coherence_defect
plain-language theorem explainer
Coherence defect quantifies potential variance across an extended object as the absolute difference of total potential evaluated at its extremities. Researchers tracing gravitational acceleration to coherence restoration cite this definition when establishing the uniqueness of the equilibrium frame. The definition is realized by direct substitution of the linearized total potential into the absolute difference operator.
Claim. Let $Φ$ be the potential function of a processing field. For an extended object with center-of-mass position $h_{cm}$ and positive extent $e$, together with frame acceleration $a$, the coherence defect is $|Φ_{tot}(e) - Φ_{tot}(-e)|$, where $Φ_{tot}(z) := Φ(h_{cm} + z) + a z$.
background
The CoherenceFall module models gravity through frame-dependent refresh rates. A ProcessingField is a structure carrying a potential function $Φ : Position → ℝ$. An ExtendedObject carries a center-of-mass position $h_{cm}$ and a positive extent. The upstream total_potential_in_frame supplies the linear approximation $Φ_{tot}(z) ≈ Φ(h_{cm} + z) + a z$ obtained by first-order Taylor expansion of the gravitational potential plus the inertial term.
proof idea
One-line definition that evaluates total_potential_in_frame at $+extent$ and $-extent$ then takes the absolute value of their difference.
why it matters
The definition supplies the left-hand side of the uniqueness claim in falling_restores_coherence, which equates the zero-defect acceleration with $-∇Φ$. It is referenced inside LevitationInevitability and ForcingChainToLevitation, which embed the coherence-seeking property of gravity into the Recognition Science chain (RCL → T5 J-uniqueness → T6 φ → T8 D = 3). The module setting treats the defect as the observable signature of non-flat potentials in accelerated frames.
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