PART A: the certificates of Section 6
-- Section 6.1 (Lemma 6.1)
ok   4-simplex: every vertex satisfies the hypothesis
ok   pyramid over the octahedron: the apex satisfies the hypothesis, and no other vertex does
ok   prism over the tetrahedron: the facets through a are the bottom and the prisms over abc, abd, acd
ok   prism over the tetrahedron: bc, bd, cd lie in the bottom, the 9 other edges avoiding a in the three prisms
ok   product of two triangles: the facets are e x Delta and Delta x e
ok   product of two triangles: every edge avoiding v = (0,0) lies in the facet named in the note
ok   product of a triangle and a square: no vertex satisfies the hypothesis
ok   polar of the hypersimplex Delta(2,5): no vertex satisfies the hypothesis
-- Section 6.2 (the cyclic polytope C(6,4))
ok   C(6,4): f-vector (6, 15, 18, 9); the graph is K_6
ok   C(6,4): the nine facets are the complements of the pairs {i,j} with j - i odd
ok   C(6,4): all triangles are 2-faces except 135 and 246
ok   C(6,4): no vertex satisfies the hypothesis of Lemma 6.1
ok   C(6,4): of the ten pairs of complementary triangles nine have lk = 0, and |lk(135, 246)| = 1 (cone method and projection method, two Schlegel diagrams)
-- Section 6.3 (the prism over the octahedron)
ok   octahedral prism: 12 vertices, 30 edges; on each level non-antipodal vertices are adjacent, and every vertex is joined to its copy
ok   octahedral prism: the facets are the two octahedra and eight prisms over triangles
ok   octahedral prism: the six sets of the note are a model of K_6, with the fifteen witness edges listed in the note
ok   octahedral prism: C and D are disjoint 6-cycles
ok   octahedral prism: the projections of C and D cross over y+ (C below D) and over y- (C above D)
ok   octahedral prism: |lk(C, D)| = 1 (cone method and projection method, two Schlegel diagrams): [(1, 1, 1, 1), (-1, -1, -1, -1)]
ok   octahedral prism: no vertex satisfies the hypothesis of Lemma 6.1
-- Section 6.4 (the truncated 4-simplex and the hypersimplex)
ok   truncated 4-simplex: f-vector (20, 40, 30, 10); (i,j) is adjacent to (j,i) and to the three (i,k)
ok   its polar has f-vector (10, 30, 40, 20) and degrees 4 (five times) and 8 (five times): the simplex stacked on all five facets
ok   truncated 4-simplex: C and D (as printed in the note) are disjoint 10-cycles through all vertices
ok   truncated 4-simplex: |lk(C, D)| = 1 (cone method and projection method, two Schlegel diagrams): [(-1, -1, -1, -1), (1, 1, 1, 1)]
ok   truncated 4-simplex: the last two sets induce paths in the order written
ok   truncated 4-simplex: the six sets of the note are a model of K_6, with the fifteen witness edges listed in the note
ok   truncated 4-simplex: no vertex satisfies the hypothesis of Lemma 6.1
ok   hypersimplex Delta(2,5): f-vector (10, 30, 30, 10)
ok   recorded: Delta(2,5) is linked and has a K_6-minor (original programs and second run)
ok   recorded: the polar of Delta(2,5) has no linked pair (complete search) and no minor in the Petersen family (exhaustive search; second run)
ok   recorded: the product of a triangle and a square has no linked pair (complete search, original programs)
ok   recorded: the same in the second run (complete search; 4 record(s) with this f-vector)
ok   recorded: octahedral prism and C(6,4) linked; simplex, prism over the tetrahedron and product of two triangles not linked (original programs)
ok   recorded: the second run finds |lk| = 1 for the same pair by its two methods, and a K_6-minor
PART B: the numbers of Section 7 against the recorded outputs
ok   Table 1: the five rows agree with the summary of the second run (no type with another status)
ok   Table 1: totals 275,478 = 9,080 + 266,398
ok   second run: ten families in the summary, 0 alerts
ok   eight vertices: 1,294 types found, as many for each f-vector as in the table of Firsching
ok   at most seven vertices: 1, 4, 31 types in the enumeration of the second run by Gale diagrams
ok   original programs: 30,266 types with nine vertices and at most 26 edges; 8,755 not linked; 21,511 linked, each with a K_6-minor
ok   original programs: a sample of 6,000 types with nine vertices and at least 27 edges, all linked with a minor
ok   the same verdict for each of the 30,266 polytopes in the stored results of the original programs and of the second run
ok   the same verdict for the 6,000 polytopes of the sample (comparison recorded by the second run)
ok   original programs: all 495 types with eight vertices and at most 22 edges; 302 not linked, 193 linked
ok   original programs: all types with at most seven vertices (1; 3 + 1; 19 + 12)
ok   498,389 pairs of disjoint cycles in 680 polytopes: the linking numbers of the original programs and of the second run agree up to one sign for each polytope
ok   0/1-polytopes: 347 classes; 160 not linked, 187 linked (original programs and second run)
ok   second run: of the 7 polytopes left undecided by its main program, 4 are linked with a K_6-minor and 3 have no linked pair (complete search), the minor being undecided
ok   second run: 194 named polytopes, 36 types with at most seven facets, 1,279 with eight facets, 2,419 with nine facets and at most ten vertices, 2,400 random polytopes
ok   second run: the named polytopes have up to 36 vertices, the random ones 10 to 14
ok   second run: 306,927 polytopes in all; 292,737 linked, each with a verified minor; 980 without a linked pair and with the minor undecided; 13210 without a linked pair and without a minor
ok   second run: every linked verdict rests on a pair with odd linking number, confirmed by its second method
ok   non-polytopal 3-spheres with nine vertices: 41,866; 41,861 linked with a K_6-minor; 5 not linked
ok   274,148 + 41,866 = 316,014 combinatorial 3-spheres with nine vertices
ok   first run: three samples of 1,500 polytopes with at most ten vertices; only the statuses odd pair + minor and no linked pair + no minor occur
ok   first run: a vertex as in Lemma 6.1 in 198 of 207 polytopes without a minor (and in none with a minor)
ok   first run: no knotted cycle detected in 564 polytopes without a minor
ok   first run: the kernel of the matrix of Theorem 5.2 confirmed numerically for seven polytopes
ok   control (original programs): a linked straight-line embedding of the graph of the prism over the tetrahedron is reported as linked and without a minor
ok   control (second run): the same
ALL CHECKS PASSED: 60
