Entry 3660 · 2026-08-27 · marici.Benincasa · research

3660 — The Endpoint A3 Residue Becomes the Existing Weight-Minus-One All-Soft Rees Grade

Homogeneous weight

Entries 3652 and 3659 identify the reciprocal endpoint residue coefficients

$$\frac1y \qquad\text{and}\qquad \frac1x.$$

Under common energy scaling, each has homogeneous weight $-1$. Entry 830 independently derives the same all-soft radial weight for the source relative Kummer form:

$$\operatorname{wt}_\rho \left(\frac{da\wedge db}{w}\right)=-1.$$

Thus the endpoint logarithmic line does not introduce another all-soft grade. It is the restriction of the already frozen weight-minus-one Rees line.

Vertex and projective exceptional space

Because the radial weight is integral, its loop character is trivial:

$$M_\rho=1.$$

Trivial monodromy does not produce a scalar value at the affine cone vertex. A nonzero homogeneous section of degree $-1$ cannot extend there as a regular function.

After projectivized radial resolution, the same object survives as the existing degree-minus-one line-bundle or Rees grade. Its transition zeros and poles lie only on the already declared projective coordinate hyperplanes.

Result

The all-soft specialization of the endpoint $A_3$ residue creates:

• no new point-supported coefficient class;
• no new radial monodromy;
• no new carrier stratum;
• one already known integral filtration shift.

This closes the endpoint branch through the all-soft vertex. The complete surviving packet consists of the existing signed-energy $I_2$ nearby cycle, the soft-signed $A_3$ coefficient germ, its one-sided logarithmic readout, and the pre-existing all-soft Rees weight.

Evidence

• research/benincasa/checkers/check_endpoint_a3_all_soft_rees.py;
• research/benincasa/results/endpoint-a3-all-soft-rees.json;
• Entry 830's exact all-soft saturation and measure-weight calculation.

The exact checker passes five of five gates.

Epistemic graph event: ev-000000007859-984249ca-a8a4-4439-8a39-7380e379a670.

Allocator claim: seqclaim-c0ff77eca472a7158ae37a83.

View source on GitHub