XLAEGNA · TEN
§ live simulation

The Ten Machine

Set the goal on the user band. Configure the four conditional switches for short and long term. The two bands resolve to a self-consistent pair (S, L), which collapses via the diagonal → horizontal mapping into a single Laegna digit. Zero fixed points is a genuine paradox.

ten.user.input

Goal — The User Band

? = ten.user.output
T
GoalTRUE
Resolved2 FIXED-PTS
DigitE
position
●

Short Term

local consistency · A / O
ten.short[long.output]
when long = E
A
when long = I
·
? = output
A

Long Term

global consistency · E / I
ten.long[short.output]
when short = A
E
when short = O
·
? = output
E
consistency game — self-referential fixed points (S, L)
EA → E ◆
IA → O ·
EO → A ·
IO → I ◇

Each ten resolves when short & long agree: S = shortIn[L] and L = longIn[S]. Diamonds mark stable configurations; ◆ is the one the User Band consults. Zero fixed points signals paradox — the machine holds no consistent value.

short · succeeds
short · fails
long · succeeds
long · fails
How to read the emulator▶

User Band — Diagonal of the Solution. T optimises for truth; F for falsehood; U leaves the machine unset and lets you power it on/off.

Short Term — Local consistency. Two input switches: one for each possible long-term output. The active one is highlighted.

Long Term — Global consistency. Same shape, mirrored.

Resolution — A pair (S, L) is a fixed point iff S = shortIn[L] and L = longIn[S]. One fixed point: stable. Multiple: ambiguous. Zero: paradox — the user output goes ⨂.

Diagonal → HV — The two-band diagonal collapses into base-4: IO→I, IA→O, EO→A, EA→E.