The Law of Alignment

Psychological Recovery Simulator

Physiological & Emotional Recovery Alignment Simulator (LAE-SDI v1.0)

Instructions & Explanation

How to Use the Physiological Recovery Alignment Simulator

Use the control sliders below to model how training volume, sleep, muscle adaptation, and hormonal effort impact an athlete’s physical capacity and performance output over a 60-day horizon.

  • Training Load / Volume (D): Daily workout volume, intensity, and physical strain.
  • Sleep & Nutrition Recovery (R): Quality of rest, active recovery, nutrition, and autonomic downregulation.
  • Anabolic Adaptation (I): Muscle protein synthesis, aerobic base building, and structural adaptation.
  • Sympathetic Reserve / Adrenaline (_A_max): Hormonal drive, caffeine/stimulants, and mental grit/willpower.
  • Overtraining Multiplier (α): Metabolic drain rate per unit of physical strain.
  • Required Power Target (P):** The required performance target or athletic output demand.

How to Interpret Results:

  • Overtraining Drift Index (SDI): Measures physical sustainability.
    • Values below 1.0 represent ANABOLIC BALANCE (recovery exceeds strain).
    • Values between 1.0 and 1.5 indicate LATENT OVERTRAINING (adrenaline masking neuromuscular fatigue).
    • Values above 1.5 signal SYSTEMIC COLLAPSE / INJURY.
  • The Chart: Observe Neuromuscular Capacity (Green) versus Athletic Output (Blue). The dashed orange line shows adrenaline/willpower maintaining steady performance while capacity drains, until capacity hits the Injury Threshold (Red) and output drops sharply.

Psychological & Emotional Recovery Alignment Simulator

Simulating Emotional Energy C(t), Functional Output P(t), Willpower/Compensation Effort A(t), and Psychological Burnout Drift Index (SDI).

Model Status: Illustrative
Scenario Presets:
Burnout Drift Index (SDI)
0.00
Exhaustion Boundary (Ccrit)
0.0
Minimum capacity before compensation can no longer preserve target function
Psychological State
EMOTIONAL BALANCE
Alignment Margin
0%
Distance from the SDI = 1.00 balance boundary
Overdrive Utilization
0%
Peak compensation effort relative to available reserve
Capacity Trend
STABLE
Time to Critical Boundary
—
Model interpretation:
Model Formulation, Equations & Normalization Assumptions

Governing Equations:

  • Emotional Capacity Dynamics: dC/dt = β·R + I − γ·D, with C(t) clamped to [0, C0]
  • Burnout Drift Index: SDI = (γ·D) / (β·R + I)
  • Executive Overdrive Effort: A(t) = min(Amax, max(0, P* − φC)), where φC = (C(t)/C0)·P*
  • Compensation Exhaustion Boundary: Ccrit = C0 · max(0, 1 − Amax/P*)

Units & Parametric Assumptions:

All psychological variables are normalized dimensionless indices. The baseline decompression unit β = 1.0 sets the recovery rate, the effective emotional drain coefficient is γ = 1.2·α as an illustrative modeling convention, C0 = 100, and the horizon is 60 days. Increasing α reflects higher stress vulnerability or environmental reactivity within the mathematical framework.

Interpretive boundary: SDI < 1 indicates that modeled restoration and integration exceed modeled stress demand; SDI = 1 is the balance boundary; SDI > 1 indicates net modeled capacity depletion. This simulator is an illustrative mathematical model. It is not a clinical diagnostic instrument, screening tool, or assessment of any individual’s mental health.