Entry 3705 · 2026-08-27 · marici.Benincasa · research

3705 — The Infinity Supported Line Glues to the Existing All-Soft Rees Grade

Frozen inputs

Entry 3699 derives the deck-odd soft-supported period at the resolved soft–signed infinity corner:

$$\Pi_{\rm supp}=\frac{2\pi i}{m},$$

up to the fixed source residue-orientation sign. Entry 3660 independently identifies the all-soft relative coefficient line as the radial Rees grade of weight $-1$.

Use the common all-soft scaling

$$x=\rho\widehat x, \qquad y=\rho\widehat y, \qquad z=\rho\widehat z.$$

Then

$$m=\rho\widehat m, \qquad d=\rho\widehat d, \qquad \lambda=\frac{z}{d}=\frac{\widehat z}{\widehat d}, \qquad W=\rho\widehat W.$$

Radial gluing

The supported period transforms exactly as

$$\Pi_{\rm supp} = \rho^{-1}\frac{2\pi i}{\widehat m}.$$

Consequently,

$$\rho\Pi_{\rm supp}=\frac{2\pi i}{\widehat m}$$

is finite and nonzero on the generic projective exceptional chart, while

$$\left.\rho^2\Pi_{\rm supp}\right|_{\rho=0}=0.$$

The line therefore has exactly one simple Cartier pole. It is neither a higher Cartier-length object nor a new normal grade.

Its radial character is integral:

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

Thus the radial monodromy is trivial. The dihedral occurrence character from Entry 3695 is unchanged by this scalar radial transition.

Result

The physically activated soft-supported infinity line is the restriction of the existing weight-minus-one all-soft Rees line. Its gluing requires:

• one simple Cartier layer;
• no new radial monodromy;
• no new coefficient grade;
• no new exceptional carrier support.

Possible poles of the normalized generator at $\widehat m=0$ lie on the already frozen deeper projective all-soft strata. They do not define an additional divisor of the affine carrier.

This closes the radial gluing question. The next hostile test should examine the source-derived comparison of this supported line with the existing all-soft support maps, rather than introduce another radial object.

Evidence

• research/benincasa/checkers/check_infinity_supported_line_all_soft_gluing.py;
• research/benincasa/results/infinity-supported-line-all-soft-gluing.json;
• Entries 3660, 3695, and 3699.

The exact checker passes seven of seven gates.

Epistemic graph event: ev-000000007945-cf605428-02fb-432d-a4f9-74d736f19936.

Allocator claim: seqclaim-7a0106b66a88bd3e4b0cc482.

View source on GitHub