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tau filaments from Alzheimer's disease display a FIBONACCI-number association by eight β-strands (F6) by Stefan Geier et al.

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  tau filaments from Alzheimer's disease display a FIBONACCI-number association by  eight β-strands (F6) by Stefan Geier et al. Common protofilament core* structure: eight β-strand regions (beta 1 to beta 8): 8 is the 6th FIBONACCI-number**. This finding may be relevant for ALZHEIMER's diesease, inclusion body myositis (IBM) and other diseases. This corroborates - however weak - GEIER's equations and GEIER's equilibrium programme** at an another actual point of scientific, and clinical medical interest. *Fitzpatrick AWP, Falcon B, He S, Murzin AG, Murshudov G, Garringer HJ, Crowther RA, Ghetti B, Goedert M, Scheres SHW. Cryo-EM structures of tau filaments from Alzheimer's disease. Nature. 2017 Jul 13;547(7662):185-190. doi: 10.1038/nature23002. Epub 2017 Jul 5. PMID: 28678775; PMCI D: PMC5552202.: Figure 3. The common protofilament core a. Sequence alignment of the four microtubule-binding repeats (R1–R4) with the observed eight β-strand regions coloured from blue t...

Critique on "Substantial cross-layer Fibonacci-Lucas organization in HIV-1 motivates a falsifiable quasicrystal-like model — Genome, proteome and fullerene-capsid geometry as three linked but evidentially distinct layers — A first approach." by Geier, S. A. et al.

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  Critique: Substantial Cross-Layer Fibonacci-Lucas Organization in HIV-1: A Model of Disciplined Hypothesis Construction Manuscript: Geier, S. A. et al. "Substantial cross-layer Fibonacci-Lucas organization in HIV-1 motivates a falsifiable quasicrystal-like model — Genome, proteome and fullerene-capsid geometry as three linked but evidentially distinct layers — A first approach." ResearchGate, 1. August 2026, DOI: 10.13140/RG.2.2.29677.55528 Overview This manuscript presents an ambitious and intellectually rigorous synthesis that examines whether the HIV-1 virion exhibits a coherent Fibonacci-Lucas organizational pattern spanning three distinct molecular layers: the RNA genome, the encoded proteome, and the assembled capsid shell. The central claim — that these three biologically different layers appear to reuse the same restricted mathematical vocabulary — is developed with a level of methodological self-awareness and epistemic humility that is uncommon in exploratory bioin...

Gastric inhibitory polypeptide (GIP) fits a LUCAS-FIBONACCI-midpoint with about 96.4% and thus corroborates Geier's equations and equilibrium concept; Tirzepatide fits with 87% to F9 - A first look by Stefan Geier et al.

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Gastric inhibitory polypeptide (GIP) fits a LUCAS-FIBONACCI-number-midpoint with about 96.4% and thus corroborates Geier's equations and equilibrium concept; Tirzepatide fits with 87% to F9 - A first look by Stefan Geier et al. Gastric inhibitory polypeptide (GIP), also known as glucose-dependent insulinotropic polypeptide, is an inhibiting hormone of the secretin family of hormones . While it is a weak inhibitor of gastric acid secretion, its main role, being an incretin , is to stimulate insulin secretion. GIP, along with glucagon-like peptide-1 (GLP-1), belongs to a class of molecules referred to as incretins , which stimulate insulin release on oral food intake. Tirzepatide is an analog of the human GIP hormone with a C20 fatty diacid portion attached, that has been approved for treatment of diabetes in the US in May 2022. The legth of the GIP peptide is 42 amino acids*. We looked for the nearest FIBONACCI- or LUCAS-number or midpoint** for the GIP protein legth. The ...

HIV genome length fits the Lucas number L19 with more than 95% - A first look by Geier Stefan et al.

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  HIV genome length fits the Lucas number L19 with more than 95% - A first look by Geier Stefan et al. The Human Immunodeficiency Virus type 1 (HIV-1) possesses a single-stranded, positive-sense RNA genome of approximately 9.2–9.8 kb , depending on the viral isolate. The widely used reference strain HXB2 contains 9,719 nucleotides , making it one of the best-characterized HIV-1 genomes. Using the standard Lucas sequence, L 0 = 2 ,  L 1 = 1 ,  L n = L n − 1 + L n − 2 , the nineteenth Lucas number is L 19 = 9349. Comparison with the HXB2 reference genome yields 9349/ 9719 × 100 % = 96.19 % . Thus, the HIV-1 reference genome exhibits a 96.2% descriptive fit to the Lucas number L 19 ​ , exceeding the 95% threshold. Because HIV genomes vary among isolates, the exact percentage differs slightly across strains but generally remains close to this Lucas target. This observation is consistent with the broader GEIER programme , in which Stefan Geier and co-workers have repo...