Geometric Pathogen Targeting Mathematical Foundations and Prototype Designs for Mutation-Resistant Antivirals and Antibiotics

This work presents a unified theoretical and applied framework for geometric pathogen targeting: an alternative paradigm in antimicrobial design that targets non-mutable geometric and topological constraints of pathogens rather than chemically specific, genetically encoded binding sites.

The manuscript is structured as a single coherent body composed of three tightly integrated parts:

(I) Mathematical Foundations.
We derive from first principles the geometric and topological constraints governing pathogen architecture, focusing on:

• Icosahedral viral capsids and the topological necessity of exactly twelve pentameric vertices (Euler / Gauss–Bonnet).

• Stress concentration hierarchies in thin elastic shells, showing a robust scaling between vertices, edges, and faces.

• Closure constraints that lead to a critical angular mismatch threshold (~2–3°) beyond which capsid assembly fails.

• The geometric necessity of 90° cross-linking in bacterial peptidoglycan with 4-fold screw symmetry.

(II) Geometric Antiviral Prototype (GeoVax-Ad1).
Based directly on the mathematical derivation, we propose a pentameric decoy molecule designed to disrupt adenovirus capsid assembly by introducing a controlled dihedral mismatch at penton–hexon interfaces.
Complete molecular specifications, geometric tolerances, synthesis routes, and quantitative falsification criteria are provided. No experimental validation is claimed at this stage.

(III) Geometric Antibiotic Prototype (GeoAb-SA1).
We introduce a wedge-shaped molecule designed to disrupt the geometrically required 90° cross-linking angle in Staphylococcus aureus peptidoglycan. A mechanical torsional-failure model is derived, along with predicted failure thresholds and standard microbiological validation protocols.

Importantly, this work does not claim experimental confirmation or clinical efficacy. Instead, it provides a mathematically derived, falsifiable framework and two prototype implementations intended to guide future experimental testing.

The central hypothesis is that geometric and topological constraints—unlike chemical binding sites—cannot be removed or altered by point mutations without catastrophic loss of structural integrity, potentially offering a route toward intrinsically mutation-resistant antimicrobial strategies.

Negative experimental results are explicitly recognized as valid outcomes within this framework and are expected to refine or falsify the proposed models.