Historical Manuscripts on the Kung–Traub Conjecture (September 2026)

This release preserves historical manuscripts documenting the development of my research on the Kung–Traub conjecture, pursued over several years and reaching a decisive stage on 17 September 2026 and during the early hours of 18 September 2026. During this stage, I discussed mathematical ideas, partial results, and unresolved difficulties with ChatGPT. These exchanges contributed to the refinement of the mathematical arguments, particularly the formalization of iterative methods, polynomial perturbations, the control of zeros, and the estimates required for the construction of an entire function. The manuscript compiled on 17 September 2026 at 23:17 (Chile time) already contained a proposed proof of the order barrier. A subsequent manuscript, compiled on 18 September 2026 at 02:22 (Chile time), included the operational formulation of the Kung–Traub bound. All manuscripts were originally written in Spanish, my native language, and are preserved without modification. The repository includes selected OneDrive records and SHA-256 checksums documenting the provenance and integrity of the files. The dates associated with the manuscripts are historical file records, distinct from the publication date of this release. The mathematical proofs remain subject to independent verification.