Representation
An item is mapped through a normalized hash and 16 sine/cosine basis functions. Learning updates coefficient θ_k using the feature value, weight and importance score. Querying computes a sum of coefficient–feature products. Agent coherence is the cosine similarity of their coefficient vectors.
Historical learning-rule variants
The raw architectural diagram uses an additive coefficient update. The January specification uses a blend with (1−α) times the old coefficient. These two rules have different forgetting and accumulation behavior; both belong in the historical record.
What the representation can establish
The equations define a compact feature sketch and a similarity/query score. Sixteen coefficients cannot uniquely preserve arbitrarily many unrelated source items. The surrounding system may also keep external logs, source records or substrate addresses; those stores are distinct from the coefficient vector.
Equations in this build
19 linked mathematical records. Each opens its notation, interpretation and source.
Golden basis function ψ0
This is basis component 0 of the documented 16-dimensional memory representation. It evaluates a sine and a cosine at the same golden-ratio-scaled frequency and adds them. The…
Golden basis function ψ1
This is basis component 1 of the documented 16-dimensional memory representation. It evaluates a sine and a cosine at the same golden-ratio-scaled frequency and adds them. The…
Golden basis function ψ2
This is basis component 2 of the documented 16-dimensional memory representation. It evaluates a sine and a cosine at the same golden-ratio-scaled frequency and adds them. The…
Golden basis function ψ3
This is basis component 3 of the documented 16-dimensional memory representation. It evaluates a sine and a cosine at the same golden-ratio-scaled frequency and adds them. The…
Golden basis function ψ4
This is basis component 4 of the documented 16-dimensional memory representation. It evaluates a sine and a cosine at the same golden-ratio-scaled frequency and adds them. The…
Golden basis function ψ5
This is basis component 5 of the documented 16-dimensional memory representation. It evaluates a sine and a cosine at the same golden-ratio-scaled frequency and adds them. The…
Golden basis function ψ6
This is basis component 6 of the documented 16-dimensional memory representation. It evaluates a sine and a cosine at the same golden-ratio-scaled frequency and adds them. The…
Golden basis function ψ7
This is basis component 7 of the documented 16-dimensional memory representation. It evaluates a sine and a cosine at the same golden-ratio-scaled frequency and adds them. The…
Golden basis function ψ8
This is basis component 8 of the documented 16-dimensional memory representation. It evaluates a sine and a cosine at the same golden-ratio-scaled frequency and adds them. The…
Golden basis function ψ9
This is basis component 9 of the documented 16-dimensional memory representation. It evaluates a sine and a cosine at the same golden-ratio-scaled frequency and adds them. The…
Golden basis function ψ10
This is basis component 10 of the documented 16-dimensional memory representation. It evaluates a sine and a cosine at the same golden-ratio-scaled frequency and adds them. The…
Golden basis function ψ11
This is basis component 11 of the documented 16-dimensional memory representation. It evaluates a sine and a cosine at the same golden-ratio-scaled frequency and adds them. The…
Golden basis function ψ12
This is basis component 12 of the documented 16-dimensional memory representation. It evaluates a sine and a cosine at the same golden-ratio-scaled frequency and adds them. The…
Golden basis function ψ13
This is basis component 13 of the documented 16-dimensional memory representation. It evaluates a sine and a cosine at the same golden-ratio-scaled frequency and adds them. The…
Golden basis function ψ14
This is basis component 14 of the documented 16-dimensional memory representation. It evaluates a sine and a cosine at the same golden-ratio-scaled frequency and adds them. The…
Golden basis function ψ15
This is basis component 15 of the documented 16-dimensional memory representation. It evaluates a sine and a cosine at the same golden-ratio-scaled frequency and adds them. The…
DNA memory learning rule
Blends each old memory coefficient with a weighted basis feature of a normalized item hash. Importance is transformed by Φ before scaling the feature. The 16 coefficients form a…
DNA memory query score
Computes an inner product between stored coefficients and basis features of the query hash. This is a retrieval score in the source representation, not a reconstruction of the…
Agent-vector coherence
Computes cosine similarity between two agent knowledge vectors. It measures their directional alignment, with values from −1 to 1 when both vectors are nonzero.