working_memory_capacity
plain-language theorem explainer
The definition sets working memory capacity to the cube of the golden ratio phi, yielding the predicted Level 1 cache size of approximately 4.236 relative to unit focal attention in a phi-optimal hierarchy. Cognitive modelers applying the J-cost function to memory architecture would cite it when deriving capacity bounds from the Recognition Science cache recurrence. It is a direct abbreviation with no proof steps.
Claim. Working memory capacity is defined as $phi^3$, where $phi$ is the golden ratio fixed point, giving the capacity of Level 1 cache relative to Level 0 focal attention of capacity 1.
background
The Local Cache module develops a phi-optimal hierarchy that minimizes total access cost under assumptions A1-A3, with the partition recurrence $K_{l+1}=K_l+K_{l-1}$ forcing the constant ratio phi as established in the sibling result fibonacci_partition_forces_phi. Working memory capacity is placed at Level 1 of this hierarchy. The module supplies the machine-verified core of the Inevitability of Local Minds paper and connects to J-cost symmetry and Hebbian gradient structure via sibling definitions.
proof idea
The declaration is a direct abbreviation that sets working memory capacity equal to phi raised to the third power.
why it matters
It supplies the explicit numerical value required by the downstream theorem working_memory_approx, which bounds the capacity between 4 and 5. The definition completes one step of the Local Cache Theorem on phi-optimal caching, linking to the self-similar fixed point phi from T6 in the forcing chain. It touches the open question of mapping the phi-ladder prediction to biological memory measurements.
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