PhaseFieldSource
plain-language theorem explainer
PhaseFieldSource enumerates three mechanisms that generate external phase fields capable of opposing gravitational coherence defects. Researchers modeling acoustic levitation or rotating superconductor experiments cite it when classifying sources that feed the modified coherence defect equations. The declaration is a pure inductive enumeration with no attached proof obligations or computational content.
Claim. The inductive type of phase field sources consists of the constructors acoustic standing wave, rotating superconductor, and rotating magnetic array.
background
In the AcousticPhaseLevitation module the structure ExternalPhaseField carries a real-valued function psi : Position → ℝ together with its gradient defined by differentiation. This structure is used to modify the total potential and coherence defect when an external field is superposed on the gravitational field. The module imports the eight-tick phase definition (multiples of π/4) from Foundation.EightTick and the pressure form from ILG.PressureForm; these supply the phase and pressure ingredients that the external field must oppose.
proof idea
The declaration is an inductive definition that introduces exactly three constructors. No lemmas are invoked and no tactics are applied; the type is supplied directly for case analysis in downstream results.
why it matters
PhaseFieldSource supplies the source parameter for any_source_suffices, which proves that gradient cancellation yields zero modified coherence defect, and for the master certificate levitation_unconditional that packages the bridge modules. It therefore closes the classification gap between classical rotating phase sources and the unconditional levitation claim in the Recognition framework.
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