Read the equation
Add sine and cosine waves at the same frequency scaled by φ^k and σ_i. The image uses a k-indexed basis function and an i-indexed scale; no relation between those indices is supplied. Other recovered MEGAMIND text omits σ_i, and the Unified AGI poster uses φ^(−k) in the cosine branch, so those are separate variants.
Its role in the build
The Megamind Equation Atlas
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 ψ_k(x) as the quantity being defined or updated by this relation.
Evaluates oscillatory sine or cosine terms using the stated phase or frequency.
Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.
Assumptions & limits
A finite set of harmonic features does not establish exact arbitrary knowledge compression. Coefficient fitting, hashing and reconstruction error must be specified and measured.
Original context
Read the surrounding source passage
The Megamind Equation Atlas: Add sine and cosine waves at the same frequency scaled by φ^k and σ_i. The image uses a k-indexed basis function and an i-indexed scale; no relation between those indices is supplied. Other recovered MEGAMIND text omits σ_i, and the Unified AGI poster uses φ^(−k) in the cosine branch, so those are separate variants.
Exact original notation
ψ_k(x) = sin(2π · φ^k · σ_i · x) + cos(2π · φ^k · σ_i · x)
Related builds
Sources & provenance
ψ_k(x) = sin(2π · φ^k · σ_i · x) + cos(2π · φ^k · σ_i · x)