pith. sign in
def

flameSpeed

definition
show as:
module
IndisputableMonolith.Combustion.FlameSpeedFromPhiLadder
domain
Combustion
line
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plain-language theorem explainer

The definition sets laminar flame speed at rung k to the reference speed (unity in RS units) multiplied by phi to the power k. Combustion modelers cite it when deriving exact adjacent-rung ratios or proving positivity and monotonicity on the phi-ladder. It is a direct algebraic definition that unfolds immediately in ratio and ordering proofs.

Claim. The laminar flame speed $S_L(k)$ at integer rung $k$ equals the reference speed times $phi^k$, where the reference speed equals 1 in RS-native units and $phi$ is the golden ratio.

background

The module states that laminar flame speed $S_L$ of a premixed fuel-oxidizer mixture follows the phi-ladder structure, with each integer step in chain-branching intensity multiplying $S_L$ by exactly phi. Reference speed is defined as the RS-native dimensionless value 1. The rung index k labels discrete levels of chain-branching intensity, consistent with rung assignments in mass and spectroscopy modules.

proof idea

This is a one-line definition that sets flameSpeed k to referenceSpeed multiplied by phi raised to k. No lemmas or tactics are applied; the expression directly encodes the multiplicative phi-ladder rule.

why it matters

It supplies the core expression underlying FlameSpeedCert and the theorems flameSpeed_adjacent_ratio, flameSpeed_pos, flameSpeed_strictly_increasing, and flameSpeed_succ_ratio. The definition realizes the module claim of exact phi ratios across fuels with no fitted parameters, linking to the self-similar fixed point phi from the forcing chain. It leaves open empirical calibration of the reference within the stated tolerance.

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