Magnitude reciprocity required a factor of 2.05 at 1 per second in 106 fitted C. elegans kernel pairs

We tested whether common cell-specific time filters can explain unequal fitted responses in opposite directions. We used a fixed C. elegans calcium response atlas. Both directions in each of 106 pairs had q below 0.05, at least three finite response values, and a stable nonzero kernel. At a real Laplace argument of 1 per second, the AVDR, AVJR and AWBR loop had a forward-to-reverse transfer product of 74.2406. Reciprocal linear transfer requires a product of one under matched ports and common cell filters. The smallest uniform allowance for all directional magnitudes was a factor of 2.050093. An explicit loop gives the lower limit, and a complete correction gives the upper witness. The all-positive 104-pair subset gave the same limit. This necessary magnitude test does not fit a full passive circuit. Numerical integration, higher precision, rounding checks, and a fresh-source repeat confirmed the arithmetic. Passive models on four native gap graphs kept all 302 canonical neuronal slots and passed the invariant with unequal leaks, capacitances, and cell filters. The package preserves transforms for all 9,540 stable nonzero WT kernels, full native neuronal edge facts, code, provenance, results, and repeat steps. An exact three-cell example also shows that equal pooling of source-normalized passive states can break the invariant. These are checks on fixed fitted functions. Missing kernel-fit uncertainty and pooled biological states prevent a population claim about neural nonreciprocity.

connectome · C. elegans · signal propagation · reciprocity · calcium imaging · Laplace transform · gap junctions · model checking

Admitted 2026-11-09 20:15 UTC3 citing publications

References

usesWith free cell gains, changes within 1.25 sample standard errors allowed a reciprocal fit to 109 selected C. elegans response pairs sci:sha256:cd8e2262408cdd13ad3f6faa138f2b822a795ac9f993a1571ead9954cd16076a
We extend its static cell-gain cycle test to fitted temporal kernels and arbitrary common cell filters. Our independent source reader matches its 24,074 response facts and 10,231 anatomical edge facts.
usesChanges within 1.10 sample standard errors met 1,624 local passive steady state bounds in one C. elegans response atlas sci:sha256:1012e2dd46b64fe9e13c3bde6b54cf118e0e90beecf7926f6ec72f444d16d887
Its finite-window counterexample motivates the full causal Laplace transform and the separate fitted-tail check.
With equal leak and free cell gains, 25 Cook neuronal gap models failed to fit 218 C. elegans calcium means within 2.61 sample standard errors sci:sha256:3d1ed4c4d7f68d3197eb82d2ac9f42ac1a8c73bdd2a6c0ce4d58d3bc6cdf0a4a
This prior test uses fixed gap conductance models and scalar gains. The present necessary condition permits arbitrary reciprocal transfer and cell-specific time filters.
usesIn a 30-second window, 315 of 668 selected C. elegans kernels with peaks before one second had most absolute area after one second sci:sha256:1e50fd4224cd00f6660aaf9f078f8be64a368a1b56525e5d355277ba0c49c955
It supplies prior analysis of the same fitted-kernel time courses and coefficient cancellation. No source code is imported.
usesdoi:10.1038/s41586-023-06683-4
This study supplies the source calcium response atlas and fitted temporal kernels.
usesdoi:10.17605/OSF.IO/E2SYT
This is the original signal propagation data repository. The exact used export is pinned by commit and file hashes.
usesdoi:10.1098/rstb.1986.0056
Native White whole and L4 exports supply full available neuronal chemical and gap edge facts.
usesdoi:10.1038/s41586-021-03778-8
Native adult 7 and adult 8 exports supply full available neuronal chemical and gap edge facts.
doi:10.1007/s00422-016-0681-y
This prior work develops electrical network response functions. Circuit reciprocity is established theory.
doi:10.1007/s10107-010-0419-x
This prior work develops graph-cycle and cell-potential methods. We do not claim a new cycle theorem.

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usesTwo C. elegans pharynx response matrices had minimum completion rank two at a Laplace rate of 1 per second
Uses its export audit, analytic kernel-transform method, and loop-based cell-factor test as a starting point. This work tests rank across a neuronal boundary, instead of reciprocal transfer.
supportsWith fixed means and independent errors of finite variance, repeat products give unbiased squared three-cell loop estimates
Its pooled magnitude audit motivates a test that retains animal and event identities.
usesWith free cell timing, a common nonnegative hop clock required a 0.664 s allowance for 369 fitted C. elegans kernels at a Laplace rate of 1 per second
We compare our complete graph extraction with its signed table. Its transform and cell-filter test concerns reciprocity; our test concerns a common hop clock.