Manuscript VI-B@1 · VI-B-v1.tex · section · 33798723
Why this is consistent with descent
Compact switching: exact defect and plateau obstruction › Why this is consistent with descent · lines 1031–1071
The geometric transformation requires
Those terms cancel in . The plateau witness instead has
Thus the switched assignment fails to supply the scalar part of the full coefficient action. It does not disprove Theorem thm:descent.
The quantified obstruction retains all four choices: the unswitched coordinate dressing, the fixed compact switch, the full compact gauge-support class, and (eq:free-identification). Changing any of them defines another problem.
| Gauge-support class | Meaning | Status here |
|---|---|---|
| All admitted compact generators | The support need not lie in the switch plateau | Exact defect and negative witness proved |
| Generators supported where | A smaller, separately specified class | VII-A's intertwiner is a documentary comparison; its second-order construction is not incorporated |
VII-A records a classical repair for the restricted class CheungVIIA. We neither use that result as a premise nor claim its second-order intertwiner as a theorem of VI-B.
Displayed formulas in this passage
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