"Protein length approximation by Lucas and Fibonacci targets – A first hint for generality?" by Stefan A. Geier et al.

 

Protein length approximation by Lucas and Fibonacci targets –
A first hint for generality?

Stefan A. Geier*, Caroline Geier, Stephanie Geier, Constantin Geier, Katharina Geier,
Nora Blättermann-Goldstein, and Michèle Geier-Noehl**

Institute for Structuralistic Theory of Sciences Simssee (ISTS), Gerhart-Hauptmann-Straße 6, 83071 Haidholzen, Germany; and Ludwig-Maximilians-Universität Munich, Germany.
**Dermatologische Klinik der Landeshauptstadt und der Ludwig-Maximilians-Universität LMU München, Thalkirchner Straße 48, 80337 Munich, Germany.
*Correspondence: Stefan A. Geier; wissenschaftstheorie.simssee.1@gmail.com

Version 0.0.0.0  | 29. September 2026 

Abstract

Protein lengths provide a simple description of molecular organisation, but numerical agreement requires explicit targets and tolerances.^1,2 Motivated by Geier’s proposals,^3,4 we “prospectively” analysed a randomly derived table of 100 human protein lengths and 100 paired reported segment lengths. Here we show that 75 of the 100 full-chain counts attain at least 95% fit to a Lucas number, a Fibonacci number, or a predefined adjacent Lucas–Fibonacci midpoint (p < 0.0001). Fit was calculated as one minus the target-relative absolute discrepancy, expressed as a percentage and maximised across the three families. Against an explicit 50% majority benchmark, the nominal exact one-sided binomial P value was 2.818 × 10⁻⁷ under an independent-Bernoulli model; the supporting normal statistic was z = 5.00. Mean fits were 96.84% for chains and 96.91% for reported segments. The source list arose from a Gemini prompt requesting random selection of 100 human proteins with their length in aa and a domain length in aa. These results establish close numerical approximation within the declared equilibrium-oriented target system. Biological generality must be included in biological and physiological theories; however further testing of our hypothesis in different fields and with larger numbers of proteins is appropriate.

Keywords
protein length; amino-acid count; Lucas numbers; Fibonacci numbers; adjacent midpoint; exact binomial test; Geier’s equations; Geier’s equilibrium programme; biology; physiology; biochemistry; biophysics; Geier’s hypothesis.

Source:
Stefan A. Geier et al., ResearchGate:
Our research is available on @ResearchGate: https://www.researchgate.net/publication/414947817_Protein_length_approximation_by_Lucas_and_Fibonacci_targets_-_A_first_hint_for_generality?utm_source=twitter&rgutm_meta1=eHNsLTVXaUxoTSsyT3UydG1VdXQzNHhLbDhPYW51dGFFN2xmVnR0am9DdzdZOTYzSWY0YUpvdVFmUnlKeGlSTW1JUktQN0xhem1ld2NVLzJCY0wyeStZNll3TT0%3D