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

Lottario Early Bird4/45 era · since Sep 2024105 draws

Pool by residue: 22 · 23
Displayed χ²: 6.46
Displayed raw p: 0.167
All-moduli p: 1.000

[2, 2]44 / 41.2

[1, 3]20 / 27.5

[3, 1]23 / 25.0

[0, 4]9 / 6.2

[4, 0]9 / 5.2

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.