Third independent verification run (made on the final text of the note), AI-assisted.
Programs written for this run; they import nothing from the other programs of the package.
Pure Python (integers and fractions); recorded with Python 3.13.5.

  python3 run2_examples.py                                         > run2_examples.out        (about 10 seconds)
  python3 run2_small_ranks.py ../verification_run_B                > run2_small_ranks.out     (about 10 seconds)
  python3 run2_rank6_classes.py ../note/rank6_bad_classes.json     > run2_rank6_classes.out   (about 5 seconds)

run2_examples.py       Section 1.1 (points, rhombi, the three printed families, ranks 1 to 10); Table 1; the inequalities
                       (1) to (20) with their right-hand sides; own rational combinations which give h = phi from the
                       fifteen inequalities and h = psi from the eighteen; the totals 25/2 and 13; the reflected point
                       phi*; the construction of Section 4 for ranks 7 to 12 with the formula for the total (18, 25, 33,
                       42, 52, 63) and single points for ranks 7, 8, 9; the matrix M_r of ranks 6 and 7 (Lemma 4.3 (a)).
run2_small_ranks.py    Theorem 1.2 and Table 2 with an own implementation (forms, sets of n forms, classes, an integral z
                       for every class); with a folder as argument also the box certificates cover_r3.json, cover_r4.json,
                       cover_r5.json of the second proof, checked with the forms of this program.
run2_rank6_classes.py  Remark 6.3: the 162 recorded classes of rank 6 (own combinations for the recorded bounds, single
                       point or positive dimension, orbits, denominators).  The completeness of the enumeration of the
                       173,839 classes is not checked by this run.

The last line of each output gives the run time, which differs from run to run.
