279 Neurons, One Signal: Hub Identity Preserved at 20:1 Compression in C. elegans

Background: M_EXT2

The earlier M_EXT2 experiment ran the Functional Proximity Law on a subset of the C. elegans nervous system: the 15 highest-degree command interneurons (AVAL, AVAR, AVBL, AVBR, AVEL, AVER, AVDL, AVDR, PVCL, PVCR, RIAL, RIAR, AIBL, AIBR, DVA).

Result: r(chemical_synapse ↔ gap_junction) = +0.777 (p = 0.004, n=15)

Both the data and the layer definitions (chemical synapse, gap junction) come from the WormAtlas biological classification — fully independent of IRDME.

This is a strong result, but it uses a curated 15-node subset. A natural question: does the law hold on the full nervous system, or was the 15-node result an artifact of cherry-picking the most prominent hubs?

F12: Full 302-Neuron Connectome

F12 ran the same test on the complete connectome.

Dataset: All 279 C. elegans neurons with at least one synapse connection (out of 302 anatomical neurons), from Varshney et al. 2011. The same chemical_synapse and gap_junction layer definitions — unchanged from M_EXT2, still fully independent of IRDME.

Pre-registered hypotheses (hash a8926052, committed 2026-05-19):
• h1: r(chemical_synapse ↔ gap_junction) > 0, p < 0.05, n ≈ 302
• h2: AVAL ranks within top 3 in chemical_synapse
• h3: The 15 M_EXT2 command interneurons occupy ≥ 10 of the top-20 positions in chemical_synapse (hub-identity preservation test)

The Result

r(chemical_synapse ↔ gap_junction) = +0.623 (Spearman = 0.313, p = 0.002, n=279, 95% CI [0.546, 0.690])
• h1: CONFIRMED
• h2: CONFIRMED — AVAL ranks #2 (AVAR is #1)
• h3: CONFIRMED — 13 of the 15 command interneurons appear in the top-20 chemical synapse hubs

The Compression Test

The drop from r=0.777 (n=15) to r=0.623 (n=279) is expected and informative. Adding 264 peripheral neurons introduces noise: these neurons have low degree in one layer and high in the other (or low in both), pulling the correlation down.

But the hub identity is preserved: 13 of the 15 neurons identified as top hubs in the 15-node study still appear in the top-20 of the full 279-node network.

That is a 20:1 compression ratio with 87% hub-identity retention. If you want to find the structurally important neurons of C. elegans from topology alone:
• The top 15 by degree give you the command interneurons
• They are still in the top 20 when you include all 279 neurons
• The correlation between chemical synapse and gap junction layers confirms both layers see the same structural hierarchy

Why Independent Replication Matters

M_EXT2 and F12 share the same biological system but are designed as independent tests:

| | M_EXT2 | F12 | |---|---|---| | n | 15 (command interneurons) | 279 (full synapse-connected) | | Selection | Highest-degree subset | All neurons with ≥1 synapse | | Layer source | WormAtlas (independent) | Same (unchanged) | | r | 0.777 | 0.623 | | p | 0.004 | 0.002 | | Verdict | CONFIRMED | CONFIRMED |

Both are pre-registered. Both confirm. The lower r at full scale is mechanistically explained by peripheral neuron noise — not by law failure.

Pre-registration Record

Hash: a8926052… — committed 2026-05-19T18:54:06 UTC. Full record: github.com/vladi160/preregistrations (commit ab02f8f).

Paper: arXiv:2604.23639