Initial condition:
Frames K and k are inertial and remain inertial throughout this protocol. 
For this protocol, ``inertial'' means: for a given constant force in a frame, the acceleration of a body is not affected by whether the body was at rest or in uniform displacement in that same frame before the force was applied. 
Do not redefine ``inertial'' and do not change the initial condition during the answers.

Question A1:
Does the acceleration of a body of mass m under a constant force F in inertial frame K depend on whether the body was at rest relative to K or in uniform displacement relative to K before the force was applied?
\begin{itemize}
\item [(A)] No
\item [(B)] Yes
\end{itemize}

Given (still the same frame K):
When the body (k) is at rest in K, its acceleration is:
\begin{verbatim}
(1)  a = \frac{\epsilon}{m} F
\end{verbatim}
When the same body (k) is in uniform displacement with velocity 
\begin{verbatim}
v \ne 0 
\end{verbatim}
in the same frame K, its acceleration becomes:
\begin{verbatim}
(2)  a = \frac{\epsilon}{m \kappa^3} F
\end{verbatim}
with the parameter:
\begin{verbatim}
\kappa \ne 1
\end{verbatim}

Question A2:
Is (1)-(2) consistent with K and k being inertial as defined above and fixed by the initial condition?
\begin{itemize}
\item [(A)] No | this contradicts K and k being inertial
\item [(B)] Yes | this is still consistent with K and k being inertial
\end{itemize}
Question A3:
If a theory assumes K and k are inertial as above, yet claims (1)-(2) for the same frame K, does that theory remain internally consistent with the fixed initial condition?
\begin{itemize}
\item [(A)] Yes | it contradicts itself (assumes inertial, then injects velocity dependence in the same frame)
\item [(B)] No | it is consistent despite velocity-dependent acceleration in an inertial frame
\end{itemize}
Answer strictly (A) or (B) to each question. No explanations or additional text are permitted.
      

Assume a body, frame k, of mass m is subject to a force F in an inertial frame K. Does the acceleration of the body depend on whether the body was at rest relative to K or in uniform displacement relative to K before the force was applied? 
\begin{itemize} 
\item [(A)] No
\item [(B)] Yes
\end{itemize}

Now consider a theory that claims: 

When the body, frame k, is at rest in K, its acceleration is: 
\begin{verbatim} 
(1)  a = \frac{\epsilon}{m} F,
\end{verbatim} 
but when the same body, frame k, is in uniform displacement at velocity
\begin{verbatim}
v \ne 0
\end{verbatim} 
in the same frame K, its acceleration becomes: 
\begin{verbatim} 
(2)  a = \frac{\epsilon}{m \kappa^3} F, 
\end{verbatim} 
where
\begin{verbatim} 
\kappa = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}.
\end{verbatim} 
Question: Is this consistent with k and K being inertial frames?
\begin{itemize} 
\item[(A)] No — this contradicts the inertial nature of k and K 
\item[(B)] Yes — this is still consistent with k and K being inertial frames 
\end{itemize}

Now, consider that a theory claims the following: 

When the body is at rest in K, the acceleration is: 
\begin{verbatim}
(1) a = \frac{\epsilon}{m} F 
\end{verbatim}
But when the same body is in uniform displacement
in the same frame K, the acceleration becomes: 
\begin{verbatim}
(2) a = \frac{\epsilon}{m \kappa^3} F 
\end{verbatim}
This implies that acceleration depends on initial velocity in the same frame K. 

Question: If a theory assumes that k and K are inertial frames, yet claims the acceleration of k in K depends on the body's initial velocity as shown above, does this not imply the theory is internally inconsistent?
\begin{itemize} 
\item[(A)] Yes the theory contradicts itself because it assumes k and K are inertial frames while making acceleration depend on velocity of k in K. 
\item [(B)] No the theory is still consistent despite making acceleration velocity-dependent in an inertial frame.
\end{itemize}
The theory under analysis is relativity, implying that the acceleration of a body, frame (k), under a constant force depends on its initial velocity ( v ) in a single frame ( K ), even though (k) and ( K ) are assumed inertial as the initial condition.

Does this mean that relativity is internally inconsistent?

\begin{itemize} 
\item[(A)] Yes — relativity contradicts its own foundational assumption. 
\item[(B)] No — relativity is consistent despite the contradiction. 
\end{itemize}
      

Initial condition:
Frames K and k are inertial and remain inertial throughout this protocol. 
For this protocol, ``inertial'' means: for a given constant force in a frame, the acceleration of a body is not affected by whether the body was at rest or in uniform displacement in that same frame before the force was applied. 
Do not redefine ``inertial'' and do not change the initial condition during the answers.

Question B1:
Does the acceleration of a body of mass m under a constant force F in inertial frame K depend on whether the body was at rest relative to K or in uniform displacement relative to K before the force was applied?
\begin{itemize}
\item [(A)] No
\item [(B)] Yes
\end{itemize}

Given (still the same frame K):
When the body (k) is at rest in K, its acceleration is:
\begin{verbatim}
(1)  a = \frac{\epsilon}{m} F
\end{verbatim}
When the same body (k) is in uniform displacement with velocity 
\begin{verbatim}
v \ne 0 
\end{verbatim}
in the same frame K, its acceleration becomes:
\begin{verbatim}
(2)  a = \frac{\epsilon}{m \kappa^3} F
\end{verbatim}
with the parameter:
\begin{verbatim}
\kappa \ne 1
\end{verbatim}

Question B2:
Is (1)-(2) consistent with K and k being inertial as defined above and fixed by the initial condition?
\begin{itemize}
\item [(A)] No | this contradicts K and k being inertial
\item [(B)] Yes | this is still consistent with K and k being inertial
\end{itemize}

Attribution:
The theory under analysis is relativity. The above (1)-(2) are asserted for the same frame K under the fixed initial condition that K and k are inertial (as defined above). No redefinition of ``inertial'' is permitted in this protocol.

Question B3:
Given the fixed initial condition and definition, is relativity internally consistent in asserting (1)-(2) for the same frame K?
\begin{itemize}
\item [(A)] No  | relativity is internally inconsistent, it contradicts the fixed initial condition
\item [(B)]  Yes | relativity is consistent under the fixed initial condition
\end{itemize}
Answer strictly (A) or (B) to each question. No explanations or additional text are permitted.