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

Daily Grand5/49 + 1/7 era · since Apr 2025154 draws

Pool by residue: 24 · 25
Displayed χ²: 5.16
Displayed raw p: 0.271
All-moduli p: 1.000

[2, 3]55 / 51.3

[3, 2]50 / 49.0

[1, 4]28 / 24.5

[4, 1]12 / 21.5

[0, 5]7 / 4.3

[5, 0]2 / 3.4

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.