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IndisputableMonolith.Physics.QuantumOpticsFromRS

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This module defines quantum optical states in Recognition Science by tying them to the J-cost function from the Cost module. It introduces coherent states as the classical light limit where J equals zero and supplies related predicates and certificates. The module is purely definitional and builds directly on the imported Cost structures to extend RS into optics.

claimThe module introduces the type $QuantumOpticalState$ together with the predicate $coherent_state$ satisfying $J=0$ (classical limit), the predicate $nonclassical_state$, the count function $quantumOpticalCount$, and the certificate $QuantumOpticsCert$.

background

Recognition Science starts from a single functional equation whose J-cost is defined in the upstream Cost module as $J(x)=(x+x^{-1})/2-1$. The present module applies that cost to optical states, marking the classical limit by the condition $J=0$. It imports Mathlib for basic type theory and Cost for the J function, then declares the sibling objects QuantumOpticalState, coherent_state, nonclassical_state, quantumOpticalCount, QuantumOpticsCert and quantumOpticsCert.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The module supplies the quantum-optics layer that later physics derivations in the Recognition framework can cite for the classical-light boundary. It directly encodes the DOC_COMMENT statement that coherent states realize the J=0 limit and therefore sits ready to feed parent results on optical phenomena derived from the T0-T8 forcing chain.

scope and limits

depends on (1)

Lean names referenced from this declaration's body.

declarations in this module (6)