029_D4.1_Kolmogorov-Complexity

D4.1 — Kolmogorov Complexity

Chain Position: 29 of 188

Assumes

• [Information Theory](./028_A4.2_Algorithmic-Depth]]

Formal Statement

** Kolmogorov Complexity K(x) ≡ length of shortest program generating x.

Enables

• 030_D4.2_Compression-Ratio

Defeat Conditions

• Demonstrate that “Kolmogorov Complexity K(x) = shortest program length” is false, inconsistent, or inapplicable to the claimed domain.
• Reject one of the upstream assumptions (028_A4.2_Algorithmic-Depth) to collapse this axiom.

Standard Objections

• Objection: “Kolmogorov Complexity K(x) = shortest program length” is just a re-labeling of the status quo without new grounding.
• Response: Each dependency 028_A4.2_Algorithmic-Depth is already defended, so rejecting them would collapse the shared foundation.

Defense Summary

• Kolmogorov Complexity K(x) = shortest program length
• Built on: 028_A4.2_Algorithmic-Depth.
• Enables: 030_D4.2_Compression-Ratio.

Collapse Analysis

• Breaks downstream: 030_D4.2_Compression-Ratio

Source Material

• 01_Axioms/_sources/Theophysics_Axiom_Spine_Master.xlsx (sheets explained in dump)
• 01_Axioms/AXIOM_AGGREGATION_DUMP.md

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Quick Navigation

Category: [[_WORKING_PAPERS/Information_Theory/.md)

Depends On:

• [Information Theory](./028_A4.2_Algorithmic-Depth]]

Enables:

• 030_D4.2_Compression-Ratio

Related Categories:

• [Information_Theory/.md)

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