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PreprintCC BY 4.0arXiv

The Generalized Lax Conjecture for Strictly Hyperbolic Polynomials

  • Mario Kummer
  • Tim Netzer
Open at sourcePDFDOICite

Abstract

We report a proof found by an artificial intelligence system for the following statement: The hyperbolicity cone of every strictly hyperbolic polynomial is spectrahedral. This establishes the generalized Lax conjecture for the generic case, while the full conjecture remains open.

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Cite

BibTeXRIS
BibTeX
@misc{kummer2026generalized,
  title = {{The Generalized Lax Conjecture for Strictly Hyperbolic Polynomials}},
  author = {Mario Kummer and Tim Netzer},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24542},
  eprint = {2609.24542},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24542},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Generalized Lax Conjecture for Strictly Hyperbolic Polynomials
AU  - Mario Kummer
AU  - Tim Netzer
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24542
UR  - https://arxiv.org/abs/2609.24542
AB  - We report a proof found by an artificial intelligence system for the following statement: The hyperbolicity cone of every strictly hyperbolic polynomial is spectrahedral. This establishes the generalized Lax conjecture for the generic case, while the full conjecture remains open.
ER  -