Growth: places priced and compared

A growth walk builds a modulus one step at a time: at each step it multiplies in a factor that meets a fixed requirement on the ring, such as being coprime to the modulus so far or raising the exponent of its unit group, most often the least such factor, least by size over the integers and by price where a page prices its moves; some pages below choose by a rate instead, draw at a temperature, or follow every tie. These pages cover the three fates a walk's limit can have (every prime taken, some prime deepened forever, the walk halting at a finite modulus), what a walk over F₂[x] or the ring of a curve over F₂ converges to, the price list each place hands a walk, the walk whose moves must be principal, whether a walk over a number ring must lock, the walk at a temperature, what a walk's state records of its own history, the primes whose p − 1 decides what a walk can reach, the state read through the exponent of its unit group, and the set of limits a walk reaches with every tie followed.

• GROWTH — a modulus grown by the cheapest move a demand admits
• LIMIT — where one greedy walk goes
• CLOCK — what a place charges a growth walk
• ELEMENT — the walk that must stay principal
• CASCADE — whether the greedy walk over a number ring must lock
• THERMAL — the growth walks at finite temperature
• MEMORY — what a grown world can know of its genesis
• BRIDGES — where growth meets open number theory
• HEADROOM — what a probe sees of a grown state
• IMAGE — the set of limits a greedy walk reaches