The 3D power law is a plane.

One single plane through all 5,524 data points with R² = 0.970.
The equation:
log⁡10(H)=0.47⋅log⁡10(P)+2.83⋅log⁡10(A)+constant.
The grey drop lines show individual residuals from the plane — the data hugs it remarkably tightly across 15 years and ~10 orders of magnitude in hash rate. The shadow projections on the three walls show the 2D marginal relationships you'd see if you collapsed any one dimension.
The key physical insight from the single fit: the three quantities don't just each follow a power law in time — they form a power law manifold together.
Hash rate is predominantly driven by addresses (exponent 2.83, ≈ Metcalfe squared) and secondarily by price (0.47).
This suggests miners respond more to long-run adoption signals than to short-term price moves, which is consistent with the hardware investment cycle being much longer than price cycles.