An interior second-order defect from a Hele-Shaw contact arc

Abstract

A detailed attributed proof/application of Ross–Witt Nyström's smooth Hele-Shaw contact-arc construction. The associated bounded weak homogeneous complex Monge–Ampère solution on P1 times the disc lacks a second-order real Taylor expansion at a genuine interior point, despite smooth strictly positive fibre boundary forms. A zero-area arc filling gives a strict Green-function time-slope gap; finite negative curvature on the smooth covering-space family and global concavity give incompatible Legendre quadratic coefficients. The contact geometry, strong flow, obstacle identity and duality are prior. Witt Nyström's joint-work Oberwolfach2021 contribution with Ross already announces and sketches an interior construction and is prominently credited. This is a modest proof/application note, not a first-discovery claim or certification of a currently open problem's novel resolution. A bounded18-entry source/list and64-query audit found no complete exact predecessor within its inspected scope; historical priority and independent discovery remain unresolved. The deposit contains a five-page note, LaTeX source, exact standard-library scalar certificates, analytic dependency audits and a source/priority record. Computation checks scalar algebra only. AI tools were used extensively. The preprint is unrefereed and has not undergone conventional human peer review.