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IndisputableMonolith.Foundation.OperatorCore.CoupledRecognitionCores

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The CoupledRecognitionCores module defines ququart states, basis operators, and Weyl monomials for modeling coupled recognition cores. Researchers extending the algebraic layer of Recognition Science would cite these when constructing operator algebras on the phi-ladder. The module consists entirely of definitions that import and extend the base CoupledRecognitionCores without introducing new theorems.

claimThe module introduces the 4-dimensional state space $H_4$, standard basis kets $|krangle$ for $k=0,1,2,3$, shift and phase operators $X_4,Z_4$ obeying the Weyl commutation relation, and monomial operators for tensor products of coupled cores.

background

This module sits in the Foundation domain and imports the base CoupledRecognitionCores to supply concrete operator representations. It defines QuquartState as the 4-level space used for recognition cores, basisKet as the computational basis, add4 for cyclic index arithmetic, and ququartX together with ququartZ as the generators satisfying the ququartWeyl_relation. The tensorWeylMonomial and localWeylMonomial encode multi-core products while coupledCoreIndex_card fixes the finite cardinality of the index set.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The definitions supply the concrete operator language required by downstream constructions that realize the eight-tick octave and spatial dimension D=3 within the T0-T8 forcing chain. They prepare the algebraic substrate for later theorems that apply the Recognition Composition Law to coupled systems.

scope and limits

depends on (1)

Lean names referenced from this declaration's body.

declarations in this module (14)