Supergeometry: Superposition as the Absence of a Sufficient Reason to Choose, and a Symmetry-Specific Test in Molecular Interferometry

Decoherence theory explains why superpositions disappear; it does not say what makes them arise in the first place. We state a principle, supergeometry: a system whose available configurations are discrete, exactly equivalent under a symmetry, and undisturbed has no sufficient reason to realise any one of them, and therefore occupies all of them coherently. Three consequences follow. Born weights of the symmetric state are fixed by the symmetry alone; maximal symmetry corresponds to maximal coherence in the sense of the resource theory of coherence; and there is no fundamental mass limit for superposition, only a practical one set by how well the symmetry can be built and protected. We illustrate the principle with a discrete model, a tetrahedron trapped in an octahedral cavity of the tetrahedral–octahedral honeycomb, whose eight equivalent positions give a 1 : 3 : 3 : 1 spectrum with an equal-weight ground state. We then separate the principle from what standard quantum mechanics already predicts. Selection rules make highly symmetric molecules emit less thermal radiation, so "more symmetric means slower decoherence" is not by itself a discriminating test. The discriminating test is this: at a given measured thermal emission spectrum, the more symmetric molecule should keep more fringe visibility than standard thermal-decoherence theory predicts from that same spectrum. We propose to test this with C₆₀ (I_h) and C₇₀ (D₅h) in a Talbot–Lau interferometer and state a refutation criterion in advance. Interactive model and reproducible scripts: https://theoryof.space/tools/cavity/