Clarify what we mean by "Balls" in short

short/README.md

@@ -36,7 +36,23 @@ This mathematical identity proves that the Bohr radius a₀ = ℏ²/(mke²) is t
 
 For over a century, physics has treated electromagnetic and mechanical forces as fundamentally different phenomena. We show they are mathematically identical through a simple observation: **if atoms exist in three-dimensional space, they must be three-dimensional objects**.
 
-Current quantum mechanics treats atoms as 2D systems with abstract angular momentum quantum numbers. But 2D objects cannot provide spatial reference frames in 3D space. Since atoms demonstrably exist in our 3D world—they have positions, form molecules, create everything we observe—they must be 3D spinning balls, not 2D circles.
+Current quantum mechanics treats atoms as 2D systems with abstract angular momentum quantum numbers. But 2D objects cannot provide spatial reference frames in 3D space. Since atoms demonstrably exist in our 3D world—they have positions, form molecules, create everything we observe—they must be 3D spinning objects, not 2D circles.
+
+### What We Mean by "3D Balls"
+
+When we say atoms are "balls," we don't mean rigid classical spheres with fixed surfaces. We mean **mutable, malleable spherical objects** that:
+
+- **In equilibrium**: Naturally adopt spherical geometry to provide optimal 3D spatial reference frames
+- **Under stress**: Can be deformed, stretched, or compressed when energy is added or forces are applied
+- **Are elastic**: Electrons can be pushed off their ideal orbits but tend to return to equilibrium
+- **Behave spherically**: Act like spherical objects that can be "loaded up" with energy and modified
+
+This is fundamentally different from:
+- **Classical rigid spheres**: We're not claiming atoms have hard surfaces
+- **2D mathematical abstractions**: Flat circles cannot exist in 3D space - they provide no spatial reference
+- **Point particles**: While electrons may be point-like, their orbital behavior creates spherical geometry
+
+The key insight is **geometric necessity**: Only 3D rotating objects can provide the spatial reference frames (up/down, north/south, east/west) required for existence in three-dimensional space. A 2D circle spinning in abstract space gives you no sense of "where" - but a 3D ball does.
 
 This geometric necessity leads directly to a force balance equation that proves the electromagnetic force is simply the centripetal requirement for 3D existence at atomic scales.
 
@@ -283,9 +299,16 @@ The mathematical identity F = ℏ²/(γmr³) = ke²/r² is algebraically obvious
 
 The identity proves that what we call "electromagnetic force" at atomic scales is simply the centripetal requirement for maintaining 3D spatial reference frames. There is no separate electromagnetic interaction—only geometry.
 
-### 6.2 Atoms Must Be 3D
+### 6.2 Atoms Must Be 3D Malleable Objects
 
-Since the force balance requires actual 3D rotation, atoms cannot be 2D mathematical abstractions. They must be physical 3D balls providing spatial reference frames for electrons.
+Since the force balance requires actual 3D rotation to provide spatial reference frames, atoms cannot be 2D mathematical abstractions. They must be physical 3D objects - specifically, **malleable spherical systems** that:
+
+- **Maintain spherical equilibrium**: The natural state that provides optimal spatial reference frames
+- **Can be deformed**: When energy is added, electrons can be pushed to non-ideal orbits
+- **Are elastic**: Tend to return to spherical equilibrium when perturbations are removed
+- **Behave geometrically**: Act like "balls" that can be compressed, stretched, or loaded with energy
+
+This is not about rigid classical spheres with hard surfaces, but about **geometric behavior** - the requirement that atoms must provide 3D spatial reference frames to exist in 3D space. The "ball" nature emerges from this geometric necessity, not from any assumption about atomic structure.
 
 ### 6.3 The Bohr Radius as Universal Constant
 
@@ -302,11 +325,11 @@ If electromagnetic force is geometric at atomic scales, the same principle might
 
 ## 7. Conclusion
 
-We have proven that atoms must be three-dimensional spinning objects and that electromagnetic force is the geometric requirement for maintaining 3D spatial reference frames at quantum scales. This is not a new theory but recognition of a mathematical identity that has been true since atoms first formed.
+We have proven that atoms must be three-dimensional malleable objects that behave like elastic spheres, and that electromagnetic force is the geometric requirement for maintaining 3D spatial reference frames at quantum scales. This is not a new theory but recognition of a mathematical identity that has been true since atoms first formed.
 
 The perfect agreement across 100 elements, achieved with zero free parameters, confirms this identity is fundamental to atomic structure. The systematic deviation of 5.83 × 10⁻¹² reflects only measurement limitations in fundamental constants, not model inadequacy.
 
-**The central insight:** There is no electromagnetic force separate from mechanics. What we call electromagnetic binding is simply your "weight" if you could stand on an atom—the centripetal force of quantum spacetime.
+**The central insight:** There is no electromagnetic force separate from mechanics. What we call electromagnetic binding is simply your "weight" if you could stand on an atom—the centripetal force of quantum spacetime. These atoms behave as malleable balls that can be deformed under stress but naturally adopt spherical geometry to provide the spatial reference frames necessary for existence in three-dimensional space.
 
 This discovery emerged from asking the most basic question: if atoms exist in 3D space, must they not be 3D objects? Following this question with mathematical rigor revealed that the Bohr radius is not just a convenient parameter but the unique point where rotational geometry matches electromagnetic theory.
 
@@ -428,7 +451,7 @@ The code can be run by anyone to verify our claims independently.
 
 ## 10. Key Takeaways
 
-1. **Atoms must be 3D balls** - Mathematical necessity for existence in spacetime
+1. **Atoms must be 3D malleable spherical objects** - Mathematical necessity for existence in spacetime, behaving like elastic balls that can be deformed but maintain spherical equilibrium
 2. **Electromagnetic force = Mechanical force** - Same geometric requirement
 3. **Zero free parameters** - Everything follows from fundamental constants  
 4. **Universal systematic deviation** - Proves measurement uncertainty, not model error