Math & Thinking Behind Genome

lag = argmax( Σ X(t) · Y(t + τ) )  over τ ∈ [-T/2, T/2]

The lag τ* that maximizes cross-correlation is the latency.
Converted from quarters to days: latency_days = τ* × 91

High latency = slow-moving system. A company with 3-quarter latency takes ~9 months to reflect input changes in output — typical of capital-intensive industrials with long procurement cycles.

gain = std(Y_detrended) / std(X_detrended)

Both series are linearly detrended before computing std.
gain > 1 → system amplifies (fragile to shocks)
gain < 1 → system absorbs (resilient)
gain ≈ 1 → proportional response

A fragile company with gain=2.5 sees revenue swings 2.5× larger than the macro inputs that drove them. This often indicates leverage, low inventory buffers, or just-in-time exposure.

ρ(k) = Corr(Y_t, Y_{t-k})   for k = 1..8

Fit exponential: ρ(k) ≈ A · e^{-λk}
damping = λ  (estimated via log-linear regression)

damping > 0.3  → fast decay, system self-corrects
damping ≈ 0    → slow decay, shocks persist
damping < 0    → explosive / non-stationary (rare)

An oscillatory company with near-zero damping continues swinging long after an input shock ends. High damping means the system returns to baseline quickly — operationally resilient.

Y_detrended → FFT → power spectrum P(f)

oscillation_frequency = f at argmax P(f),   f > 0
oscillation_period_weeks = 1 / oscillation_frequency × 13

spectral_power_fraction = P(f*) / Σ P(f)
(fraction of total variance in the dominant frequency)

Companies with spectral_power_fraction > 0.4 have strong cyclical behavior — demand or inventory cycles dominate their output. Low spectral power means noise-dominated, non-cyclical response.

Sort X ascending. Split into 4 quartiles.
Compute Δ(output) / Δ(input) in each quartile.

saturation_threshold = fraction of input range where
slope drops to ≤ 50% of lower-quartile slope

saturation = 1.0 → full saturation (hits hard ceiling)
saturation = 0.0 → no saturation detected

A saturated company shows strong output response at low input levels but the response flattens as inputs grow — classic capacity constraint. This maps directly to the X1 Physical Constraint node.

vol_trans = std(ΔY) / std(ΔX)

where ΔX = first difference of input (shock proxy)
      ΔY = first difference of output

vol_trans > 1 → amplifies volatility (fragile)
vol_trans < 1 → absorbs volatility (resilient)
vol_trans ≈ 1 → passes through unchanged

Volatility transmission is the single best fragility indicator. High vol_trans companies respond to macro noise as if it were signal — their operations lack the buffers to absorb routine variation.

High amplification + high volatility transmission. Operationally leveraged, brittle to shocks. Any supply disruption or demand spike cascades through the system without buffering.

Throughput hits a ceiling at moderate input levels. Revenue doesn't scale proportionally with demand — a physical, workforce, or capital constraint is binding.

Dominated by cycles that don't self-correct quickly. Demand cycles, inventory cycles, or procurement cycles run through the system with low damping — the pattern repeats.

Capacity-limited but stable. The system is hitting a ceiling but handles it gracefully — no fragility signature. Classic late-stage growth or mature capacity-constrained industrial.

Slow to respond, low amplification. Appears insensitive to macro inputs — either highly vertically integrated, long-contract revenue, or operating in a niche with structural demand insulation.

Absorbs shocks, self-corrects, proportional response. Strong operational buffers (inventory, workforce flexibility, diversified customer base). The benchmark all others are compared against.

Signal insufficient to classify, or fingerprint dimensions are contradictory. Typically means too few data points or a company in structural transition between archetypes.