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

Big Sky Bonus4/31 + 1/16 era · since Oct 2024734 draws

Pool by residue: 15 · 16
Displayed χ²: 1.76
Displayed raw p: 0.780
All-moduli p: 1.000

[2, 2]293 / 293.9

[1, 3]185 / 196.0

[3, 1]177 / 169.8

[0, 4]42 / 42.5

[4, 0]37 / 31.8

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.