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 Million Plus 2pm6/39 + 1/39 era · since Jul 20162,554 draws

Pool by residue: 19 · 20
Displayed χ²: 4.96
Displayed raw p: 0.549
All-moduli p: 1.000

[3, 3]864 / 864.7

[2, 4]683 / 648.6

[4, 2]545 / 576.5

[1, 5]239 / 230.6

[5, 1]170 / 182.0

[0, 6]33 / 30.3

[6, 0]20 / 21.2

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.