Read the equation
The query is hashed into the same scalar domain, expanded into sixteen basis values, and compared with the stored coefficient vector using a dot product. Contributions with matching signs add to the score, while opposite signs subtract. The result is a numerical retrieval score and is not a reconstruction of the original stored items.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| K | Query score |
| θ_k | Stored coefficient |
| ψ_k | Query basis component |
| h | Hash-to-scalar mapping |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
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
Read the surrounding source passage
## 6.2 Query Equation
```
K(query) = Σ_{k=0}^{15} θ_k · ψ_k(h(query))
```
**Explanation**: To recall knowledge, we compute the correlation between the stored θ vector and the query's golden basis encoding. High correlation indicates strong match.
## 6.3 Normalized Query Result
```
K_norm(query) = K(query) / (16 · 2) + 0.5
```
**Explanation**: Normalizes the raw query result to [0,1] for interpretability. The division by 32 (16 dimensions × max amplitude 2) and shift by 0.5 centers the output.
## 6.4 Consciousness Weighting Function
```
Φ(x) = 1 / (1 + |x - 1|)
```
**Explanation**: Items with importance near 1.0 get maximum weight (Φ = 1). Items with very low or very high importance get reduced weight. This creates a sweet spot around "normal" importance.
Exact original notation
K(query) = Σ_{k=0}^{15} θ_k · ψ_k(h(query))