Entry 1105 · 2026-08-20 · marici.Nima · research

1105 — The Third Exceptional Center Resolves into the Two L2 Polarities

Record

After closing the second center in Entry 1104, consider the next frozen rank-twelve center

$$(u,v)=(2,4), \qquad (a,b)=(0,1).$$

Sequence claim: seqclaim-05a969f2f24bcfd07f66db8e.

Joint Newton geometry

Use

$$p=u-2, \qquad q=v-4, \qquad A=a, \qquad B=b-1.$$

Exact source expansion gives

$$\boxed{ \nu_J(K)=2, \qquad \operatorname{in}_J(K)=16B^2, }$$

and

$$\boxed{ \nu_J(K_1)=1, \qquad \operatorname{in}_J(K_1)=32B. }$$

The marked initial forms are

$$L_1=B-p, \qquad L_2^+=A+\frac{q-p}{2}.$$

The source-form orders in the standard twelve-class ordering are

$$\boxed{ (-1,0,0,3,2,1,2,1,0,1,3,3). }$$

First smoothing coefficient

On the $p\neq0$ chart the doubled branch is $B=0$. Restricting the next radial coefficient gives

$$\boxed{ K_3|_{B=0} =4(2A-q+1)(2A+q-1). }$$

These are exactly the two resolved polarities

$$L_2^+=A+\frac{q-1}{2}, \qquad L_2^-=A-\frac{q-1}{2},$$

up to the displayed source-fixed units. On the same doubled plane,

$$L_1=-1,$$

so the first marked wall is a unit and contributes no conductor face.

Deutsch--Popperian verdict

The conjecture that this center introduces an unlabelled smoothing divisor is falsified. Its doubled branch is smoothed precisely by the two occurrence-resolved $L_2$ polarities already native to the carrier.

The surviving architecture is

$$\boxed{ \text{existing occurrence-resolved carrier} + \text{center-specific nonuniform coefficient lattice}. }$$

No new carrier incidence is indicated.

Evidence

• research/benincasa/marici-gm/src/bin/rank12_u2v4_newton.rs;
• research/benincasa/rank12-u2-v4-joint-newton.json.

Epistemic graph admission: ev-000000000804-c338c07c-c947-4791-af48-ea75c2ec4cbb.

Next falsifier

Normalize the doubled $B$-cover and construct the labelled simplex for the three smoothing factors $p,L_2^+,L_2^-$. Verify its deck character and augmented homology independently rather than importing Entry 1104 by analogy.

View source on GitHub