A whole nervous system, and the sentence it does not support

Run: gate/celegans.py → gate/celegans.json Date: 2026-09-21. Plan §6A item 4 — the Empirical rung.

Question or issue resolved

gate/RESULT-TOPOLOGIES.md gave this program's one surviving candidate a stated domain of validity. Negated delta_spread tracks integrated information where a substrate is distance-structured — a chain at −0.99, a ring at −0.91 — and fails or reverses where influence is concentrated in few sources: an Erdős–Rényi graph at +0.08, a hub topology at +0.49. That document then wrote a sentence no measurement stood behind:

Cortex is. A star network is not.

It is an assertion about real substrates drawn entirely from constructed ones, and it is load-bearing twice over. It is the reason the measure was not withdrawn when the hub result came in, and it is the concrete argument METHOD §3.4 makes for why an artificial system is the riskier extrapolation. Nothing in the register tested it.

This tests it against the only system whose causal graph has been measured pair by pair and whose boundary is not a judgment call: 23,433 stimulated neuron pairs covering 186 of 188 head neurons of Caenorhabditis elegans (Randi et al. 2023), obtained as a packaged matrix through wormneuroatlas 0.0.7.3 (GPL-3.0) and used entirely offline.

The comparison is possible because the same object exists on both sides. The atlas is a matrix whose entry [i, j] is how much neuron i moved when neuron j was stimulated. For a linear-Gaussian system that object has a closed form — the largest absolute entry of Aᵏ over k — so the seven synthetic families of gate/topologies.py reduce to exactly the same kind of matrix and are described by exactly the same four functions. Distance comes from wiring on both sides: hops in the anatomical connectome for the worm, hops in the coupling graph for the families.

The finding: it is neither, and it does not place at all

Read across the row. The worm's influence is distributed as unequally as the hub family's — it sits at the 87th percentile of the entire synthetic ensemble in gini_out — and yet it has no hub: its most influential neuron carries a tenth of the share the hub family's does. And its response falls off with wiring distance more weakly than any distance-structured family, more weakly even than a random graph.

Concentrated without a center, and barely distance-structured. The synthetic ensemble does not contain that shape, and the placement says so directly: five of the seven families sit at the same distance from the worm, 0.98 z-units, with a gap between the two nearest of 0.000. Under the resolution rule fixed before the worm was placed — a gap of at least a quarter of the ensemble's own within-family spacing — the placement is unresolved, and the nearest-family label is not reportable.

That is not a shortcoming of the run. It is the answer to the question asked. The sentence under test assumed the axis was a line with brains at the distance-structured end; the one whole-organism causal graph anyone has measured sits off the line.

gate/RESULT-TOPOLOGIES.md's domain sentence does not survive contact with a nervous system, and this register carries the correction rather than the claim. What can be said is narrower and still useful: delta_spread works on distance-structured substrates, that property is not established for any real nervous system, and the one measured case is not obviously an instance of it.

Robustness: the finding holds across the cut, the label does not

The significance threshold is a parameter, and this register's own record shows what a parameter does to a measure — a protocol change moves PCIst by 2.07× on the same electrodes in the same patient (gate/RESULT-CHOCS.md). The comparison ensemble is rebuilt at each cut's own density, because a Gini computed on more edges falls mechanically and reusing one ensemble would have reported that bias as a trend.

Every substantive statement survives all four cuts: top of the ensemble in concentration, an order of magnitude below the hub family in top_share, decay always weaker than half a distance-structured family's. The nearest-family label changes at every cut, which is the sweep demonstrating rather than the author asserting that the label carries nothing.

What carries the placement, measured rather than assumed

Two nulls, each removing one thing: permuting the responses across their own support destroys how strongly pairs respond while leaving which pairs respond intact; a degree-preserving rewiring destroys which pairs respond while leaving every neuron's count intact.

Both are small, and both are small for the same reason: gini_out and top_share are functions of the out-degree sequence, which both nulls preserve. So the concentration above is a statement about how many neurons each stimulation significantly moves, not about how far it moves them. That is a weaker claim than the table might suggest and it is stated here rather than left for a reader to find.

This began as a gating control — shuffling had to move the placement — and it failed. The failure was in the control: no correct implementation could have passed it. A control that nothing can pass tests nothing, so it was replaced by a decomposition that is reported whichever way it comes out. The four gating controls are 1, 2, 3 and 5.

The strain contrast is coverage, not biology

The atlas also carries unc-31 mutants, in which dense-core vesicle release — and with it most extrasynaptic signalling — is disabled. That is a paired whole-organism manipulation of a signalling channel, and it looked like a result: influence is more concentrated in the mutant, gini_out 0.560 against wild type's 0.464.

It is not. The mutant was measured on 9,228 pairs against wild type's 24,075, and a Gini on fewer edges is biased upward. Subsampling wild type's own support down to the mutant's edge count, 200 times, gives 0.582 [0.554, 0.611] — the mutant's value sits below the mean of that null and comfortably inside it. The contrast is entirely coverage.

Nothing about extrasynaptic signalling is claimed here. The check cost one function and it stopped a wrong biological claim from being written up, which is the same service the activity-matching check performed in gate/RESULT-CALIBRATION-MATCHED.md.

Four defects found while building this, all of the same kind

Each produced a confident number that looked reasonable, and each is now a control.

1. Thinning kept everything. The top-k selection used a magnitude threshold, and when the k-th value was zero, R >= 0 retained the whole matrix. Selection is now by index, and zeros are never kept.
2. Every wiring distance was 1. topologies.build puts a weight of t on cross edges rather than removing them, so the binarized coupling graph is complete for any t > 0 and no family had any distance structure to decay over. The wiring graph is now thinned to the measured anatomical density, which recovers each family's designed topology — the near-neighbour band for a chain, the spokes for a hub.
3. A pinned descriptor decided the answer. Density matching fixes reach_frac by construction, so its spread across the ensemble was 1.5 × 10⁻¹⁷ rather than 0 — the divide-by-zero guard did not fire, the z-score came out at −4.7 × 10¹⁴, and the placement was settled by floating-point noise while every printed number looked plausible. reach_frac is now excluded from placement and control 5 asserts a variance floor for every descriptor placement is allowed to use, so the class cannot recur silently.
4. An unpassable control. Described above, and replaced.

Defect 3 is the one worth keeping in view. It is the failure mode this whole program was built around — a silent wrong answer wearing the clothes of a result — and it was caught by a control written to catch something else.

Conclusion

The Empirical rung is built, used, and it did what the ladder exists to do: it removed a claim rather than confirming one. A sentence asserting that real nervous systems are distance-structured, written on constructed evidence and carrying weight in both gate/RESULT-TOPOLOGIES.md and METHOD §3.4, is withdrawn. The measured causal graph of a complete nervous system is concentrated without a center and only weakly distance-structured — a shape the seven-family ensemble does not contain — and it is one organism, invertebrate, and not cortex, which is exactly why the claim it displaces should never have been made without it.

Two cautions travel with this file. C. elegans is not a mammalian brain, and its sitting off the axis does not establish where cortex sits; it establishes that nobody has checked. And the synthetic families are near-symmetric while the worm's graph is directed, so the comparison is fair in what it measures and incomplete in what it covers.

The rule from gate/RESULT-SPREAD-REAL.md binds harder after this run. Three runs of constructed-system evidence did not survive one contact with mouse tissue; a sentence written on constructed evidence did not survive one contact with a worm. Constructed systems are where a measure is developed. They are not where anything about a brain is decided.