How can information increase in computation if output is logically implied by input?

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• Information increase in computation arises from data reduction and making implicit information explicit, not logical increase.claim0.876
  Author's proposed resolution to the information increase paradox: computation gains utility through extraction and filtering, not creation of logically new content.
• Does information increase in computation?question0.861
  Fundamental puzzle motivating the paper: how can computation produce new information when output is logically implied by input and thermodynamics suggests information cannot increase?
• information increase in computationconcept0.836
  The puzzle that computation appears to gain information despite logical closure; resolved by relative to subsystems/observers.
• Information can increase in computation only relative to subsystems and observersclaim0.834
  The author argues that while total system information is conserved (thermodynamic), computation gains information for the observer by making implicit information explicit and discarding irrelevant data.
• Information increase in computation is observer-dependent, relative to the computational direction chosen.claim0.798
  Extension of information dynamics: direction of information increase (e.g., forward multiplication vs. reverse factorization) depends on observer's goals.
• The direction of information increase is relative to the observer or user of the computationclaim0.771
  Example: 3×5→15 is a natural computation, but 15→3×5 (prime factorization) is also useful, showing that the 'gain' depends on the choice of normal form.
• Information flow and increase must be understood relative to subsystems and their interaction with environment.claim0.771
• Why do we compute? The natural answer is: to gain information (which we did not previously have)! But how is this possible?concept0.759
  Opening framing of the central puzzle driving the entire investigation into information dynamics.