dedekind::sequences::IsAbsorptiveSequence Concept Reference

An eventually-constant sequence. The simplest convergent case (limit = the absorbing value); period-1-eventually dual to IsPeriodicSequence. More...

Concept definition

template<typename Seq>
concept dedekind::sequences::IsAbsorptiveSequence =  IsSequence<Seq> && is_absorptive_sequence_v<Seq>

Detailed Description

An eventually-constant sequence. The simplest convergent case (limit = the absorbing value); period-1-eventually dual to IsPeriodicSequence.

Mandelbrot connection

This concept's canonical consumer is the escape-time divergence path in :numbers::mandelbrot. orbit_divergence_path produces a monotone Path<Ternary> that is Unknown until the orbit escapes and True forever after — eventually constant, i.e. an IsAbsorptiveSequence whose absorbing value is the Kleene-True that is the absorbing element of Kleene OR. The partition's own comment names this: "True is the absorbing element of Kleene OR, so once the path reaches True it stays there."

This is where the absorptive reading earns its keep: not via :species's lattice-absorption is_absorptive_v (a looser, shared-name analogy — there is no orbit-style theorem linking the two), but via escape-time dynamics, where the eventually-constant escape indicator is genuinely an absorptive sequence.