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

Québec Max7/52 era · since Apr 202644 draws

Pool by residue: 26 · 26
Displayed χ²: 3.64
Displayed raw p: 0.457
All-moduli p: 1.000

[3, 4]10 / 12.8

[4, 3]15 / 12.8

[2, 5]10 / 7.0

[5, 2]4 / 7.0

[1, 6]3 / 2.0

[6, 1]1 / 2.0

[0, 7]1 / 0.2

[7, 0]0 / 0.2

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.