Compression Lab

Can the sequence be said too simply?

Repeated motifs require fewer dictionary phrases. Three declared encodings ask the question from different angles, while shuffled draw order preserves the draws themselves.

LZ78 phrase complexity

Daily Million Plus 2pm6/39 + 1/39 era · since Jul 2016600 draws

Whole-lab p: 0.150
Encodings: 3
Relabellings: 199

quantised whole-draw ranks325 · pᵃ 0.150

successive overlaps152 · pᵃ 1.000

within-draw spacings1384 · pᵃ 1.000

LZ78 order-permutation testlz78-permutation-v1seed 20260827one-sided compression; Bonferroni across three encodings

Fewer observed phrases than shuffled histories means more repeated temporal structure.

The maths, in plain language

Description length as a test statistic

LZ78 reads symbols left to right and adds each first-seen phrase to a dictionary. Repeated structure tends to create fewer new phrases. The laboratory encodes chronology as quantised whole-draw ranks, consecutive-draw overlaps, and within-draw spacings.

The null shuffles complete draws, then rebuilds every encoding. For phrase count $L$ , the one-sided Monte Carlo value is

$p=\frac{1+\#\{L_{\mathrm{shuffle}}\le L_{\mathrm{observed}}\}}{R+1}.$

The story behind it

Random does not mean patternless

Short random streams repeat, alternate, cluster, and occasionally compress well. That is why “this looks designed” is not a statistic.

Compression turns the intuition into a reproducible number and compares it with histories containing the same draws in different orders. A small adjusted p-value would justify investigation of chronology; it would not identify a cause or forecast what comes next.