Quantum Mechanics in the Label Framework: One Body, Many Bodies, Statistics, Spin and Internal Quantum Numbers

In the label framework, matter is a field of comoving labels with volume-preserving relabellings. A label medium with a Fisher term gives the Schrödinger equation for one field, given irrotational initial data and a phase on a circle. Its density is |ψ|² by construction and carries no Born rule. Labels in space carry no entanglement. On configuration space, relabellings of each particle admit the Fisher–Rao metric and further marginal metrics. These make evolution non-linear and allow signalling; within the family tested, no signalling leaves linear many-body quantum mechanics. Statistics is a phase condition that densities do not see. For a stable SU(3) soliton at a Wess–Zumino level equal to the number of colours, half-integer spin follows from an odd number of colours. The global SU(2) anomaly requires it for three generations. For the given finite algebra C ⊕ H ⊕ M₃(C), unimodularity yields the Standard-Model gauge algebra and hypercharge ratios, but no value.