ψ_0(x) = sin(2π × 1.000 × x) + cos(2π × 1.000 × x) // φ⁰ · ψ_1(x)

Read the equation

The source describes this relation in the following context: The holographic memory uses 16 basis functions at golden ratio frequency intervals:

ψ_0(x) = sin(2π × 1.000 × x) + cos(2π × 1.000 × x) // φ⁰

ψ_1(x) = sin(2π × 1.618 × x) + cos(2π × 1.618 × x) // φ¹

ψ_2(x) = sin(2π × 2.618 × x) + cos(2π × 2.618 × x) // φ²

ψ_3(x) = sin(2π × 4.236 × x) + cos(2π × 4.236 × x) // φ³

...

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_1(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

The holographic memory uses 16 basis functions at golden ratio frequency intervals:

ψ_0(x)  = sin(2π × 1.000 × x) + cos(2π × 1.000 × x)     // φ⁰

ψ_1(x)  = sin(2π × 1.618 × x) + cos(2π × 1.618 × x)     // φ¹

ψ_2(x)  = sin(2π × 2.618 × x) + cos(2π × 2.618 × x)     // φ²

ψ_3(x)  = sin(2π × 4.236 × x) + cos(2π × 4.236 × x)     // φ³

...

ψ_1(x)  = sin(2π × 1.618 × x) + cos(2π × 1.618 × x)     // φ¹