An injective C*-power series violating the Bieberbach coefficient bound

A normalized norm-entire power series on C([0,1],C) is globally injective and has an everywhere norm-convergent formal derivative series, but its second coefficient violates the general C*-Bieberbach order bound. A continuous exponential period anchored at zero proves global injectivity without assuming univalent scalar fibers. Lean proves the full source Conjecture 1.2/1.4 counterexample as one common outcome. Invertible-coefficient, polynomial, Robertson and Lebedev–Milin variants remain unclaimed. AI-assisted preprint by Myeongjin Kang, with no affiliation. Internal AI review is not external journal peer review. The accompanying Lean certificate covers the precise scoped main statement; inspect the formal endpoint, assumptions and provenance in the supporting package. Prior-art investigations are documented bounded searches, not worldwide-priority certification. Original prose is offered under CC BY 4.0 and original code/Lean under MIT; third-party rights and existing notices are preserved. The public supporting ZIP contains original proof sources and verification evidence, with bibliographic links and hashes instead of redistributed third-party source manuscripts. Recorded prior-art/source-access limits: DirectPreprintsPDF403 persists; actual authorZenodo6917925 bytes and fresh live md5 verified, normalized source text agrees, no binaryidentityclaim; Bounded citation/web/superposition/registry screen, not worldwide-priority certification; SemanticScholar429 and no exhaustive subscription-index search

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-27
DOI
https://doi.org/10.5281/zenodo.23718290
Primary Topic
Analytic and geometric function theory
Type
preprint
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preprint

An injective C*-power series violating the Bieberbach coefficient bound

Myeongjin Kang
Zenodo (CERN European Organization for Nuclear Research)
Analytic and geometric function theory
preprint

An injective C*-power series violating the Bieberbach coefficient bound

Myeongjin Kang
preprint en

Abstract

A normalized norm-entire power series on C([0,1],C) is globally injective and has an everywhere norm-convergent formal derivative series, but its second coefficient violates the general C*-Bieberbach order bound. A continuous exponential period anchored at zero proves global injectivity without assuming univalent scalar fibers. Lean proves the full source Conjecture 1.2/1.4 counterexample as one common outcome. Invertible-coefficient, polynomial, Robertson and Lebedev–Milin variants remain unclaimed. AI-assisted preprint by Myeongjin Kang, with no affiliation. Internal AI review is not external journal peer review. The accompanying Lean certificate covers the precise scoped main statement; inspect the formal endpoint, assumptions and provenance in the supporting package. Prior-art investigations are documented bounded searches, not worldwide-priority certification. Original prose is offered under CC BY 4.0 and original code/Lean under MIT; third-party rights and existing notices are preserved. The public supporting ZIP contains original proof sources and verification evidence, with bibliographic links and hashes instead of redistributed third-party source manuscripts. Recorded prior-art/source-access limits: DirectPreprintsPDF403 persists; actual authorZenodo6917925 bytes and fresh live md5 verified, normalized source text agrees, no binaryidentityclaim; Bounded citation/web/superposition/registry screen, not worldwide-priority certification; SemanticScholar429 and no exhaustive subscription-index search

Zenodo (CERN European Organization for Nuclear Research)
Analytic and geometric function theory
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