Gauge Without a Slice

Question

What can be reconstructed from gauge-invariant data without choosing a global gauge slice?

What the note explains

An invariant observable has the same value on gauge-related representatives. That fact removes representative dependence from the observable; it does not establish that the chosen observables distinguish every orbit.

Example

For a closed loop, conjugation changes its holonomy matrix while leaving its trace unchanged. Ask separately whether an entire chosen family of such traces separates the configurations of interest.

What the approach gains

The approach keeps physical observables available when a global slice fails, then makes representation, descent, projection, and scale comparison explicit additional tasks.

Reading route

Start with Part I and its orbit-factorization statements. Then use the theorem-status ledger to distinguish proved implications, imported results, and conditions on later reconstruction stages.

Scope and limits

Preserve the source's reconstructed-text provenance. Gauge invariance alone supplies neither orbit separation nor all analytic hypotheses needed for a physical continuum theory.