Visible charge walks through cancellation and sign reversal. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The checked row reaches finite cancellation

The diagram pins a six coulomb source and a negative six coulomb response. The visible ledger is zero before any boundary claim is made.

6 C+(6 C)=0 C6\ \text{C}+(-6\ \text{C})=0\ \text{C}
Shielding boundary sourceSource, response, and visible charge are checked.sourcefieldsource=6 Cresponse=-6 Cvisible=0 Cscale2=12 m^2density=3lambda2=4 m^2

More negative response walks through the boundary

The source stays fixed. The response column moves from partial shielding to cancellation and then to a sign flip.

QsQrQvisible642660682\begin{array}{c|c|c}Q_s&Q_r&Q_{\text{visible}}\\6&-4&2\\6&-6&0\\6&-8&-2\\\end{array}
Visible charge boundary scanThe middle row is the checked source diagram.sourcefieldsource=6 Cresponse=-6 Cvisible=0 Cscale2=12 m^2density=3lambda2=4 m^2

Past zero, visible charge reverses sign

The last row is not a new particle model. It is the signed finite budget showing that over-response changes the sign of the outside ledger.

Qr<QsQvisible<0\begin{array}{c}Q_r<-Q_s\\Q_{\text{visible}}<0\end{array}
Over-shielding sign boundaryThe checked zero row marks the sign boundary.sourcefieldsource=6 Cresponse=-6 Cvisible=0 Cscale2=12 m^2density=3lambda2=4 m^2