Aboral slow-wave frequency gradient
The intestinal slow-wave frequency falls monotonically aboral, reproducing the duodenum-to-ileum gradient. One gastric-anchored clock (K_TIME=2400 cpm per model-Hz) converts each segment's FitzHugh–Nagumo frequency to cycles per minute, predicting duodenum 11.1 cpm and ileum 7.5 cpm with no intestinal anchor (the intestinal τ_s values are chosen; see below). The gradient direction is a [consistency] result of τ_s chosen to grow aborally; absolute rates inherit the cited clock [L].
A linearly growing recovery constant along the gut yields a monotone falling slow-wave gradient. The single gastric clock predicts duodenum 11.1 cpm (cited ~12) and ileum 7.5 cpm (cited ~8) with no intestinal tuning. The gradient shape is [code output]; the absolute rates inherit the cited clock [L].
The intestinal slow-wave frequency falls monotonically in the aboral direction, reproducing the physiological duodenum-to-ileum gradient. A single segment property — the FitzHugh–Nagumo recovery constant τ_s growing linearly along the gut — produces the entire descending profile.
One gastric-anchored clock converts each segment's intrinsic frequency to cycles per minute with zero intestinal tuning, predicting duodenum 11.1 cpm (cited ~12), jejunum 9.0 cpm (cited ~10), and ileum 7.5 cpm (cited ~8). The duodenal prediction lands within 8% of the cited value despite the clock being fixed by the stomach alone.
| segment (proximal→distal) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| cpm | 11.1 | 10.5 | 10.2 | 9.9 | 9.6 | 9.0 | 8.7 | 8.7 | 8.4 | 8.1 | 7.8 | 7.5 |
The gradient direction follows from τ_s chosen to grow aborally ([consistency]); the absolute rates inherit the cited clock [L]. Monotonic decrease holds across segment counts N ∈ {8,12,16,20} and the full drive sweep, so the falling gradient is a property of the mechanism, not of a particular discretization.
Input dependence (review run, 2026-09-29): the intestinal τ_s values are chosen constants (duodenum 95, ileum 95 × 1.5 = 142.5 in repro/digestive/repro/_engine/vp_dig_engine.py). With the same gastric clock a duodenal τ_s of 80 / 90 / 100 / 110 / 120 gives 12.9 / 11.7 / 10.5 / 9.6 / 9.0 cpm. The frequencies are read from an FFT over a fixed window, so they fall on a 0.3 cpm grid (hence the repeated 8.7); a 6000-unit window gives a duodenal 12.0 cpm, a 12000-unit window 11.0, and an inter-spike-interval estimate 11.0. These are [code output]. [observation] Measured human small-intestinal slow waves run at about 11–12 cycles/min in the duodenum and about 8 in the terminal ileum (Huizinga & Lammers 2009, Am. J. Physiol. Gastrointest. Liver Physiol. 296:G1).