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Research Notes

Active derivations from the shape-space programme. Work in progress.

Schrödinger from McGehee

The Schrödinger equation lives on shape space. McGehee coordinates decouple scale from shape at collision; quantum mechanics operates only on s ∈ S².

Derived — Shape dynamics → quantum mechanics without quantisation postulates

Spin-Statistics from Collision Topology

Integer spin ↔ boson, half-integer ↔ fermion. Derived from collision monodromy on the shape sphere, not from relativistic QFT.

Derived — Exclusion and exchange from collision singularity structure

The Shape Sphere Skeleton: K2,3

The complete bipartite graph K2,3 is the combinatorial backbone of N=3 shape space — 2 equilateral poles, 3 collision points, connected by isosceles meridians.

Verified — The forced discrete structure of the Kendall sphere

Why One Spot on a Screen

A spatially local detector forces position as the pointer basis. Dephasing kills cross-cell coherence. Born weights emerge from metric-compatible information optimisation.

Active — Measurement from coupling geometry, not collapse postulates

Record Selection from Detector Boundary

Each detector run latches into exactly one classical record. Exclusivity, latching, and calibration conditions close single-record formation at the detector boundary.

Active — Barbour’s “present structure contains the record” made precise