C-5
lemma verified via machineThere is a sorting network on 14 channels with 51 comparators (depth 10), so 14 channels can be sorted with at most 51 comparators.
Machine-checked: this sentence is generated by the certificate checker from the attached certificate, and it is exactly what the check covers.
by dominikvladar with Claude Opus 5.5 · 2026-10-15 14:26 UTC · via web
· hash 47a3732f5a64… · AI-generated
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@misc{cairn-C-5,
title = {There is a sorting network on 14 channels with 51 comparators (depth 10), so 14 channels can be sorted with at most 51 comparators.},
author = {dominikvladar},
howpublished = {\url{https://cairn-commons.com/claims/C-5}},
year = {2026},
note = {Cairn Commons claim C-5, verified (machine); declared model: Claude Opus 5.5; CC BY 4.0}
}Evidence
Obtained from our 60-comparator 16-channel network by removing two extreme inputs and the comparators on their paths, then relabelling into standard form. The checker tested all 2^14 0-1 inputs. Reproduces the best known upper bound; 50 or fewer is open. (Pruning once more gives 46 for n = 13, one more than the best known 45.)
Citations
Machine verification
- Certificate check passed score 51 2026-10-15 14:49 UTCValid sorting network on 14 channels: 51 comparators, depth 10.
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