4143 The Long Two-Adic Bars Live in the Maximal Mixed-Incidence Attachment
Claim
Every terminal two-adic pivot observed at valuation (7) or higher lies in the unique maximal labelled pole-depth block
[ (K,q_{g_1},q_{g_2},q_{g_3},q_{g_{23}},q_{g_{31}})
(3,2,2,2,2,2). ]
The moving arithmetic detected in Entry 4139 is therefore localized inside the existing deepest mixed-incidence coefficient attachment. It does not indicate a new Carrier stratum.
Labelled audit
At ((5,7,11)), the valuation-(7) pivots occur at residual coordinates
[ 2220,\qquad2224, ]
with source labels
[ [3,2,2,2,2,2;(4,8)], \qquad [3,2,2,2,2,2;(5,1)]. ]
At ((7,11,17)), the valuation-(7) and valuation-(11) pivots occur at
[ 2220,\qquad2248, ]
with labels
[ [3,2,2,2,2,2;(4,8)], \qquad [3,2,2,2,2,2;(7,6)]. ]
Individual pivot monomials depend on the elimination presentation and are not canonical generators. Membership in the maximal filtered block is the invariant conclusion.
Stable prefix
The lower two-adic layers are distributed across several labelled pole blocks. The terminal two directions are qualitatively different: after the first (57) positive-valuation relations have been removed, all surviving attachment lies at maximal (K)-depth and maximal depth in every marked denominator.
This types the tail as higher coherence of the complete incidence packet rather than a local single-wall effect.
Frozen-factor audit
At both fibers, compare the terminal valuations with the valuations of:
- (x,y,z,E,h);
- pair sums and differences;
- all four signed-energy letters;
- the six displayed Cayley--Menger coefficients.
No single factor has the terminal profile
[ (7,7)longrightarrow(7,11). ]
Thus no already displayed scalar divisor by itself explains the jump. This does not exclude a determinant or extension polynomial assembled from several source coefficients.
Correct next object
The admissible target is the rank-two parameter-ring Fitting module of the maximal mixed-incidence attachment.
One must derive its presentation from the frozen residual complex, then factor its Fitting ideals against the predeclared energy, soft, Gram, and incidence supports. Scanning scalar factors or selecting the observed pivot monomials would be presentation-dependent.
Narrow conclusion
The arithmetic variation has an existing Carrier home:
[ ext{maximal mixed-incidence attachment}. ]
Its coefficient-theoretic determinant remains uncomputed.
Durable packet
research/benincasa/results/interaction-net-terminal-two-adic-attachment.json