Paper 186 · Live Simulation · Seventh Substrate

The Explaining-Away Penalty
in C. elegans

299 neurons running live in your browser. Real OpenWorm connectome. Leaky integrate-and-fire dynamics, proprioceptive feedback, chemotaxis — no pre-computed playback. The same explaining-away penalty I(D;M|Y) > 0 that governs transformers and quantum circuits, running in a biological neural circuit on your machine.

299
neurons
3,363
synapses + gap junctions
0
free parameters
670×
signal / noise ratio
9/10
kill conditions pass
Loading connectome (299 neurons)…
0.0s LIVE — 299 neurons running on your machine
Click worm head (reversal) or tail (acceleration)
live state
position—
heading—
C at head—
dist to source—
command interneurons
AVBL
0.00
AVBR
0.00
AVAL
0.00
AVAR
0.00
sensory (chemoreception)
ASEL
0.00
ASER
0.00
motor (sample)
DB1
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DB4
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VB6
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Headline Result

Three scales, two directions, one framework prediction

The explaining-away penalty I(D;M|Y) exists in this circuit and follows framework predictions at every scale tested. At sensory boundaries, external grounding reduces the penalty (three-point fix). At internal junctions, external drive correlates D and M downstream, raising it (Structure Theorem). Both directions predicted; both measured.

Population
D = ASE, M = AVB−AVA, Y = bend
0.32vs0.79
↓ 2.48× with grounding · three-point fix
Sensory boundary
ASEL → AVBL synapse
1.07vs1.28
↓ with grounding · three-point fix
Internal dual junction
8 chem+gap pairs (KSG, k=5)
0.75vs0.65
↑ with grounding · Structure Theorem

Permutation control: shuffling gap junction current (M) at each dual junction → I(D;M|Y) ≈ 0.001 bits. Real coupling: 0.75 bits. That is a 670× ratio, Wilcoxon signed-rank p = 0.004. The penalty is structural, not an estimator artifact.

Vector Pe · §219

Why scalar Pe failed and vector Pe works

The worm sim broke the scalar Pe formula. sim_v9f showed scalar collapse captures only 4.3% of the joint MI ceiling because the three dimensions carry XOR-style synergy (II = −0.631 bits). The fix (§219): vector Pe per axis, zero fitted constants.

Scalar Pe (superseded)

4.3%
of H(class) captured. C = 1−(O+R+α)/9 collapses three independent axes into one number. Misses the synergy entirely.

Vector Pe (§219)

67.6%
of H(class) captured. Pe_i = (Pe^O, Pe^R, Pe^α) per channel with Pe^x = sinh(2(B_A − x·B_G)). 21.4× improvement. Zero fitted constants.

II(O;R;α) = −0.631 bits — strong negative interaction information. The three dimensions are synergistic: knowing any two tells you almost nothing about the third. This is the signature of obstructions that are irreducibly 3-dimensional with respect to a Cencov-canonical Y (§218).

Kill Conditions

v0 sanity to v3.6 molecular Fantasia

v0 KC1Connectome alone fails — body required for oscillationPASS
v1 KC2Dual e/m readout produces D/V antiphase (172-177°)PASS
v1 KC6GluCl receptor biology → AVA-AVB anti-correlation (−0.93)PASS
v2 KC7Closed-loop chemotaxis: real 100%, ablated 0%, random 80%PASS
v3 FB1Layer 1 Fantasia Bound holds (max excess +0.01 bits)PASS
v3 FB2I(D;M|Y) > 0 in working biological circuit (0.27-0.43)PASS
v3 FB3Three-point fix: penalty ↓ with grounding (ρ = −1.000)PASS
v3 FB4Ablated 2.48× higher penalty (in vivo three-point fix)PASS
v3.6 MOL2Permutation control: real >> shuffled (670×, p=0.004)PASS
v2 KC4Forward/reverse command discrimination — fails everywhereFAIL
Substrate Independence

Seven substrates, one Fisher metric

The explaining-away penalty I(D;M|Y) > 0 has been confirmed on seven independent substrates. Cencov's uniqueness theorem (1972) guarantees the Fisher metric is the only invariant metric on a statistical manifold — the penalty is substrate-independent by mathematical necessity. No technology substitution routes around it.

∇TransformerGPT-2 small, KC-(ii)✓
ψQuantum simStim, Test 4✓
ℏQuantum HWIBM Heron, Test 7✓
∂Thermothrml-rs✓
σSoftmaxAbstract channels✓
∞BiologyC. elegans + Drosophila✓
φLanguagePhoneme manifold✓
Zero free parameters. B_A = √3/2 (derived). B_G = π/√2 (Cencov). The Fisher metric does not care whether the channel is silicon, photons, thermodynamic noise, or 1 mm of nematode. The fix is architectural — three-point geometry — not technological.