916 — Off-Diagonal Maximal Flags Require a Rees Direction
Uniformity falsifier
Entries 912–914 close the (D_3)-orbit of the diagonal maximal flag
[ (a,x,q)=(s_{14},s_{23},s_{235})=0. ]
The same source block also contains off-diagonal subchannel poles
[ y=s_{35}, \qquad z=s_{25}, \qquad q=x+y+z. ]
The next question is whether
[ (a,y,q)=0 ]
and its reflected (z)-partner carry the same ordinary or filtered packet.
Numerical discovery
For the source-normalized transition
[ widehat T_3= sin(pi q)sin(pi a), M_{ m block}mathcal S^T, ]
the diagonal approach (a=q=y=h) has a finite nonzero limit. The corresponding (z)-approach behaves likewise. By contrast, the (x)-flag norm decays linearly, in agreement with Entry 912.
This numerical distinction does not define an ordinary corner value; it only motivates the exact order test.
Exact six-route test
Keep (X) tangential and use multiplicative Laurent coordinates
[ Q=XYZ, \qquad Z=\frac{Q}{XY}. ]
The six orders of
[ A_4 o1, \qquad Y o1, \qquad Q o1 ]
give the following numbers of nonzero matrix entries:
[
\begin{array}{c|c}
ext{order}& ext{nonzero entries}
hline
(A_4,Y,Q)&0
(A_4,Q,Y)&0
(Y,A_4,Q)&6
(Y,Q,A_4)&6
(Q,A_4,Y)&0
(Q,Y,A_4)&6
end{array}
]
Every route is finite after exact cancellation, but the routes disagree.
Therefore
[ \boxed{ operatorname{Sp}_{a=y=q=0}widehat T_3 ext{ is not an ordinary order-independent specialization.} } ]
The finite diagonal-path limit is a chosen normal direction, not a canonical pullback.
Reflection
The source reflection exchanging labels (2leftrightarrow3) fixes (x=s_{23}) and exchanges
[ y=s_{35} longleftrightarrow z=s_{25}. ]
Hence the same classification applies to the (z)-flag.
Narrow conclusion
The maximal flags split into at least two coefficient-geometric types:
[
\boxed{
\begin{array}{c|c}
x ext{-flag}& ext{ordinary value }0, ext{first conormal grade rank }1
y/z ext{-flags}& ext{ordinary iterated specialization order dependent}
end{array}
}
]
This falsifies uniformity of the local coefficient packet. It does not require a new carrier stratum: all three flags already belong to the frozen associahedral/channel carrier.
Next falsifier
Construct the source-derived multi-Rees space for the off-diagonal ideal
[ (a,y,q) ]
using valuations read from the complete transition, not a fitted diagonal path. Determine its exceptional divisor, chart transitions, and whether the finite diagonal limit descends to a canonical associated-grade class.