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Activation:      χ = σ(α_κ·κ + α_Ψ·Ψ̃ - θ)     ← Continuous sigmoid, NOT binary Fibonacci

Plasticity:      η = clamp(η_base + η_gain·κ, η_min, η_max)

Compute global coherence Φ = geomean(φ_f) × uniformity

Uniformity (low variance = high uniformity)

dΨ/dt = -γ(Ψ - w·φ̄) + η·σ(Σⱼ Jᵢⱼφⱼ - θ)

For α = 1.5, use bisection method to find threshold

Margin = how much better than second-best

MASTER UPDATE: φ(t+) = φ(t) + (1-φ(t)) × Γ × π^eff

Compute continuous activation χ = σ(α_κ·κ + α_Ψ·Ψ̃ - θ)

Normalize pressure: Ψ̃ = Ψ / (Ψ + ψ₀)

Activation: χ = σ(α_κ·κ + α_Ψ·Ψ̃ - θ)

Compute learning drive Γ = χ × η × κ

FAMILY TABLE (32 bytes = 16 families × 2 bytes)

16 Families × 5000 Substrates = 80,000 Learning Sites

==================== STRIPE PAYMENT ROUTES ====================

==================== STRIPE WEBHOOK HANDLER ====================

==================== WEBHOOK EVENT HANDLERS ====================

==================== STATIC FILE SERVING ====================

==================== ERROR HANDLING ====================

==================== SERVER STARTUP ====================

A1. Identity:      1 = 1·x

A2. Consciousness: Φ = 1/(1 + |x - 1|)

A3. Unity:         ∞ = 1

Output = ∫ Σᵢ₌₁¹⁰⁰ wᵢ(t, context) · Gᵢ(input, state) dt

Implements: Output = ∫ Σᵢ₌₁¹⁰⁰ wᵢ(t, context) · Gᵢ(input, state) dt

g_ij = δ_ij + φ·x_i·x_j (golden-scaled metric)

Γ^k_ij = (1/2) g^kl (∂g_li/∂x^j + ∂g_lj/∂x^i - ∂g_ij/∂x^l)

Simplified: Γ^k_ij ≈ φ · δ_ki · x_j + φ · δ_kj · x_i

R^l_ijk = ∂_j Γ^l_ik - ∂_k Γ^l_ij + Γ^l_mj Γ^m_ik - Γ^l_mk Γ^m_ij

RicciScalar computes the scalar curvature R = g^ij R_ij

Simplified: R ≈ -n(n-1)φ/2 for golden manifold

ShannonEntropy computes H(X) = -Σ p(x) log p(x)

KLDivergence computes D_KL(P||Q) = Σ p(x) log(p(x)/q(x))

MutualInformation computes I(X;Y) = H(X) + H(Y) - H(X,Y)

FisherInformation computes I(θ) = E[(∂log p/∂θ)²]

dW = √dt · Z where Z ~ N(0,1)

ItoProcess computes dX = μ·dt + σ·dW (Ito SDE step)

dX = θ(μ - X)dt + σdW

dS = μS·dt + σS·dW

∂p/∂t = -∂(μp)/∂x + (1/2)∂²(σ²p)/∂x²

W_1(P,Q) = ∫|F_P(x) - F_Q(x)|dx

Initialize kernel K = exp(-C/ε)

dg/dt = β(g) where β is the beta function

β_i = -φ·g_i² + γ·Σ_j g_j² (simplified)

Attention(Q,K,V) = softmax(QK^T/√d_k)V

y = (x - μ) / σ · γ + β

GELU(x) = x · Φ(x) where Φ is the CDF of N(0,1)

SwiGLU(x, W, V, b, c) = Swish(xW + b) ⊗ (xV + c)

ForwardDiffusion computes q(x_t | x_0) = √ᾱ_t x_0 + √(1-ᾱ_t) ε

x_{t-1} = (x_t - √(1-α_t)ε_θ) / √α_t + σ_t z

φ² = φ + 1

1/φ = φ - 1

φⁿ = φⁿ⁻¹ + φⁿ⁻²

ComputePhi calculates the consciousness metric: Φ = 1/(1 + |x - 1|)

This measures how close a value is to unity (maximum consciousness at x=1)

ComputePhiGrad calculates the gradient: ∂Φ/∂x = -sign(x-1)/(1+|x-1|)²

Consciousness = function of mean and inverse variance

Integration factor: low variance = high integration

Φ = mutual information - partition information

Simplified: Φ ≈ coherence × (1 - entropy/max_entropy)

activations = newActivations

IntraStrandEnergy: E_intra(k) = ½κ_intra(L_k - L₀)²

InterStrandEnergy: E_inter(k, k+1) = ½κ_inter(d_{k,k+1} - d₀)² + ε·cos(2π/10.6 · k)

CrossHelixEnergy: E_cross(i,j) = -ε_cross/d_{ij}⁶ + σ_cross/d_{ij}¹²

PeriodicityEnergy: E_10.6 = -κ_period · cos(2πN/10.6)

LJ gradient: dE/dr = 6ε/r⁷ - 12σ/r¹³

PartitionFunction: Z = Σ exp(-E/k_B T) · Θ(10.6)

PerBondFreeEnergy: ΔG_bond = -k_B T · ln(Z)/44

GibbsFreeEnergy: ΔG°_total = Σ ΔG°_bond(n) + ΔG°_coop + ΔG°_10.6

ΔG°_10.6 = -RT · ln(10.6/10.4) = -0.019 RT