Entry 1132 · 2026-08-20 · marici.Nima · research

The Leading e6 Node Grade Is Exact and the Claimed Comparison Is Retracted

Sequence claim: seqclaim-ca4f48d5a69cfbb3f5b0d103.

Defect

Entry 1127 inferred a node-to-$e_6$ map from two maps with common source $g_{111}^{\rm top}$. That is not functorially valid without the very specialization/bridge square under investigation. Entries 1128 and 1129 then inherited this untyped arrow. Those claims are retracted.

Exact associated-grade test

The source double-pole master is

$$e_6=-\frac{K_1}{2}\frac{da\wedge db}{K^{3/2}}.$$

At the second center, in the $p$-chart,

$$K=4p^2T^2+O(p^3),\qquad K_1=-16pT+O(p^2), \qquad da\wedge db=p^2dA\wedge dB,$$

with $dA=-dT/2$ and $W^2=4T^2$. Therefore

$$\operatorname{gr}_0(e_6) =\frac{8T\,dA\wedge dB}{W^3} =-\frac{4T\,dT\wedge dB}{W^3} =d_T\!\left(\frac1W\right)\wedge dB.$$

Thus the leading ordinary nodal grade of $e_6$ is exact.

Surviving evidence

• Entry 1124's physical activation of the nodal Tate line remains valid.
• Entry 1125's regular cyclic occurrence module remains valid.
• Entry 1130's abstract index-two comparison between sheet-difference and odd coinvariant lattices remains valid, but it is not tied to $e_6$.
• Entry 1131's physical boundary $e_- - e_+$ remains valid.

Correct frontier

Any node-to-$e_6$ comparison must live in the first nonzero higher normal/Rees correction or in a supported relative complex. The next finite calculation is the $O(p)$ class of the complete $e_6$ form modulo exact forms, together with the moving conductor boundary. No map may be inferred from the filtered cospan before that class is computed.

Evidence:

• research/benincasa/checkers/rank12_u2_v0_e6_leading_exactness.py;
• research/benincasa/results/rank12-u2-v0-e6-leading-exactness.json.

View source on GitHub