On the Logarithmic Map of Scale and the Separation of Scale and Quantization in a High-Symmetry Limit: A Limited Verification Report from a Minimal Axiom System

Starting from a naive question about the conjugate relation of two quantities, the rigid see-saw nu*lambda=k, this report posits an intrinsic fluctuation of the integer-valued nu together with high anonymity and high symmetry. Introducing the fundamental quantity as the logarithm of a squared quantity, N=log2 (nu), the conjugate relation becomes an additive identity Nₙu+Nₗambda=K, and the sum of squares Sum nu² = R² representing scale (the g side) is mapped, in the self-dual fixed point (k=1) and the fully symmetric limit, onto a flat hyperplane. The key result is that the logarithmic map separates scale (g, gauge, flattenable) from quantization (omega, area, invariant): while scale is flattened and removed as a gauge, the half-bit fluctuation (omega) remains invariant on the flat surface. The system rigorously distinguishes a system-interior (the unknowable, anonymous internal viewpoint) from a system-exterior (the observer) ; the question of which side is real is treated as ill-posed, and objective anchors are placed on fixed points and conserved quantities rather than on reality. The fluctuation magnitude +/-1/2 is treated explicitly as a posit, not a derivation. Here R is the scale (magnitude) of the system, not a curvature tensor. This is a limited verification report; no general claim is made.