The survey becomes easier to reason with once you see the three cases in one finite toy: true in-sector gauge motion, objective degeneracy across sectors, and fake symmetry caused by a coarse readout.
This page is not about new formal difficulty. It is about compressing the ontology into one mental picture you can actually carry around.
Lean anchors.
sectorLocked_preserves_weightedCharge,
transitionCurrent_zero_of_sectorLocked,
sectorLeaky_exists_nonzeroTransitionCurrent
Math statement.
In English. If an operator only reshapes payload inside one sector, weighted sector charge stays unchanged. If it truly leaks between sectors, some charge current becomes nonzero.
Physical intuition. Gauge-like motion is invisible to sector charge. Real inter-sector transport is not. And a coarse readout can still hide the difference if it refuses to look at the payload carefully enough.
The toy helps you keep three ideas separate: invisible internal reshaping, real relabeling degeneracy, and fake equivalence caused by a weak readout.
Payload changes inside one sector but charge does not. This is the clean analogue of coordinate freedom.
Different sector allocations can share the same coarse statistic or loss value.
A coarse observable declares sameness that vanishes once payload-sensitive observables are allowed.
Feynman reading: same equations, same coarse thermodynamics, and same lousy detector are three different reasons for two states to look the same. The whole survey is about not confusing them.