A brain state is a point in connectome space. Disease is a path through it.
Mannone, Ribino, Fazio, and Marwan (arXiv:2603.22296) construct a formal brain space where each point represents a connectome configuration — the full pattern of functional connections between brain regions. A healthy brain occupies one region of this space. Parkinson's occupies another. Schizophrenia another. The progression from healthy to diseased is not a degradation of a single network but a trajectory through a space of possible networks.
The Krankheit-Operator maps between configurations — transforming the connectivity pattern of a healthy brain into the pattern characteristic of a specific disease. This is not metaphor. The operator is a mathematical object that encodes which connections weaken, which strengthen, and which new connections form as the disease progresses. Different diseases correspond to different operators acting on the same initial space.
The framework makes disease comparison geometric rather than symptomatic. Parkinson's and Alzheimer's are different paths through the same brain space, starting from nearby healthy configurations and diverging toward distinct attracting regions. The distance between disease states can be measured. The rate of progression is a velocity along the path. Recovery — if possible — is a return trajectory.
The formalization exposes a structural question: is the brain space simply connected, or does disease progression create topological barriers? A simply connected space allows continuous paths between any two configurations. A space with holes might have disease states reachable only through specific routes — explaining why some treatments fail despite targeting the right endpoint. The path matters, not just the destination.
What's missing is dynamics. The brain space provides a static map of possible configurations. The forces that drive trajectories — neurodegeneration, compensatory plasticity, pharmacological intervention — are not yet encoded. The map shows where diseases live; it doesn't yet explain why the brain moves toward them.