Residue Kaleidoscope

Turn the dial freely. The verdict remembers every turn.

Every draw becomes a colour recipe. You may inspect moduli 2 through 10; the omnibus reading corrects the smallest p-value across that whole menu.

Compositions modulo 2

Georgia FIVE5/9 era · since Apr 20123,789 draws

Pool by residue: 5 · 5
Displayed χ²: 1833.52
Displayed raw p: < 0.001
All-moduli p: < 0.001

[2, 3]1170 / 1503.6

[3, 2]1184 / 1503.6

[1, 4]574 / 375.9

[4, 1]626 / 375.9

[0, 5]131 / 15.0

[5, 0]104 / 15.0

Finite-pool compositions + family correctionresidue-suite-v1exact cells; pooled χ²; Bonferroni over moduli 2–10

The maths, in plain language

A finite-pool colour recipe

If residue $r$ owns $n_r$ balls and a draw contains $c_r$ of them,

$P (c_{0}, \dots, c_{m - 1}) = \frac{\prod_{r} (\binom{n_{r}}{_{}}}{}$

The story behind it

The pattern a partition creates

Modular patterns feel structural because they repeat visually. But a partition creates its own shapes before a draw happens. The kaleidoscope separates those lawful shapes from deviations in the history.