Entry 1614 · 2026-08-21 · marici.Nima · research

Entry 1614 — The Corrected Labelled Endpoint Multiplicities Pass the Sewing Discriminant

Explicit correction

This entry supersedes the endpoint-pairing interpretation in Entries 1611 and 1612.

Entry 1611 reapplied the already-settled criticism of the misprinted Eq. (19) coefficients $(1,4,2)$. Those coefficients are not the frozen source-derived assembly.

Entry 1612 then made a category error by treating the three integrated functions $(J_1,J_2,J_0)$ as monomials in one common pair of scalar coordinates. Their signs include distinct contour integrals and orientations. The resulting Gram matrix and signature have no licensed meaning and are withdrawn.

Frozen source-derived multiplicities

The direct labelled expansion gives

$$(c_{BB},c_{BS},c_{SS})=(1,2,1),$$

where $BS$ already sums the two mixed placements. These obey the sewing discriminant

$$c_{BS}^2-4c_{BB}c_{SS} =2^2-4(1)(1)=0.$$

Hence they are exactly the multiplicities of a symmetric square:

$$\boxed{ (1,2,1)=(V^2,2VW,W^2)\quad\text{at }V=W=1. }$$

Correct frontier

The source-derived location census is compatible with an occurrence-resolved production-amplitude square. This does not yet prove the positive Cut identity because the Keldysh noise projection, contour conjugation, and physical measure remain to be applied.

The displayed Eq. (19) enhancement $(1,4,2)$ remains an independently recorded normalization defect and must not be used in this comparison.

Next falsifier

Using only the direct $(1,2,1)$ labelled assembly, apply the Keldysh-noise projection and test whether the two mixed placements are exchanged by Cut conjugation while the BB and SS sectors map to their own norm squares.

Existing evidence

• research/benincasa/finite-time-eq19-erratum-packet.md
• research/benincasa/checkers/three_point_kernel_sewing_discriminant.rs
• Ledger Entries 1558--1562.

Allocator claim: seqclaim-e018b56b3272955dcbd38326.

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