A NON-GORENSTEIN POINT ON A SMOOTHABLE HILBERT SCHEME
Verification scripts for Appendix A

These programs verify the auxiliary smooth point of Hilbert function (1,5,4)
used in the paper: the explicit ideal J of Appendix A, its smoothing, and the
dimension 50 of its tangent space. They do not check the rest of the paper. The
determinant weights of Section 3 and the dimension count of Section 5 are proved
in the text, using the cited results.

FILES
    verify_small_witness.py          exact rational verifier
    small_witness_certificate.json   ranks and selected minor indices
    verify_small_witness_output.txt  expected output of the Python verifier
    check_small_witness.m2           independent computation of Hom(J,S/J)
    check_small_witness_output.txt   expected output of the Macaulay2 script
    SHA256SUMS                       checksums of the other files

PYTHON
    python3 verify_small_witness.py

This needs Python 3.8 or later and only the standard library, and takes about a
second. It checks the polynomial matrix smoothing, its cyclic basis, the eleven
quadratic generators, and the exact rational ranks 35, 49 and 11. It also checks
nonzero minors modulo 32003, with determinants 21492, 9763 and 4926. It rewrites
small_witness_certificate.json, which should come out unchanged, and prints the
contents of verify_small_witness_output.txt.

The script does not compute the characteristic polynomial of T(s). The paper
states it, and it follows from the block form of T(s).

MACAULAY2
    M2 --script check_small_witness.m2

This works over the rationals and computes Hom(J,S/J) directly, giving dimensions
0, 0, 6, 44 in internal degrees -3, -2, -1, 0. It was last checked with
Macaulay2 1.26.06 through the Macaulay2 web interface, entering the commands
interactively, and gave the contents of check_small_witness_output.txt.
