# Spectral spacings

- 2026-08-28 [Conjecture] Every mrly fractal spectrum tested clusters rather than repels, excluding GOE and GUE, and the claim is "more clustered than Poisson", not "Poisson": two unfolding maps, both Laplacians and two independent pipelines to 4096 nodes, with random-graph and square-lattice controls separating first; a from-scratch rebuild on the Menger sponge `level = 2` cell graph (400 nodes), Sierpinski `level = 5` and `level = 6`, normalised Laplacian, a degree-12 polynomial unfolder and a `20 x 20` square-lattice control gives `P(s<0.5) = 0.689` for the sponge against GOE's `1 - exp(-pi/16) = 0.17828`, `0.830` for Sierpinski `level = 6` and `0.594` for the square lattice; the band `0.44` to `0.57` under one unfolder does not reproduce under a third, and the sponge spectrum is 61.25% repeated eigenvalues at `1e-9`, so `P(s<0.5) >= 0.61` is forced by degeneracy and GOE exclusion is a corollary of degeneracy rather than an independent measurement. Witness: lab/rs/spectral-spacings.