Golden-frequency sine–cosine feature

Read the equation

The diagram defines a feature as the sum of sine and cosine at the same golden-scaled phase. The cosine continuation was on the next diagram line and is included here. This gives one deterministic scalar feature per index k; its periodic and finite-precision behavior does not provide lossless storage of arbitrary content.

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

1. Read ψ_k(x) as the quantity being defined or updated by this relation.

2. Evaluates oscillatory sine or cosine terms using the stated phase or frequency.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

GOLDEN RATIO φ
1.618033988749895

ψ_k(x) = sin(2πφ^k·x)
+ cos(2πφ^k·x)

MATHEMATICAL CORE
Learning:  θ_k += α·w·ψ_k(hash(item))·Φ(importance)
Query:     K = Σ θ_k·ψ_k(hash(query))
Coherence: C_ij = θ_i·θ_j / (||θ_i||·||θ_j||)

ψ_k(x) = sin(2πφ^k·x) + cos(2πφ^k·x)

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