Five outgoing centers in a 16-realization cube move

This note specifies six fixed algebraic boundary points admitting an incoming alpha=16 realization and at least five distinct outgoing centers. Exact rational bounds, the intermediate value theorem and monotone polynomial root definitions prove the construction. It contradicts the at-most-three expectation in Melotti–Ramassamy–Thévenin (2023), Remark 4.8, in the realization setting allowing crossings. A fixed boundary crossing excludes proper embeddings. The exact total count and universal maximum remain unknown. The curves are members of the earlier weighted-distance and p-power families of Ash–Bolker (1986), Bourne–Peletier–Roper (2014) and Bourne–Roper (2015). A bounded search through 15 October 2026 located no earlier pure-power four-or-more shared-focus example in its checked corpus; historical priority remains unestablished. AI was used extensively. This preprint is unrefereed and has not received conventional human peer review.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-15
DOI
https://doi.org/10.5281/zenodo.23392408
Primary Topic
Mathematics and Applications
Type
preprint
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preprint

Five outgoing centers in a 16-realization cube move

Kriebel Alec
Zenodo (CERN European Organization for Nuclear Research)
Mathematics and Applications
preprint

Five outgoing centers in a 16-realization cube move

Kriebel Alec
preprint en

Abstract

This note specifies six fixed algebraic boundary points admitting an incoming alpha=16 realization and at least five distinct outgoing centers. Exact rational bounds, the intermediate value theorem and monotone polynomial root definitions prove the construction. It contradicts the at-most-three expectation in Melotti–Ramassamy–Thévenin (2023), Remark 4.8, in the realization setting allowing crossings. A fixed boundary crossing excludes proper embeddings. The exact total count and universal maximum remain unknown. The curves are members of the earlier weighted-distance and p-power families of Ash–Bolker (1986), Bourne–Peletier–Roper (2014) and Bourne–Roper (2015). A bounded search through 15 October 2026 located no earlier pure-power four-or-more shared-focus example in its checked corpus; historical priority remains unestablished. AI was used extensively. This preprint is unrefereed and has not received conventional human peer review.

Zenodo (CERN European Organization for Nuclear Research)
Mathematics and Applications
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