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IndisputableMonolith.Foundation.UniversalForcing

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The module supplies the forced arithmetic object extracted from any Law-of-Logic realization. Category theorists and discrete-physics modelers cite it to obtain the initial Peano algebra guaranteed once identity and step data are supplied. The module imports the arithmetic extraction and re-exports the construction for continuous, modular, order, and natural-number realizations.

claimGiven a realization supplying identity and step data, the forced arithmetic object is the initial Peano algebra generated by that data.

background

The module imports ArithmeticOf, which extracts arithmetic from an abstract Law-of-Logic realization. The central mechanism is initiality: once a realization supplies identity and step data, the forced arithmetic object is the initial Peano algebra generated by that data. Initial objects are unique up to unique isomorphism; this supplies the mechanism behind Universal Forcing.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the common arithmetic foundation used by downstream realizations including DiscreteLogicRealization (discrete Boolean carrier) and ContinuousRealization (positive-ratio wrapper). It fills the universal-forcing step that ensures every realization yields the same initial Peano structure, with the NaturalNumberObject submodule providing the Lawvere characterization.

scope and limits

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declarations in this module (6)