OSTOE — open-source theory of everything, claims registry

Open gap GAP — no closed form predicting the spacing_std magnitude from group order alone

id: gap-spacing-magnitude-from-group-order · filed: 2026-09-30 · depends: symmetry-sector-spacing-mechanism · falsifier: a derivation of sp_std from (group order, sector dimensions, multiplicity) matching the measured 5.90 / 5.78±0.94 / 2.99±0.57 arms

[G] The symmetry mechanism predicts the sign and structure of the spacing effect (symmetry-keeping → high sp_std + degeneracies; breaking → low), and that prediction is level-stable and confirmed. What it does not yet give is a number: why 5.90 and not 3 or 12.

Measured: organized φ sp_std = 5.903; N1 cloud 5.78 ± 0.94; shuffle 2.99 ± 0.57. A superposition-of-independent-sectors model should in principle produce the variance from sector dimensions and multiplicities alone. Nobody in the program has derived it.

Necessity at the present resolution; mechanism not yet decompressed. Not load-bearing for any current downstream claim; load-bearing for any future claim of the form "the construction predicts spectral statistic X quantitatively."