spaced_bonus
plain-language theorem explainer
The spaced_bonus definition supplies a logarithmic increment to the learning rate for events with temporal spacing in the memory ledger. Modelers of spaced-repetition effects within Recognition Science thermodynamics cite it to quantify how interval length modulates retention strength. The definition reduces directly to the ratio of natural logs of one plus normalized spacing over the golden-ratio logarithm.
Claim. For a learning event with spacing interval $s$, the spaced bonus equals $frac{log(1 + s/8)}{log phi}$, where 8 is the fixed working memory window and $phi$ the golden ratio.
background
The Memory Ledger module treats memory as a thermodynamic system in which retention competes with free-energy decay under Recognition Science rules. A LearningEvent packages a ledger trace with bounded attention, repetition count, and spacing interval. The working memory window is defined as the constant 8, providing the normalization scale for spacing effects in the eight-tick structure.
proof idea
The definition is a direct one-line expression that applies the logarithmic spacing formula normalized by the working memory window of 8 and divided by the logarithm of phi.
why it matters
This definition feeds the learning_rate and learning_compounds theorems that establish non-negative compounding of learning under spaced repetition. It operationalizes the benefit of spacing within the eight-tick octave of the Recognition framework, linking memory retention to phi-ladder scaling.
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