Data & measurement
Shining metrics emphasize reach, prestige, digital adoption, and economic visibility. Pair usage counts with denominators that reflect realistic audience size. Write explicit operational definitions for each symbol in your protocol, even when abbreviations look standard. Log instrument versions, sample frames, and cleaning rules whenever estimates are refreshed so longitudinal comparisons stay valid.
Solution & proof
Conceptual summary: Rate of language domain expansion. Treat this as a measurement recipe: map each symbol to an empirical quantity, substitute estimates, and simplify with ordinary algebra (including logarithms, min/max caps, or piecewise branches where shown). Where limits or integrals appear, approximate with discrete sums on cohorts or time steps when closed forms are impractical. Interpret the result against thresholds in the cited source and report uncertainty on inputs.
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Open the playground to test sample values, review worked scenarios, and explore how this formula behaves across multiple cases.
Source & tags
Source
ALL_FORMULAS.md — Shining