A rung the surrogate family can stand on, and the candidate falling off it

Run: gate/chaotic.py → gate/chaotic.json Date: 2026-09-21. Plan §6A item 3b — the nonlinear constructed ground truth.

Question or issue resolved

gate/RESULT-SURROGATE.md ended on a constraint rather than a result. Surrogate- normalized permutation entropy passed every control it was given — including real evoked responses phase-shuffled and scored as genuine at exactly 1.000 — and then could not be evaluated at all. A linear-Gaussian process is completely described by its spectrum, so phase-shuffling one produces a statistically identical process: the surrogate is the original in everything the measure can read, and the ratio is pinned at 1 however integrated the system is. The Closed form rung of the validation ladder is built on exactly that class, so no surrogate-normalized measure can ever be scored on it. Two rungs of this program's own ladder turned out to be mutually exclusive.

This builds the rung that resolves it, and then uses it.

The rung works, and the control that proves it is the whole point

A coupled map lattice: twenty nodes each running the logistic map deep in its chaotic regime, wired into two modules with the between-module coupling swept continuously. The dynamics are deterministic and broadband — a spectrum that looks like noise while every step is fixed by the last. The ground truth is cross-module mutual information, estimated by plain binning on long stationary runs, deliberately sharing no machinery with the candidate: delta_spread was once scored against a target computed on the same construction it was reading, and that shared structure took two runs to rule out.

That last pair is the reason this file exists. Phase-shuffling the lattice's own output destroys its cross-module information completely — the shuffled value sits at the estimator's floor at every coupling level, while the real value climbs 22-fold above it. The structure here is entirely non-spectral, which is precisely the property the linear-Gaussian bed lacked. A surrogate-normalized measure can be scored on this rung.

Two controls failed on the way, and both were real design errors. The lattice was first built at within-module coupling 0.30, where its largest Lyapunov exponent came out at −0.41: coupled map lattices synchronize above a threshold and a synchronized lattice is not chaotic, so the construction had lost the one property it was built for. A scan places the transition between 0.18 and 0.30; the run uses 0.10, where the exponent is +0.44 and the nodes stay desynchronized. The Lyapunov probe also perturbed a single coordinate, which measures how fast the lattice returns to its synchronized manifold rather than the system's largest exponent — it now perturbs in a random direction.

Control 4 then failed at a margin of 0.0084 against a threshold of 0.05, on a quantity that lives around 0.01. That threshold was mis-scaled, not the rung. Binned mutual information has a positive bias floor, so the only meaningful comparison is how far each value sits above it, and the control is now written that way.

On the rung built for it, the candidate does not move

Surrogate-normalized permutation entropy is flat. Not weakly related, not inverted — flat, across a target that varies by more than an order of magnitude on a system built specifically so that this family of measures could see it.

Taken with the tissue result — 4 of 6 sessions at p = 0.34, against PCIst's 6 of 6 at p = 0.016 — the measure is now refuted rather than untested. That distinction is the one thing the previous run could not supply, and supplying it was worth building a rung for.

The conclusion

The candidate is closed. Surrogate-normalized permutation entropy reads something real and consistent — it scores deterministic chaos at 0.743 where binarized Lempel–Ziv managed 0.978 — but what it reads is not integration, on constructed systems or on tissue.

The rung is the durable output of this run, and it outlasts the candidate that motivated it. The validation ladder now has a level where deterministic, broadband, modular systems carry a graded information-theoretic target that survives none of phase randomization. Every future measure whose currency is non-spectral structure gets scored there in an afternoon instead of being written up on constructed evidence that cannot reach it. The ladder gains a rung and loses an internal contradiction in the same step.

The screening sequence is now fixed by three runs of evidence. A candidate is scored on a constructed bed whose structure it can actually read, then on tissue, and only then written up. delta_spread skipped the second and was withdrawn after three rounds of work. This measure had no bed that could read it and consumed a run establishing why. Both costs were paid once; neither needs paying again.