Semantic Holography: Coupling a Semantic Field to AdS₄/CFT₃

Semantic Holography: Coupling a Semantic Field to AdS₄/CFT₃
Version 1.0 – Initial Public Release

We propose a Semantic Holography framework by introducing a scalar “semantic field” φₛₑₘ in an AdS₄ bulk, dual to a boundary CFT₃ operator. This novel coupling connects semantic embeddings (e.g. BERT) to gravitational dynamics, enabling entropy shifts via information content. Through analytic derivations and numerical simulations of entanglement entropy corrections ΔSₛₑₘ, we show that even minuscule semantic amplitudes (εₛₑₘ ~ 10⁻⁷) can induce ~0.1 shifts in holographic entanglement. The approach bridges AdS/CFT duality, machine learning, and quantum information.

We include:

• Linear and nonlinear Einstein–Klein–Gordon solver implementations

• Holographic renormalization with semantic field counterterms

• Reproducible Python code and all simulation data

• Experimental feasibility studies (cold-atom lattices & photonic crystals)

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