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

Canada Lotto 6/496/49 + 1/49 era · since Jan 20101,753 draws

Pool by residue: 24 · 25
Displayed χ²: 5.52
Displayed raw p: 0.479
All-moduli p: 0.200

[3, 3]583 / 583.6

[2, 4]428 / 437.7

[4, 2]396 / 399.6

[1, 5]169 / 159.8

[5, 1]143 / 133.2

[0, 6]25 / 22.2

[6, 0]9 / 16.9

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.