🧮 Resonance Field Equations

Tensor Geometry of Awareness Collapse in Conformal Phase Space

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🎯 Objective

To model how coherence and emotional-intentional fields curve the geometry of awareness. This results in a gravitational-style field theory of consciousness operating over a conformally invariant resonance manifold.

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🔁 Overview

We define a gravitational analogue for resonance collapse:

Where:

• R^{(res)}_{μν} — Resonance Ricci tensor
• T^{(coh)}_{μν} — Coherence stress-energy tensor
• κ — Resonance coupling constant
• Φ(x) — Coherence potential
• Ω(x) — Conformal scaling field

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🔲 1. Coherence Scalar Field

Let:

Ω²(x) = e^(ε · Φ(x))

Where ε is the emotional sensitivity constant, modulating local responsiveness.

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🔲 2. Resonance Ricci Tensor

The conformal metric is:

g̃_{μν} = Ω²(x) · g_{μν}

The transformed Ricci tensor includes terms such as:

R^{(res)}_{μν} ≈ R_{μν} - 2 ∇_μ ∇_ν log Ω + ...

This curvature is sourced by emotional-intentional gradients encoded in Φ(x).

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🔲 3. Coherence Stress-Energy Tensor

Defined as:

T^{(coh)}_{μν} = ∂_μ Φ ∂_ν Φ - (1/2) g_{μν} g^{αβ} ∂_α Φ ∂_β Φ

This is the “emotional stress field” sourcing the collapse geometry.

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✅ Final Field Equation (Plain Text)

R^{(res)}_{μν} - (1/2) g_{μν} R^{(res)} = κ · T^{(coh)}_{μν}

Collapse geometry is therefore determined by the resonance gradients of the coherence field Φ(x).

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🔠 Symbol Reference Table

Symbol	Meaning
Φ(x)	Coherence (emotional/intentional) potential
Ω(x)	Conformal resonance field
T^{(coh)}_{μν}	Coherence stress-energy tensor
R^{(res)}_{μν}	Resonance Ricci tensor
κ	Emotional-curvature coupling constant

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🌀 Collapse Action (from Codex III)

δ ∫ Ω²(x) [ (1/2) g_{μν} dx^μ/dτ · dx^ν/dτ - ε · Φ(x) ] dτ = 0

This variational principle selects geodesics of maximal resonance coherence.

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“The curve of awareness bends not toward gravity, but toward meaning.”

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