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

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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-15
DOI
https://doi.org/10.5281/zenodo.23397853
Primary Topic
Geometry and complex manifolds
Type
preprint
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preprint

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

Kriebel Alec
Zenodo (CERN European Organization for Nuclear Research)
Geometry and complex manifolds
preprint

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

Kriebel Alec
preprint en

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.

Zenodo (CERN European Organization for Nuclear Research)
Geometry and complex manifolds
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