Here is a live disagreement in the published literature, sitting in exactly the regime this lab already calibrated. Push a crowd of oscillators gently — apply a weak external pull — and measure how much more synchronized it becomes. That ratio is the susceptibility, and it blows up as you approach the critical coupling. The question is whether it blows up at the same rate on both sides. Daido, across a series of papers from 1986, says no: the exponent is one-quarter approaching from above and a full 1 approaching from below. Hong, Chaté, Tang and Park, in 2015, say yes: one-quarter on both sides. Both statements are about the same configuration this instrument already runs.
So the lab built the two-sided measurement. And then it refused to make it.
Not once — repeatedly, and each refusal was earned. Four different estimators were tried and all four were disqualified, every one of them having first produced a precise and wrong answer. The fluctuation estimator that worked beautifully for the earlier rungs turns out to be flat below the critical point — the crowd never leaves its random-noise floor there, so the estimator saturates at a fixed value and reads pure noise as an exponent of −0.121. A second estimator, fitted through the origin, is wrong above the critical point where the crowd already has spontaneous order to fold into the slope; it manufactured an exponent of −0.306 at R² = 0.9949 — a fit that looks, by every conventional diagnostic, excellent. A third sat outside the linear-response regime entirely on both branches, voiding the one result that had looked physical. A fourth measured the wrong quantity altogether.
What the lab built instead of a fifth estimator is a gate that refuses. Before any exponent is extracted, the response is measured at several field strengths and the successive slopes are compared. If they disagree, the response is not linear, no susceptibility exists to extract, and the column is thrown out with its reason recorded. On the most recent run — 2026-08-15 — five of eight columns were refused, every one of them for non-linear response. The three that cleared the gate do not add up to a measurement either: they are scattered across both branches, and the surviving lower-branch column returned a susceptibility of the wrong sign entirely.
No exponent is claimed. Nothing is measured. The refusals are the result — and the panel below lets you watch one happen.
left · the crowd and the external
pull; drag h up and watch it lean. right · the field ladder itself, not
a fitted curve — three readings at h = 0, h, 2h, with the two successive slopes
drawn as separate segments. When they disagree, the response is not linear, there is no
susceptibility to extract, and the column is refused.
observable ⟨r⟩ · secants — · spread — vs tolerance 0.15 · verdict —
Field inertness check at h = 0: — — the pinning term is short-circuited when the field is off, so every K01 and K02 trajectory is bit-identical to the pre-field code rather than merely close.
The panel opens on one of the few settings that clears: the upper branch, far from the critical point, with a genuinely small field. The two secants lie almost on top of each other and the gate lets the column through. Now drag the field up. The response curve bends away from straight, the second secant rotates away from the first, the tolerance wedge is exceeded, and the panel refuses in real time. Watching a measurement refuse itself is an unusual thing to put on a web page, and it is the honest centrepiece here.
Then try moving the offset ε closer to the critical point, or flipping to
the lower branch. Almost everything refuses. That is not the panel being fussy — it is
the same wall the published run hit, and it is why five of its eight columns came back
empty. The honest window is narrow from both sides: too strong a field and the response
is no longer proportional to it; too weak a field and the signal drops below the noise
of the crowd's own wandering centroid, which is why the slider does not go lower than it
does. Squeezed between those two, there is not much room left to measure an exponent
in.
The button marked force a fit anyway is the other half of the lesson. It overrides the gate and draws the disqualified through-origin fit across the same three points, and reports what that estimator returned on the real run. The number it prints first is an R² of 0.9949 — by every conventional diagnostic, an excellent fit. The exponent underneath it is −0.306. The two published values under debate are +¼ and +1. A negative exponent is not a near-miss; it is a different kind of object entirely. The lesson is how good a wrong answer can look, which is why the panel reverts to REFUSED a few seconds later instead of staying on the fake result.
The saturation number is worth dwelling on. Below the critical coupling the
fluctuation estimator χ = N·Var(r) sits at the Rayleigh value
1 − π/4 = 0.2146 and varies by only 1.3× across a 25× range in the
coupling offset. It is not weakly measuring a small exponent; it is carrying no
subcritical exponent at all. Read a slope off it anyway and you get −0.121, which is a
number describing noise.
On an earlier corrected run, 1 of 12 columns passed. That is the honest verdict on whether the measurement happened: it did not. The configuration behind the latest attempt is N = 200, γ = 0.5, K_c = 1.0, dt = 0.01, t_burn = 30, t_measure = 60, seed 42, with a symmetric log-spaced field grid of ε = 0.02, 0.050, 0.127, 0.32 run on both branches.
The crowd this all runs on, and the closed form it was calibrated against, is K01. The finite-size scaling of that same crowd at the exact critical coupling — which did succeed — is K02.