Supergeometry — where superposition comes from, and a test that can kill it

Today the preprint Supergeometry went on Zenodo: doi:10.5281/zenodo.23626824.

The principle. If the configurations available to a system are discrete, exactly equivalent under a symmetry, and nothing distinguishes them, the system has no sufficient reason to be in any one of them — so it occupies all of them coherently. A measurement is an interaction that supplies a reason and breaks the equivalence. The philosophical root is Leibniz's principle of sufficient reason; related results are decoherence-free subspaces and Zurek's envariance. What we add is the inversion (symmetry produces the superposition rather than merely protecting it), a discrete mechanism, and an experimental test.

The model. A regular tetrahedron fits exactly into an octahedral cavity of the tetrahedral–octahedral lattice, in eight equivalent positions. Its ground state is the equal superposition of all eight, 1/8 each; an outside influence closes the "doors" one by one (8 → 4 → 2 → 1). Try it: [interactive model](/tools/cavity/) with the scripts that reproduce every number.

Why a square? Amplitudes live on a sphere, probabilities on an octahedron; the Born rule p = |a|² is exactly the map from one to the other. The sphere is a description of states, not an object in space.

The test. Standard theory already says that symmetric molecules emit less heat radiation, so "symmetric decoheres more slowly" proves nothing. The sharp prediction: at the same measured emission spectrum, C₆₀ should keep more fringe visibility than standard thermal-decoherence theory predicts, while C₇₀ should agree with it (it already does). Refutation criterion, fixed in advance: if R(C₆₀)/R(C₇₀) ≥ 0.9 within the uncertainty, the principle in this form is refuted.

Status: a hypothesis with a testable prediction. We have no experimental data for or against yet.