SS-BIO: Scale-Extended Biological Dynamics in Scale Space: Configurational Structure, Transport, and Reaction–Diffusion Tests

This paper develops the biological component of the Scale Space research programme, representing physical logarithmic scale as a proposed configuration coordinate distinct from ordinary spatial directions and from instrumental resolution. It introduces observable-dependent scale profiles and calibrated measurement projections, giving admissibility-qualified conditions for reconstruction and for predicting withheld observations without requiring unique recovery of every latent configuration. The framework retains a configurational-stress balance and examines idealized scale-boundary conditions while keeping gravitational source interpretations separate. A proposed biological validation programme first compares scale-profile predictions with conventional three-dimensional imaging using paired multiresolution dentin microscopy, then considers correlated light and electron microscopy of synaptic structures. A conditional scale-extended reaction–diffusion construction provides a worked dynamical illustration. Eliminating unresolved scale modes produces a memory kernel and a leading higher-order spatial correction; a Gaussian-carrier example yields a model-dependent Turing-instability threshold shift under stated kinetic and transport assumptions. The paper distinguishes formal scale extension, transported modes, physical concentration and dilution, and experimental evidence. Its numerical calculations are reproducible, but no experimentally calibrated physical scale transport or distinctive biological confirmation of Scale Space is claimed. The contribution is a structured, extensible mathematical and experimental programme for measuring and testing cross-scale biological structure against conventional alternatives.