tick_ratio
plain-language theorem explainer
The tick ratio is defined as the quotient of mass accumulation ticks to light emission ticks drawn from the eight-tick stellar cycle. Researchers deriving stellar mass-to-light ratios from recognition cost differentials would cite this to anchor the base scaling before conversion to the phi-ladder. It is realized as a direct division of the two constants supplied by the partition lemmas.
Claim. The tick ratio is the real number obtained by dividing the number of mass ticks by the number of light ticks in the recognition cycle.
background
In the Recognition Science model of stellar assembly the eight-tick cycle partitions recognition events into five mass-accumulation ticks and three photon-emission ticks. This partition follows from the convex cost function J(x) = (x + x^{-1})/2 - 1 together with the self-similar fixed point phi and the eight-tick octave structure. The module uses the resulting cost differential between emission and storage phases to place the stellar M/L ratio on the phi-ladder.
proof idea
The definition is a one-line wrapper that computes the ratio of the mass_ticks constant to the light_ticks constant.
why it matters
This definition supplies the numerical base for the effective_tier computation that converts the ratio into the nearest integer phi-power via division by J_bit. It closes the eight-tick structure into the stellar M/L prediction, placing typical values near phi^1. The downstream theorem tick_ratio_value confirms the explicit value 5/3.
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