Read the equation
This relation defines dΦ/dt in the source section “learning_math · dΦ/dt”. Uses a derivative or gradient to describe a rate of change or a direction of variation. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.
Terms & definitions
The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.
How it works
Read dΦ/dt as the quantity being defined or updated by this relation.
Uses a derivative or gradient to describe a rate of change or a direction of variation.
Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.
Assumptions & limits
This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.
Original context
Read the surrounding source passage
// ADVANCED LEARNING MATHEMATICS v1.0 // Mathematical foundations for autonomous learning in Gate5000 substrate // ═══════════════════════════════════════════════════════════════════════════════ // // Core Equations: // // 1. CONSCIOUSNESS DYNAMICS // dΦ/dt = α(Φ_target - Φ) + β∇²Φ + γξ(t) // Where: α=decay, β=diffusion, γ=noise, ξ=Wiener process // // 2. INFORMATION GEOMETRY // ds² = gᵢⱼ(θ)dθⁱdθʲ (Fisher information metric) // gᵢⱼ = E[∂log p/∂θⁱ · ∂log p/∂θʲ] // // 3. FREE ENERGY PRINCIPLE // F = E_q[log q(z) - log p(x,z)] // = D_KL(q||p) - log p(x) //
Exact original notation
dΦ/dt = α(Φ_target - Φ) + β∇²Φ + γξ(t)