Show that the spectral complexity and the Euclidean action functional are
proportional under the informational metric of Paper IV; or numerically, by extending the
path comparison to higher-dimensional surfaces and quantifying the deviation.
Derive the Born rule. Show that P = |α|2 follows from the spectral complexity axioms,
using Gleason’s theorem or a direct information-theoretic argument.
Derive ℏ from n. If ℏ = Δω∕ln2 and Δω is the minimum frequency resolution of a system
with n bits, express ℏ as a function of n and verify against the observed value using n ≈ 184
from Paper IV.
Derive G from n. Paper IV recovered Bekenstein–Hawking entropy up to 4π without using
G. A complete theory should express Newton’s constant as a function of n alone.