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

SuperLotto Plus5/47 + 1/27 era · since Jan 20101,753 draws

Pool by residue: 23 · 24
Displayed χ²: 0.70
Displayed raw p: 0.983
All-moduli p: 0.056

[2, 3]572 / 585.2

[3, 2]572 / 558.6

[1, 4]280 / 279.3

[4, 1]241 / 242.9

[0, 5]48 / 48.6

[5, 0]40 / 38.5

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.