# Verification of unbounded disjoint line pinning

The five-page English manuscript gives an explicit construction for every
integer m >= 3, with m+4 pairwise disjoint full-dimensional convex bodies in
R^3 and m indispensable members. It extends to every d >= 3 with m+3d-5 bodies.

The written proof verifies compactness, nonempty interiors, positive pairwise
separation, distinct single-point axis contacts, a genuine open line-space
neighborhood, uniform convexity of the oscillatory epigraph functions, an exact
intersection criterion, isolation and explicit deletion-witness sequences.
It never substitutes path isolation for point isolation.

The exact standard-library checker verifies the derivative by sparse formal
product and chain rules, the strict rational curvature estimate, the anchor
and square-completion identities, rational circular-phase bookkeeping, and
extra-coordinate midpoint controls. Normal and Python -O runs agree:
120483 checks, 15625 anchor trials, 103974 rational phase trials, and 28125
extra-coordinate trials. These finite diagnostics are not a formal proof of
the infinite parameter family. That proof is contained in the manuscript.

Every page was visually inspected, the current LaTeX source passed the built-in
compiler, and the portable archive was rebuilt and its checker rerun in both
Python modes. The PDF contains the author name at the top, the Mercury Software
GmbH affiliation in a footnote, and AI assistance in ordinary body text.

This is an originating-researcher self-audit, not independent external review
or proof-assistant verification. The four-constraint regulus reduction is
classical and credited. The arbitrary-convex-set question is answered, but the
separate disjoint-polytope question is not. No absolute priority is asserted.