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We give a necessary and sufficient condition, depending only on algebraic properties of the polynomial $v$, for when there exists a smooth real function $f$ whose graph $x+if(x)$ lies on a level curve of $v$ connecting $z_1$ to $z_2$. Inspired by GIT, we construct a Kempf-Ness functional on an appropriate function space, and prove the functional is bounded from belo"},"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":"2204.01875","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2022-04-04T22:37:45Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"d304c1cce0a4e83553844b3f83591ee680a15acb45c93eca1d46f2a64c989f6c","abstract_canon_sha256":"659e2b73d112a83c1be43880541de9e8b0334668aa5fa47abbac015790b2aebf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:11:34.171495Z","signature_b64":"Gh6VvCael5MI33iGeCpDO+MXFlMgXWYxk2gzIaptZ4wVZq0QhaAF1Y+ZzccAlZUnhvHQENSUavAntSA8glNiAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8787ace8bb95cf37d353f075a05463327362c09c6197650579f53949c7735ced","last_reissued_at":"2026-07-05T04:11:34.171120Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:11:34.171120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Deformed Hermitian-Yang-Mills Equation and Level Sets of Harmonic Polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Adam Jacob","submitted_at":"2022-04-04T22:37:45Z","abstract_excerpt":"Suppose $v(x,y):\\mathbb C\\rightarrow \\mathbb R$ is an entire harmonic polynomial with no critical points in the right half plane. 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