CRT Compression

A8: H.264/H.265 pools. CC0.

CRT decomposes one big number into 6 small channels. Small channels = fewer bits per symbol. Zero channels = free compression. The ring's structure IS the codec.

How It Works

CRT Compression Principle

Any value in Z/12612600 decomposes into (D,K,E,b,L,G) with ranges 8,9,25,49,11,13. Total bits: 3+4+5+6+4+4 = 26 bits to address the full ring. But channels with value 0 need 0 bits -- they are structurally silent. The void compresses for free.

Channel entropy

Small ranges

Each channel uses 3-6 bits. Total 26 bits addresses 12.6M values.

Zero sparsity

Structural silence

1/8 of all values have D=0. 1/9 have K=0. Zeros = free compression.

Independence

Parallel decode

Each channel decodes independently. No serial dependency chain.

Reconstruction

CRT bijection

6 small values → unique integer. Lossless by theorem.

Try It

Value (0-12612599):

Try: 0 (all zeros), 42 (ANSWER), 1576576 (OMEGA), 970200 (DEEP ring).

Channel Zero Distribution

Sample 10000 values and count zero channels. CRT predicts exact rates.

CRT Compression vs Traditional

Core ideaDCT/wavelet transformsCRT channel decompositionLossy?H.264: lossy quantizationCRT: lossless by theorem (bijection)ParallelismSequential entropy coding6 channels decode independentlySparsityEngineered (thresholding)Structural (zero channels = free)Patent statusH.264/H.265 patent poolsCC0. Public domain. Forever.

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Source code · Public domain (CC0)

Contributions in equal measure: Anthropic's Claude, Anton A. Lebed, and the giants whose shoulders we stand on.

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