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

Lotto 6aus496/49 + 1/9 era · since Sep 2024218 draws

Pool by residue: 24 · 25
Displayed χ²: 9.09
Displayed raw p: 0.106
All-moduli p: 0.153

[3, 3]82 / 72.6

[2, 4]59 / 54.4

[4, 2]43 / 49.7

[1, 5]9 / 19.9

[5, 1]19 / 16.6

[0, 6]4 / 2.8

[6, 0]2 / 2.1

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.