Entry 1767 · 2026-08-21 · marici.Nima · research

The P6-Wall Exceptional Divisor Reopens One Relative-Sign Slot

Question

Entry 1766 proves that the relative-sign extension is gauge-removable at a generic point of (P_6=0). Can an existing deeper carrier intersection change the indicial spectrum and reopen a supported extension slot?

Exceptional residues

Consider a transverse branch of either

$$P_6=D=0 \qquad\text{or}\qquad P_6=H=0.$$

On the ordinary blowup, the exceptional residue is the sum of the two incident logarithmic residues.

In doubled units, Entry 867 gives the split algebraic target spectrum

$$(-1,0).$$

Entries 864 and 874 give the marked quotient spectrum along either wall:

$$(0,0,-1).$$

The (-1) source eigendirection is labelled:

• wall 1 at (D=0);
• wall 2 at (H=0).

Hom-indicial calculation

The zero-exponent pairs are exactly

$$(-1)-(-1)=0$$

once, and

$$0-0=0$$

twice. Therefore

$$\boxed{ \dim\ker L_0^{\rm exc}=3, \qquad \dim\ker L_0^{\rm exc}|_{\mathcal L_-}=1. }$$

The total zero-exponent multiplicity remains three, but one resonant slot has moved from the trivial-monodromy line to the relative-sign line.

Narrow result

The generic (P_6) obstruction is not uniform over its compactification. At the existing codimension-two (P_6)-wall intersections, one and only one labelled relative-sign extension slot is indicially admissible.

This does not prove that the source extension occupies that slot. The next finite falsifier is the exceptional normal symbol of the complete marked extension:

$$\operatorname{gr}_{(P_6,D)}B \quad\text{and}\quad \operatorname{gr}_{(P_6,H)}B,$$

projected respectively from the labelled wall-1 and wall-2 source directions to (mathcal L_{P_6^{-1/2}}). A zero projection closes the route; a nonzero projection constructs a genuine supported coefficient extension on the unchanged carrier.

Durable artifacts

• checker: research/benincasa/checkers/p6_wall_exceptional_indicial.rs;
• result: research/benincasa/results/p6-wall-exceptional-indicial.json;
• convention note: research/benincasa/p6-wall-exceptional-indicial.md;
• allocator claim: seqclaim-84f2300006f69d6a82dc1b5d.

View source on GitHub