acoustic_levitation
plain-language theorem explainer
When an external phase field's gradient exactly opposes the gravitational gradient at an object's center of mass, the modified coherence defect vanishes at zero acceleration. Researchers deriving acoustic or phase levitation from Recognition Science first principles would cite this result. The proof is a direct term reduction that rewrites the defect expression via its simplification lemma and applies cancellation identities for addition and multiplication.
Claim. If the derivative of the external phase potential equals the negative derivative of the gravitational potential at the object's center of mass, then the combined coherence defect under both fields equals zero at zero acceleration.
background
ProcessingField supplies the gravitational potential phi. ExternalPhaseField is the structure carrying an additional phase potential psi whose gradient is defined by deriv ext.psi h. The modified coherence defect combines the two potentials into a single defect measure whose zero set determines equilibrium acceleration. Upstream arithmetic lemmas establish that n + 0 = n and n * 0 = 0 for the underlying LogicNat arithmetic used in the defect expansion.
proof idea
One-line term proof that first rewrites via the sibling simplification lemma for the modified defect, substitutes the given cancellation hypothesis, then simplifies the resulting expression with add_neg_cancel, add_zero, mul_zero, and abs_zero.
why it matters
This supplies the direct cancellation step inside LevitationInevitability and forcing_chain_complete. It closes the local argument that opposing external phase gradients produce stationary coherence (zero defect at zero acceleration) and is invoked by any_source_suffices and concrete_levitation. The result sits inside the Gravity module that assembles the RS forcing chain from coherence restoration to acoustic levitation.
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