GENERIC BOUNDARY LEMMA
Let the common base R move0 to r!=0. Suppose the exceptional off-top pair
does not touch r. Immediately before an action the previous emitted card is
at0; the base moves it to r. If the action is ordinary with selected slot p,
p=r would emit the same card and cause an observed double. On a nondouble,
p!=r, so the top swap leaves the previous card at r. The exceptional action
also leaves it there because its pair avoids r. Thus after every observed
nondouble, the previous emitted card occupies the same known position r.

E4[67]=26 and W4[70]=26. The following outputs E4[68] and W4[71] differ from26,
so their incoming states before corrected actions69/72 both have card26 at r.
Under a common action word, the positional correspondence between the two
decks is constant. Its initial26->26 correspondence must therefore persist.
But shared action position90/93 emits E4card26 and W4card21, contradiction.
Hence the exceptional pair must touch R(0). In the normalized explicit bases
R(0)=1, so only pairs(1,b) need the more expensive path calculation.
Only the first22 actions of the corrected primary29-action word are needed
for this lemma. No equality at the preceding boundary action is assumed.

The argument does not apply when R fixes0; that unresolved case is separate.
It also depends on fixed-output position0, deterministic shared action
permutations and one-to-one card/ciphertext labels. Independent initial decks
do not weaken it. The tiny controls enumerate arbitrary R, not just cycles.

REPORT SCOPE REVIEW
The inspected lab/report.py distinguishes conditional alignment assumptions,
model exclusion from decipherment, independent initial decks from shared
decks, and unrestricted82-slot witnesses from plausible26/27-letter models.
It correctly reports solver UNKNOWN and failed blind planted recovery as
non-exclusions. It acknowledges that the incoming-state distinction is
existing GAK theory, that the exact exclusion was only not found in bounded
sources, and that two data encodings can share an upstream transcription.

The row describing other cycle structures was stale while this audit began;
the parent is updating it with the exact checked82+1 and five80/81 shapes.
No broad statement excluding arbitrary mixed-cycle bases is justified.
The main headline is emphatic, but the tag and accompanying explanation
explicitly qualify the result as conditional and narrowly scoped.
