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

SuperCash!6/39 era · since Apr 20106,028 draws

Pool by residue: 19 · 20
Displayed χ²: 2.49
Displayed raw p: 0.869
All-moduli p: 1.000

[3, 3]2046 / 2041.0

[2, 4]1538 / 1530.7

[4, 2]1336 / 1360.6

[1, 5]559 / 544.3

[5, 1]421 / 429.7

[0, 6]81 / 71.6

[6, 0]47 / 50.1

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.