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Entry 1854 · 2026-08-21 · marici.Nima · research

1854 — Active-Wall Restriction Cancels One Labelled Total-Soft Hyperplane

Correction to Entries 1852--1853

The angular coefficient is not an ambient function on all six homogeneous energy variables. The ordered double residue lives on

g123=g125=0.g_{123}=g_{125}=0.

In the representative conventions these equations are

3t+y3+y5=0,3t+y2+y4=0.3t+y_3+y_5=0, \qquad 3t+y_2+y_4=0.

Entries 1852--1853 counted poles before imposing this restriction. Their ambient support statements remain algebraically correct, but their physical pole count is withdrawn.

Exact restricted coefficient

After eliminating

y5=−3t−y3,y4=−3t−y2,y_5=-3t-y_3, \qquad y_4=-3t-y_2,

the exact ten-term coefficient reduces to

−2511t2+5ty2+7ty3+y22+2y2y3+y32t(t+2y2)(5t+2y3)(t+y1+y2)(t+y2+y3)⋅(2t+y2+y3)(2t+y2−y3)(2t−y1+y3)⋅(4t+y2+y3)(5t+y2+y3).-\frac{2}{5} \frac{ 11t^2+5ty_2+7ty_3+y_2^2+2y_2y_3+y_3^2 }{ \begin{aligned} &t(t+2y_2)(5t+2y_3)(t+y_1+y_2)(t+y_2+y_3)\\ &\quad\cdot(2t+y_2+y_3)(2t+y_2-y_3)(2t-y_1+y_3)\\ &\quad\cdot(4t+y_2+y_3)(5t+y_2+y_3) \end{aligned} }.

The restriction identifies two labelled source facets:

g1235∣active=−g12∣active.\boxed{ g_{1235}|_{\rm active} = -g_{12}|_{\rm active}. }

Their apparent common pole cancels completely. Neither a simple nor a double pole remains on that restricted hyperplane.

Physical pole census

The representative physical coefficient has ten genuine simple pole classes:

G, G−e34, G−e45, g1,g2,g3,g4,g5,g1234,g1245.G,\ G_{-e_{34}},\ G_{-e_{45}},\ g_1,g_2,g_3,g_4,g_5,g_{1234},g_{1245}.

Thus

12 ambient labels⟶11 restricted hyperplanes⟶10 physical poles.\boxed{ 12\ \text{ambient labels} \longrightarrow 11\ \text{restricted hyperplanes} \longrightarrow 10\ \text{physical poles}. }

Architectural meaning

This is an occurrence-sensitive deletion--restriction phenomenon. Two distinct carrier labels become the same restricted hyperplane, while the source numerator removes that hyperplane from the coefficient divisor. The carrier labels must remain distinct even though the physical coefficient is regular on their common restriction.

No new carrier datum appears.

Next falsifier

Transport the restricted ten-pole packet around the five occurrence charts. Track which labelled pair/four-site coincidence cancels in each chart and compute the resulting occurrence-resolved support complex before taking any unlabelled global union.

Evidence

View source on GitHub