algebraic rigidity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Yunlei Wang","submitted_at":"2026-08-03T04:07:59Z","abstract_excerpt":"We study sparse supports of eigenfunctions on the standard lattice $\\mathbb{Z}^d$. 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