Shared-Substrate Cardiorespiratory Spectrum
The same three primitives — the R19 switch, the FitzHugh–Nagumo oscillator, and the delayed chemoreflex loop — reproduce a spectrum of cardiorespiratory phenomena with no new mechanism: Mayer waves, the airway-tone switch, the obstructive-apnea loop-gain regime, the periodic-breathing spectrum, fever heart-rate co-scaling, and excitable cough. Signatures [interpretation]; absolute magnitudes [O].
One substrate, six signatures: Mayer waves near 0.1 Hz, an airway-tone bistable switch, the obstructive-apnea loop-gain regime, the periodic-breathing spectrum, fever HR–RR co-scaling, and all-or-none cough — each a reuse of §2/§4/§7 with no new primitive. Mechanisms [interpretation]; absolute magnitudes [O].
The three primitives established above — the R19 bistable switch, the FitzHugh–Nagumo oscillator, and the delayed chemoreflex loop — reproduce a spectrum of cardiorespiratory phenomena with no new mechanism added. These are dynamical signatures of the shared substrate, stated as mechanism, not as clinical, diagnostic, or management statements.
Mayer waves: a baroreflex resonance near 0.1 Hz
Slow arterial-pressure waves near 0.1 Hz emerge as a resonance of the same delayed baroreflex loop that §7 derives. The frequency is a cited physiological value [L]; the mechanism is the loop, reused without modification [interpretation].
Airway-tone switch (asthma regime)
Reversible airway-tone collapse is the R19 switch run as a reversible bias rather than the one-way carcinogen bias of §8. The bistable shape and its hysteresis are the reused content [interpretation]; the absolute provocation magnitude is open [O].
Pharyngeal patency and loop gain (obstructive-apnea regime)
Obstructive sleep apnea is read as a two-part dynamical regime: a pharyngeal patency switch on top of the ventilatory loop-gain instability of §4. The loop-gain endotype is the reuse of LG / LGc = 1 [interpretation]; the absolute collapse pressure is open [O].
Periodic-breathing spectrum (central-apnea family)
Altitude, low cardiac output, and opioid-driven periodic breathing form one spectrum: the same chemoreflex Hopf instability with different loop delays and gains, reusing §4 and §6. The directions and the delay scaling are an [interpretation] of §4 and §6; the absolute thresholds are open [O].
Fever: heart-rate and respiratory-rate co-scaling
Because both organs are one oscillator, a thermal speed-up raises the cardiac and the respiratory rate together rather than independently. This co-scaling direction is a [consistency] consequence of the shared time anchor (both rates are divided by the same κ by construction), not an independent prediction; [observation] heart rate rises by roughly 8–10 bpm per °C of fever (Karjalainen & Viitasalo 1986, Arch. Intern. Med. 146:1169), and breathing rate also rises; the absolute slope is open [O].
Cough: an all-or-none excitable threshold
Cough is the FitzHugh–Nagumo unit in its excitable regime: a sub-threshold stimulus decays, a supra-threshold stimulus fires a full response. The all-or-none excitation is the reused mechanism [interpretation]; the absolute stimulus threshold is open [O].
| phenomenon | reused primitive | verified signature | open magnitude |
|---|---|---|---|
| Mayer waves ≈ 0.1 Hz | baroreflex loop (§7) | resonance exists [interpretation] | frequency cited [L] |
| airway-tone switch | R19 reversible bias (§8) | bistable + hysteresis [interpretation] | provocation [O] |
| obstructive-apnea regime | loop gain (§4) + patency switch | loop-gain endotype [interpretation] | collapse pressure [O] |
| periodic-breathing spectrum | chemoreflex Hopf (§4, §6) | directions + delay scaling [interpretation] | thresholds [O] |
| fever co-scaling | shared oscillator (§2) | HR–RR co-scaling [interpretation] | slope [O] |
| excitable cough | FHN excitable regime (§2) | all-or-none firing [interpretation] | threshold [O] |
Review note: repro/cardioresp/repro/run_all.py itself marks the airway-tone hysteresis, the OSA collapse, fever co-scaling and cough as “[V?]” (unconfirmed); on this page they are read as [interpretation].
What is open
Across this spectrum the verified content is the mechanism reuse; every absolute magnitude is grade [O]. Obstacle: the switch noise scale and the stimulus-to-bias conversion are not fixed by substrate geometry and need an external calibration — the same obstacle that keeps absolute organ size and absolute cancer relative-risk open. The open items are collected in §9.