PreprintCC BY 4.0arXiv
Elimination of René Peschmann's 968 Remaining Hard Fibers for the Perfect Cuboid Problem
Abstract
Recently, René Peschmann proved perfect-cuboid nonexistence on 1,072 explicit master-tuple fibers with max(m,n)≤100, leaving 968 fibers in the same bounded parameter range. In this paper, I eliminate all 968 remaining fibers. Most fibers fall to fairly short rank-zero or covering arguments, while the final cases need the stronger local-global sieves. Together with Peschmann's theorem this excludes perfect cuboids on all 2,040 admissible fibers with m≤100; the result is still a bounded-fiber theorem rather than a proof of the full perfect-cuboid conjecture.
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BibTeX
@misc{cipollini2026elimination,
title = {{Elimination of René Peschmann's 968 Remaining Hard Fibers for the Perfect Cuboid Problem}},
author = {Ricky Cipollini},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14526},
eprint = {2609.14526},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14526},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Elimination of René Peschmann's 968 Remaining Hard Fibers for the Perfect Cuboid Problem
AU - Ricky Cipollini
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14526
UR - https://arxiv.org/abs/2609.14526
AB - Recently, René Peschmann proved perfect-cuboid nonexistence on 1,072 explicit master-tuple fibers with max(m,n)≤100, leaving 968 fibers in the same bounded parameter range. In this paper, I eliminate all 968 remaining fibers. Most fibers fall to fairly short rank-zero or covering arguments, while the final cases need the stronger local-global sieves. Together with Peschmann's theorem this excludes perfect cuboids on all 2,040 admissible fibers with m≤100; the result is still a bounded-fiber theorem rather than a proof of the full perfect-cuboid conjecture.
ER -