Delayed negative feedback through sealed microchannels: threshold, pressure-tuned rhythm and readout-noise limit in a chain test of a chemical signalling layer

In the chemical layer of the ORBA design, signal molecules released at one wall travel through sealed microchannels 35 mm long to receptor-coated sensing electrodes at the opposite wall, and the channel pressure sets the transit delay (about 1.95 s to 195 s between 10 kPa and 100 Pa). We ask whether a regulator that corrects the release from the sensor reading turns this delay into a self-sustained rhythm, what sets its threshold and period, and whether the sensor can resolve it. The test is a chain test: the layer's own transport, receptor-kinetics and sensor kernels and its parameter table are closed by one added design element, a proportional controller acting on a release port that cannot run backwards. The linearised loop is the classical equation dx/dt = −a x − b x(t − τ); the kernels reproduce its characteristic roots (threshold to 1 × 10⁻⁴, open-loop gains to 0.011 %). The loop becomes unstable at a static loop gain b_c/a = 1.002–1.016 between 100 Pa and 1 kPa, and channel pressure tunes the onset period from 5.383 s to 392.6 s. Above threshold, a finite-amplitude cycle limited by the port's zero-current constraint is present from 0.2 % above threshold, with amplitude given by 1 + b/a in units of the steady-state coverage; closer to threshold the onset was not resolved. At the design receptor affinity, the delivered concentration (0.055 nM at 1 kPa) is about 1,800 times below K_d, and the in-band signal at 1 kPa is 0.63 µV against 2.15 µV of nominal readout 1/f noise (signal-to-noise ratio 0.29; 0.30–0.49 with literature levels scaled to the design gate). Matching K_d to the delivered concentration raises the sensitivity 455-fold but requires a binding rate 463–905 times the design entry. All results are numerical and model-bound; no hardware has been built or measured. This record contains the preprint (13 pages, 8 figures, 4 tables) and an archive with the run records behind every reported number, the script that regenerates every number, table and figure of the manuscript from those records, the LaTeX source, the run ledger and logs of the Notes #2 runs (including failed runs), the literature ledger, and the slide summary published before the preprint. The ORBA layer code is not part of this record. The author is an independent undergraduate researcher; this work is not affiliated with or funded by any university or institution. It has not been peer reviewed.