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Proof Path TheoryReading edition

Compression, representation, and memory

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The wording and mathematics follow the retained manuscript. This reading format does not add a proof review or extend Lean coverage.

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Part III Compression, representation, and memory

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Compression changes which questions can still be answered. A certificate may preserve every required deduction while erasing distinctions that later inquiry needs.

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Two archives have the same certificate C 0 but different side records. Compression forgets that record. A single decoder receiving C 0 cannot return both answers to the side-record query. This is the collision criterion in its smallest finite form.
Figure 15. Two archives have the same certificate \(C_0\) but different side records. Compression forgets that record. A single decoder receiving \(C_0\) cannot return both answers to the side-record query. This is the collision criterion in its smallest finite form.

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The governing distinction

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A valid certificate can be sufficient for checking the present theorem and insufficient for a later question. The lost distinction, not the length of the file, determines the failure.

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Source SHA-256: ce05e88b439e9fd55ef6eb04da708a63ce02e6627424e6daac0dca4177b8ab51

Unsupported prose commands stop the build. The mathematical expression sequence is checked against the source, with manuscript macros expanded for display.

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