fixed point.md

tags	cyber, core
alias	fixed points, fixed-point, Schelling point, schelling points, focal point, focal points
icon	◎
crystal-type	pattern
crystal-domain	cyber
crystal-size	atom

a state the system maps to itself: $T(x^) = x^$. apply the rule again — nothing moves. that is the mathematical root. under a contraction ([[banach fixed-point theorem]]), every starting point is pulled to the same unique $x^*$

[[Schelling]] named the social twin: a focal point — the place minds meet without a meeting. two people lose each other in a city; they both go to the clock tower. no message, no vote — shared structure picks the rendezvous

in cyber these are the same object. the [[tri-kernel]] is $T$; its unique fixed point is collective [[focus]] $\phi^$. every node that runs the same arithmetic on the same [[cyberlinks]] lands on the same root — a mathematical Schelling point of attention. [[cyberank]] is that root per [[particle]]; [[foculus]] finality is $\phi^_i > \tau$: enough of the focal mass has gathered. the [[collective focus theorem]] is the proof that the rendezvous exists and is unique

see [[rank]], [[rational neuron]], [[tri-kernel]]

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