Compression and information

Compression as extracting what persists and rejecting what is entropic.

Plain

The idea

Compressing a file means removing what repeats or what does not help reconstruct the essential part. In PT language: one looks for what persists.

This is one of the best entry points into GFT: structured information is kept, noise is costly, and the total budget imposes a limit.

compression = structure + résidu

Standard

Standard reading

Efficient compression increases the usable share of structure relative to a raw representation. It does not create information; it reorganizes the budget.

PT can present compression as a concrete case of the $D_{KL}+H$ partition: structure detectable against uniformity on one side, irreducible entropy on the other.

Takeaways

Compression extracts persistence.
GFT gives the budget language.
A very good pedagogical bridge to information.

Technical

Technical formulation

The pt-compress project can serve as a laboratory: measuring entropy, redundancy, divergence from uniformity, and reconstruction cost.

The canonical mathematical point remains GFT. The performance of a particular compressor is an experimental validation matter.

GitHub repository to publish: Igrekess/pt-compress; monograph ch04_gft, ch_PM.

Formulas

$\text{raw budget}=\text{compressible structure}+\text{entropic residue}$

$\log_2(m)=D_{KL}+H$

public code

Code and scripts

The links below point to public resources or planned GitHub repositories. No local working path is exposed to the reader.

GitHub

Igrekess/pt-compress

GitHub repository to publish before this can become a download link.

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Compression and GFT

Compares a redundant string and a pseudo-random string through empirical entropy.

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