Process S (Homeostatic Debt)
Process C (Circadian Drive)
Cognitive Alertness Curve
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Scrub Time:
Hour 14.0h
Real-Time Physiology Telemetry
Avg Reaction Delay
480
ms
Baseline: ~250ms
Microsleep Hazard
High (74%)
Vulnerability Window
Min Alertness
32
%
Lowest phase capacity
Peak Process S
0.88
S-Units
Max homeostatic load
2.0 hrs
4.0 hrs
Recovery Trajectory Projection
Required 8h Nights to Clear Debt:
3 Days
Based on standard homeostatic discharge dynamics ($k_d = 0.21 \text{ h}^{-1}$), returning to baseline alertness after extreme 2-hour sleep shifts requires cumulative slow-wave sleep cycles across consecutive uninhibited night rests.
The Physiological Reality of 0–3 Hour Sleep Schedules
Process S (Homeostatic Debt)
Sleep pressure builds exponentially during wakefulness ($S_t = 1 - (1-S_0)e^{-t/\tau_w}$) and decays during sleep. Under 2-hour sleep, discharge is truncated, leaving massive residual debt compounding daily.
Process C (Circadian Oscillator)
Controlled by the suprachiasmatic nucleus (SCN), alertness follows a 24-hour sinusoidal wave independent of sleep. When Process C trough aligns with peak Process S, cognitive function collapses.
Cognitive Latency & Involuntary Microsleeps
When alertness drops below 35%, reaction times delay by 200–300ms (equivalent to 0.08% BAC intoxication), triggering uncontrollable 2–15 second microsleep episodes during continuous tasks.
Proof Target: Active Simulation
Avg Delay: 480 ms
Microsleep: High (74%)
Min Alertness: 32%
Peak S: 0.88
Recovery: 3 Days
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