flameSpeed_succ_ratio
plain-language theorem explainer
Flame speed at rung k+1 equals flame speed at rung k multiplied by phi. Combustion theorists cite it to obtain parameter-free ratios across fuels on the integer phi-ladder. The proof is a direct algebraic reduction: unfold the power definition, apply the successor exponent rule, and normalize.
Claim. For every natural number $k$, let $S_L(k) := S_0 · ϕ^k$ where $S_0$ is the reference speed. Then $S_L(k+1) = S_L(k) · ϕ$.
background
The module treats laminar flame speed as following the phi-ladder: each integer increase in chain-branching rung multiplies speed by exactly phi. The definition states flameSpeed k equals referenceSpeed times phi raised to k. The local setting asserts that adjacent-rung ratios equal phi with no fitted parameters, as illustrated by methane-air (rung 0), ethylene-air (rung 1), and hydrogen-air (rung 2) examples whose measured ratios lie near phi and phi squared.
proof idea
The term proof unfolds the flameSpeed definition, rewrites the exponent via pow_succ, and closes by ring normalization.
why it matters
This supplies the one-step multiplier used by flameSpeed_adjacent_ratio, flameSpeed_strictly_increasing, and the FlameSpeedCert structure. It realizes the module claim that the structural prediction is exact on integer rungs and feeds the Recognition Science phi-ladder construction without adjustable constants.
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