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

Toto Auswahlwette6/45 + 1/45 era · since Sep 2024105 draws

Pool by residue: 22 · 23
Displayed χ²: 3.13
Displayed raw p: 0.680
All-moduli p: 1.000

[3, 3]32 / 35.2

[2, 4]30 / 26.4

[4, 2]25 / 23.9

[1, 5]10 / 9.5

[5, 1]8 / 7.8

[0, 6]0 / 1.3

[6, 0]0 / 1.0

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.