localCacheStatus
plain-language theorem explainer
localCacheStatus defines a string constant that reports Lean verification status for theorems on caching cost reduction and phi-optimal hierarchies. Researchers auditing the inevitability of local minds paper would reference it to confirm machine-checked results on J-cost properties and working memory bounds. The definition is a direct string concatenation with no computation or lemmas applied.
Claim. The constant string reporting verification status of results including: caching reduces total access cost; Fibonacci ratio forces $r^2 = r + 1$; Fibonacci partition forces ratio $r = phi$; $J'(r) = (1 - r^{-2})/2$; $J' > 0$ for $r > 1$; $J(1) = 0$; $J(r) > 0$ for $r > 0$, $r ≠ 1$; $4 < phi^3 < 5$; and J-cost symmetry forces geometric boundary.
background
The module provides the machine-verified core of the inevitability of local minds paper under the Recognition Science framework. Key definitions include J-cost (recognition cost) with upstream lemma Jcost_eq_sq giving $J(x) = (x-1)^2/(2x)$ for $x ≠ 0$, and Jcost_pos_of_ne_one establishing $J(x) > 0$ for $x > 0$, $x ≠ 1$. The phi-ladder sets hierarchical capacities with working memory at phi^3 relative to focal attention at capacity 1. Local setting is the phi-optimal cache hierarchy where the recurrence $K_{ℓ+1} = K_ℓ + K_{ℓ-1}$ with constant ratio forces phi under assumptions A1-A3.
proof idea
Definition that builds the status string by direct concatenation of fixed text lines. No tactics or lemmas are invoked; the body is a literal string literal. Upstream results Jcost_eq_sq and Jcost_pos_of_ne_one are referenced only in the reported status text for the J-cost items.
why it matters
This definition summarizes the verified results that constitute the local cache theorem, feeding the module's main claims on cost reduction via caching and phi forcing from Fibonacci partitions. It aligns with framework landmarks T5 (J-uniqueness), T6 (phi fixed point), and the Recognition Composition Law by confirming J-cost positivity and symmetry in information hierarchies. No open questions are closed here; it serves as a status checkpoint for the paper's machine-verified core.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.