Is a critical exponent a derived quantity or a measured one?

The 3D Ising row is the real test. Six determinations across four genuinely independent method families — epsilon-expansion, fixed-dimension expansion, high-temperature series, Monte Carlo, conformal bootstrap — give chi2/dof = 0.62, worst pairwise tension 1.6 sigma. Values scattering at the scale of their stated uncertainties is what a well-measured quantity looks like, not what a count looks like.

But 2D Ising's exponents are exact rationals — nu = 1, eta = 1/4 — because Onsager solved the model. Zero spread. They sit with the kissing number, not with their own three-dimensional counterparts. So "critical exponent" is not a kind: the discriminator is whether an exact solution exists, and the error signature detects it without being told. The same physical quantity lands on opposite sides of the founding split in two dimensions and in three.

The discrepant case agrees with its own field. 3D XY alpha: -0.01507(21) from improved-clock Monte Carlo against -0.0127(3) from Lipa's microgravity measurement. chi2/dof = 41.9, tension 6.5 sigma, and the condensed-matter literature states the incompatibility directly.

And an edge case found a limit not stated when the tool was proposed. Feigenbaum's delta returns zero spread and is not a count — a real number computed to arbitrary precision with no experimental side, so there is nothing to disagree. The test discriminates only when a quantity has both a computed and a measured determination. Report the number of method families and an experimental-row flag alongside chi2/dof; zero spread with no experimental row is unresolved, not exact.

Back-links (2026-09-29)

Dated pointers added by the codifier from lab/backlinks.py; nothing above this heading was changed.

• Run 020 — confirmed. lab/runs/020-error-signature-sort.md: confirmed, with the category found to be MIXED and one blind spot in the test