A Structural Study of the 4π Patch: of the four claims about the Yamagishi patch, two have been overtaken by their own author. Second edition.

Is 6 pi really 4 pi plus 2 pi? The same number, and the supports do not meet.

The pi in Stokes’ 6 pi is a solid angle – the 6 does not cross dimensions.

The Wigner angle is an area – velocities do not add plainly because the place they live in is curved.

The pi that carries no dimension – the pi on Ramanujan’s page did not come from a circle.

We measured the curvature – of which manifold? Gauss’s triangle saw the ground.

Unsolvable has three distinct roots – the separator is which tools were allowed.

The one-way speed of light cannot be measured – the convention of simultaneity, and its fence.

Making the curvature constant does not fix the density – what Yamabe’s theorem can and cannot do to the component light leaves behind.

Three ceilings over one inequality – and no two are held down by the same thing.