A measure that passes every control and cannot be validated by the test bed built for it

Run: gate/surrogate.py → gate/surrogate.json Date: 2026-09-21. Constructed systems and six sessions of DANDI:000458, in one run.

Question or issue resolved

Every compression measure this program has screened failed for one reason, named in gate/RESULT-MEASURES.md: compression ranks randomness as maximal, so phase-shuffling an evoked response — which destroys its structure — raises the score. The proposed repair was to stop asking how incompressible a response is and ask how incompressible it is compared to itself with its structure removed:

ratio = H(response) / H(phase-shuffled surrogates of that response)

Phase randomization preserves each channel's power spectrum exactly and destroys its temporal structure, so the surrogate differs from the original only in the thing the measure is meant to detect. gate/RESULT-SPREAD-REAL.md made this property worth selecting for: the measure that failed there was scale-free by circumstance, and the circumstance did not travel to tissue. A surrogate normalizer rebuilds its denominator from the numerator's own spectrum every time, so it is scale-free by construction.

Under the rule that failure established, this ran on constructed systems and on tissue in the same run, before anything was written up.

The controls killed the first version before it saw any data

The measure was first built on Lempel–Ziv complexity of a median-binarized signal, the currency every previous screen used. Its own control rejected it:

Deterministic chaos is broadband, so its spectrum says nothing, yet every sample is fixed by the last. It is exactly what surrogate normalization exists to detect, and binarized LZ scored it at 0.978 — indistinguishable from noise. Binarizing about the median discards precisely the amplitude relations determinism lives in, so no normalizer could have rescued it. The problem was never the denominator; the numerator could not see the thing.

Ordinal patterns keep those relations and are scale-free by construction — multiply a channel by any positive number and every ordering is unchanged. Permutation entropy scores the same chaos at 0.743. All four controls then pass, including the strongest one: real evoked responses, phase-shuffled and fed back in as if genuine, score exactly 1.000.

An earlier control demanded that a pure sinusoid score low and failed the run at 0.857. That control was wrong, not the measure. Phase-randomizing a pure tone returns a pure tone, because a sinusoid's structure is its spectrum and the surrogate preserves it exactly. This is recorded as a blind spot rather than repaired, and it turns out to matter more than a footnote.

The blind spot swallows the entire constructed test bed

Against closed-form integrated information on linear-Gaussian systems:

No relationship, and the reason is structural rather than empirical. A linear-Gaussian process is completely described by its spectrum. Phase-shuffling one produces a statistically identical process, so the surrogate is the original in every respect the measure can read, and the ratio is pinned at 1 no matter how integrated the system is. The measure did not fail this test. The test cannot be run.

That is a constraint on the validation ladder itself, not on one candidate. The Closed form rung exists because linear-Gaussian systems are the only ones where integrated information has an analytic value at scale — and no surrogate-normalized measure can ever be scored on that rung, because the rung's defining property is the one that blinds the whole family. Two of the ladder's rungs are mutually exclusive, and nothing in the plan said so until now.

On tissue, it does not separate states

Six sessions with both wakefulness and isoflurane: 4 of 6 in the predicted direction, sign test p = 0.34. For comparison, PCIst on the same responses under the same channel and trial rules separates 6 of 6 at p = 0.016 (gate/RESULT-SPREAD-REAL.md).

One detail is worth recording because it was not predicted. Every ratio is above 1 — real evoked responses are ordinally less predictable than their own phase-shuffled surrogates, most strongly under anesthesia (1.20 at sub-543394). Phase randomization smooths a response, and a smoother signal has fewer distinct ordinal patterns. So the measure is reading something real and consistent; it simply is not reading state.

The conclusion

Surrogate-normalized permutation entropy is not adopted, and it is not discarded either. It is the first candidate in this program to pass every control it was given, including one no previous measure could have passed, and it is untested rather than refuted: the constructed bed cannot evaluate it, and six sessions cannot settle 4 of 6.

Three things follow, and the middle one is the most useful thing in this run.

The screening currency changes. Binarized Lempel–Ziv is retired from this program. It cannot distinguish deterministic structure from noise, which is a stronger objection than the randomness problem that motivated the surrogate normalizer in the first place, and it has been the input to every measure screened so far. Ordinal patterns replace it.

The validation ladder needs a rung this family can stand on. A measure that reads non-spectral structure requires a ground truth whose structure is not spectral, and every constructed system this program has built — threshold networks, linear-Gaussian systems — is either too small for a gradient or entirely spectral. The candidate for that rung is a nonlinear system with a known partition: coupled chaotic maps in a modular arrangement, where the modularity is fixed by construction and the dynamics are deterministic and broadband. That is the next build, and it is now blocking, because until it exists this whole family of measures cannot be scored against anything.

The tissue test stays cheap and stays early. It cost an afternoon, it ran before anything was written up, and it kept a 4-of-6 from being reported as a success. That rule is holding.