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 Poker5/13 era · since Aug 2025398 draws

Pool by residue: 6 · 7
Displayed χ²: 37.91
Displayed raw p: < 0.001
All-moduli p: < 0.001

[2, 3]144 / 162.4

[3, 2]111 / 129.9

[1, 4]82 / 64.9

[4, 1]40 / 32.5

[0, 5]13 / 6.5

[5, 0]8 / 1.9

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.