ExtendedObject
plain-language theorem explainer
ExtendedObject supplies a minimal model of a finite-size body whose center of mass sits at a real coordinate and whose spatial size is strictly positive. Workers deriving acoustic or phase levitation from Recognition Science first principles cite this structure whenever they need to track how an object samples a gravitational or external phase gradient. The declaration is a plain structure definition whose three fields are introduced without further computation or proof.
Claim. An extended object is given by a center-of-mass coordinate $h_{cm}inmathbb{R}$, a positive real extent $e>0$.
background
Position is the abbreviation for the real line, used throughout the module to locate both the object and the evaluation points of gravitational and phase fields. The surrounding module CoherenceFall develops the linear approximation to total potential in an accelerating frame, Φ_tot(z)≈Φ_grav(h_cm+z)+a·z, and introduces coherence-defect quantities that depend on the object’s location and size. The upstream dependency on UniversalForcingSelfReference.for records only that the meta-realization axioms are available; it does not alter the local gravitational definitions.
proof idea
Structure definition with three fields: center-of-mass position, extent, and the positivity constraint extent>0.
why it matters
Every levitation theorem in AcousticPhaseLevitation (acoustic_levitation, complete_cancellation_is_levitation, anti_coherence_reduces_coupling, etc.) takes an ExtendedObject as an explicit argument. The structure therefore supplies the concrete position and extent data required to evaluate modified coherence defects and effective gravitational couplings. It closes the gap between the abstract Recognition Composition Law and the concrete frame-dependent calculations that produce the levitation statements.
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