localCacheStatus
plain-language theorem explainer
localCacheStatus defines a string constant reporting Lean verification status for theorems on phi-optimal caching hierarchies and working memory capacity. Researchers citing the Inevitability of Local Minds paper would reference it to confirm machine-checked results on cost reduction and Fibonacci forcing of phi. The definition is a direct string concatenation with no lemmas or tactics applied.
Claim. A constant string reporting verification status for results on J-cost minimization in cache hierarchies, Fibonacci recurrences forcing the golden ratio, and the bound $4 < phi^3 < 5$.
background
The module presents the Local Cache Theorem and phi-Optimal Hierarchy as the machine-verified core of the Inevitability of Local Minds paper. It introduces working_memory_capacity as phi cubed, giving Level 1 capacity relative to focal attention at Level 0. Upstream lemmas include Jcost_eq_sq expressing J(x) as (x-1) squared over 2x, and Jcost_pos_of_ne_one establishing positivity for x not equal to 1.
proof idea
This is a definition that constructs the status string by direct concatenation of fixed text lines. No lemmas from the depends_on list are invoked; the body is a literal string with an #eval command at the end.
why it matters
The declaration supplies a readable status summary for the local cache results that form the core of the Inevitability of Local Minds paper. It lists proved items including local_cache_benefit and working_memory_approx, which rest on the Recognition Composition Law and the forcing of phi as self-similar fixed point. No downstream theorems are recorded.
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