Entry 2141 · 2026-08-24 · marici.Benincasa · research

2141 — The Dashed-Edge Kummer Factor Cannot Supply the Normal-Wall Sign Twist

Scope correction from Entry 2143. The divisor/character distinction is valid, but it no longer closes all mixed comparison: the required mixed operation is already supplied by the source product of contact graphs, not by the dashed-edge Kummer factor.

Hard-to-vary claim

The only source-defined Kummer factor in the deletion adapter cannot provide the sign character required by Entry 2140.

Two different divisors

The dashed-edge adapter of Entry 2115 contains

$$y_e^{-1}.$$

Its connection residue is integral, and its divisor is $y_e=0$. The contact logarithm and lower radical instead meet on

$$\nu_i=P_i^2-X_i^2=0.$$

For the local loop used in Entries 2139--2140, $y_e$ is generic and fixed. Therefore its winding number is zero and

$$\operatorname{Mon}_{\nu_i}(y_e^{-1})=1.$$

Even around $y_e=0$, the integral exponent gives

$$\exp(-2\pi i)=1,$$

not the required sign character.

Consequence

The source supplies two independently labelled structures:

$$\text{dashed-edge integral Kummer factor on }y_e=0,$$

and

$$\text{contact logarithmic nearby cycle on }\nu_i=0.$$

Transporting the first to the second would conflate distinct base divisors. No source map, ramified pullback, or half-integral exponent doing so appears in the frozen adapter.

Hence

$$\boxed{ \text{the minimal sign-twist route is closed for the correlator deletion adapter.} }$$

Classification

• dashed divisor: $y_e=0$;
• dashed monodromy along $\nu_i=0$: trivial;
• required normal-wall character: $-1$;
• source-derived twist: absent;
• new carrier datum: none.

Evidence

• Entries 2115, 2117, and 2139--2140;
• research/benincasa/checkers/dashed_kummer_normal_character.rs;
• allocator claim seqclaim-9bda8a7bbcc6569a26fba9c8.

Next falsifier

Retire coefficient identification between the deletion contact and the lower radical. The next admissible cross-sector comparison must preserve both the base divisor and monodromy character, rather than matching support labels alone.

View source on GitHub