From Topological Invariants to Autoimmune Diseases: A Paradigm Shift?

Abstract

A Thought Experiment: "What If Our Hair Strands Were Metal?" Let’s do an interesting analogy: Imagine that instead of hair, people naturally grew copper or aluminum wires with the same geometric structure—pointed at the ends and thicker towards the root. In such a scenario, we would probably recognize the potential risks of these structures even before any hypothesis was needed. After all, copper has a tensile strength of 210–480 MPa and aluminum ranges from 70–600 MPa—almost identical to the average tensile strength of a human hair strand, which is 200–260 MPa! On top of that, the sharp-ended metal wires would likely create mechanical stress on the skin, with unpredictable consequences. However, because we have always considered our hair strands to be "innocent" and "harmless" since birth, this possibility never even crossed our minds. Perhaps what we have overlooked is the combined effect of geometry and material properties. Let’s consider structures that exist from birth, such as hair whorls and nevi. These can include hair strands and are known to extend into the dermis. If we imagined these structures made not of hair, but of metal wires (like copper or aluminum), we could have predicted from the outset how such features might morphologically affect the human body. This is because our skin is adaptive; even though its physical characteristics change throughout life, it has evolved to protect our body and will adapt to any persistent structure it encounters. This adaptability also applies to multi-angled micro-mechanical forces. It could have been foreseen that the forces exerted by hair strands—or even just a few hair strands—might, as we age, create a kind of chaos within the analytic continuity of the skin and body. Why Does This Matter? This analogy invites us to question traditional perspectives on the origins of diseases. Sometimes, what we think we know may actually hide a much more complex dynamic. Considering the scientific fact that the tensile strength of hair strands is similar to many metal alloys - I thought of metal strands instead of hair strands. A topological invariant involving metal strands can cause hair strands to function as an extension of this invariant (similar to an organ) and can lead to morphological changes that develop and strengthen with age due to the body's adaptive structure. Micromechanical forces are invisible to the naked eye and occur between the layers of the skin. This indicates that the immune system is responding to a non-existent signal. According to the hypothesis, the immune system is performing its normal function. There is only a mechanical force - the tension between them. By combining observations, the characteristic features of diseases, the geometric-topological location of diseases/tumors, the movements of certain types of tumors and the surface patterns observed in these individuals, the Human Topological Hypothesis (HTH) presented to you today has been created. It offers an original and holistic hypothesis aimed at understanding certain medically unexplained or misinterpreted conditions, especially those affecting the skin and connective tissues. The model based on the Hodge Hypothesis has been extended through a topological, biomechanical, and dynamical systems framework. The hypothesis proposes that microstructural spiral formations, topological knots, and epidermal folds generate structural stresses that can physically displace hair follicles, produce localized fibrosis, and trigger chronic inflammatory responses. These patterns may underlie dermatological conditions such as rosacea, alopecia, and basal cell carcinoma, which are usually addressed through molecular or immunological paradigms. Key theoretical contributions include the application of pseudo-Anosov flow dynamics, known for its stretching and folding behavior in negatively curved manifolds, to stress flow and tissue deformation in the human scalp. These flow patterns are proposed to reflect deeper cohomological structures, consistent with the Hodge-theoretic interpretation of biological surfaces as analytically continuous and geometrically expressive. HTH does not exclude the possibility of an immune response, but suggests that the primary factor is mechanical and the secondary factor is the immune response.