# Verification of the nodal decic counterexample

The complete geometric proof is in main.tex. It constructs a degree-ten
threefold with exactly the sixty prescribed H4 nodes, not merely a point
set or an example with unidentified extra singularities. The projection
assertion fails because 60 > 54, while the strict node bound 60 < 81 holds.
Ambient curves satisfy the stronger incidence bound 7k.

The exact checker reproduces three local nodal Hessian determinants:
-8, 4194304 and -13107200. Rational Groebner bases prove finiteness of
every active-coordinate singularity stratum over C. A 60-by-60 evaluation
minor in degree six has determinant 39 modulo 101 with phi=23; two exact
implementations agree. Its nonzero reduction certifies characteristic-zero
interpolation. Normal and optimized Python runs produce identical reports.
The modular calculation is not used to replace the known general-projection
theorem or the characteristic-zero singular-locus argument.

The author's self audit checks pointwise base-locus separation, simultaneous
choice of g outside the finite unwanted set, the nondegenerate quadratic
terms at all prescribed points, and the five independent jet conditions
that exclude every remaining singularity for generic h. It also checks
irreducibility, general-projection injectivity and the precise source scope.
The construction asserts existence of suitable g and h; no particular
numeric coefficients for them are claimed.

The main manuscript was compiled by the built-in LaTeX compiler and by
Tectonic. Final page inspection and portable-package build evidence are
recorded in build_record.json and manifest.json when the package is sealed.

This is originating-researcher self-audit, not independent expert review.
No formal proof-assistant verification, peer review or absolute priority
is claimed. The known H4 and factoriality inputs remain attributed. The
counterexample resolves the projection assertion, not every subquestion
of the multi-part frozen record.