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
- Kriebel Alec (ORCID: https://orcid.org/0009-0001-9320-500X)
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