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 Plus 16/47 + 1/47 era · since Sep 2024218 draws

Pool by residue: 23 · 24
Displayed χ²: 6.81
Displayed raw p: 0.235
All-moduli p: 0.448

[3, 3]75 / 72.8

[2, 4]53 / 54.6

[4, 2]60 / 49.6

[1, 5]14 / 19.8

[5, 1]10 / 16.4

[0, 6]3 / 2.7

[6, 0]3 / 2.0

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.