effective_gravitational_coupling
plain-language theorem explainer
The definition computes the magnitude of the summed gradients of the gravitational potential and an external phase field, evaluated at an extended object's center of mass. Researchers analyzing acoustic or coherence-driven modifications to gravity would cite it when quantifying weight reduction or levitation thresholds. It is realized directly as the absolute value of the sum of the two derivatives at the center-of-mass position.
Claim. For a gravitational processing field with potential function $Φ$, an external phase field with potential $ψ$, and an extended object whose center of mass lies at position $h_{cm}$, the effective gravitational coupling is defined by $|Φ'(h_{cm}) + ψ'(h_{cm})|$.
background
ProcessingField is the structure carrying the gravitational potential function $Φ : Position → ℝ$. ExternalPhaseField is the structure carrying an external potential $ψ : Position → ℝ$ that represents acoustic standing waves or phase-locked mechanisms altering the local processing environment. ExtendedObject is the structure supplying the center-of-mass coordinate $h_{cm}$ together with a positive spatial extent. The definition appears inside the AcousticPhaseLevitation module, which augments the coherence-fall model by allowing external fields to shift the equilibrium acceleration away from the pure gravitational gradient.
proof idea
The definition is a one-line wrapper that applies the absolute-value operator to the sum of the derivative of the gravitational potential and the derivative of the external field, both taken at the object's center-of-mass position.
why it matters
This definition supplies the central quantity used by anti_coherence_reduces_coupling, complete_cancellation_is_levitation, weight_reduction_factor, and the LevitationInevitability structure. It closes the step from coherence-seeking gravity to external-field cancellation inside the ForcingChainToLevitation, connecting the Recognition Composition Law through J-uniqueness and the eight-tick octave to observable levitation. It leaves open the quantitative threshold at which acoustic power suffices for full cancellation in laboratory settings.
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