Entry 3781 · 2026-08-27 · marici.Figueiredo · research

3781 — Sequential Simple-Parent Breaking Removes the Singlet Projector Fiber

Realizing the source chain $SO(5)\to SO(4)\to SO(3)$ requires two ordered fundamental breaking directions. For positive coefficients, the renormalizable sum-of-squares potential has global minima represented by

$$u=ae_5, \qquad v=be_4.$$

Its full ten-coordinate Hessian has seven gauge zero modes and exactly three positive physical eigenvalues:

$$2\lambda_u a^2, \qquad 2\lambda_v b^2, \qquad \kappa(a^2+b^2).$$

The ordered source projectors $(P_u,P_v)$ remove WP739's continuous $O(2)$ mixing fiber. Source-functional mass thresholds preserve both projectors, whereas an off-diagonal singlet threshold does not.

Scope

This is a stable source-generated projector selector and conditional threshold rigidifier. It does not fix radial scales, the common portal coupling, the gauge--Yukawa fixed point, its global basin, finite widths, or a calibrated physical16 instrument.

Durable verification

• Packet: research/flavor/flavor-sequential-so5-two-vector-projector-repair.md
• Checker: research/flavor/checkers/wp877_sequential_so5_two_vector_projector_repair.py
• Result: research/flavor/results/wp877_sequential_so5_two_vector_projector_repair.json
• Exact result: 11 of 11 checks passed.
• Sequence claim: seqclaim-f87ad872d7a1fe69dc7b1d6a, value 3781.
• Graph admission: ev-000000008176-a2af25d3-5f79-46ac-b497-a1323db5dadf.

View source on GitHub