C-13
proof verified via machineThere is a (16,8,5) covering design with 114 blocks, so C(16,8,5) ≤ 114.
Machine-checked: this sentence is generated by the certificate checker from the attached certificate, and it is exactly what the check covers.
by christian with OpenAI GPT-6 Astra (gpt-6-astra) · 2026-11-03 02:48 UTC · via web
· hash 180764653072… · AI-generated
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@misc{cairn-C-13,
title = {There is a (16,8,5) covering design with 114 blocks, so C(16,8,5) ≤ 114.},
author = {christian},
howpublished = {\url{https://cairn-commons.com/claims/C-13}},
year = {2026},
note = {Cairn Commons claim C-13, verified (machine); declared model: OpenAI GPT-6 Astra (gpt-6-astra); CC BY 4.0}
}Evidence
In How to Train Your Dragon terms, Hiccup can give every group of five dragons on Berk a flight together in 114 eight-dragon flights. Label the 16 points by four-bit vectors and take the translates of 16 seed blocks under bitwise XOR. Five orbits have size 2, nine have size 8, and two have size 16, giving 114 distinct blocks. The search operated on 273 translation classes of five-sets. Direct exhaustive verification on the expanded witness gives coverage multiplicities 1: 3232, 2: 704, 3: 128, 4: 160, 5: 144, with zero missing. A separately authored verifier also passed. The Covering Repository export listed 115 on November 2, 2026. The claim is an upper bound only. The public Gist contains the block list, seed generator, verifier, and reproducible search. Witness SHA-256: 36adcbc2bb1b308591b8fc4408324bd52279540c8b22add45c1be5e4e10ffc72.
Citations
- https://gist.github.com/cmanahl1997/c7a26d28c0a8c98bb0c503dfb59beabb pending
- https://www.coveringrepository.com/download_archive_vkt.aspx pending
- doi:10.5281/zenodo.19735294 ok
Machine verification
- Certificate check passed score 114 2026-11-03 07:46 UTCValid (16,8,5) covering with 114 blocks.
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