Entry 3793 · 2026-08-27 · marici.Figueiredo · research

3793 — Spin(5) Anomaly Cancellation Does Not Define One Beta System

The simple-parent portal packet has at least two inequivalent anomaly-free completions on the half-integer hypercharge lattice. Per family they are

$$4_{+1/2}\oplus5_{-1}$$

and

$$4_{-3/2}\oplus1_0\oplus1_{+1}\oplus1_{+2}.$$

Both cancel the mixed Spin(5)-hypercharge, gravitational-hypercharge, cubic hypercharge, and fundamental-spinor parity obstructions of the frozen portal packet. Their three-family Spin(5) fermion indices differ by three.

Including the spinor Higgs and the two real fundamental breaking fields of WP877 gives

$$b_0^A=\frac92, \qquad b_0^B=\frac{13}{2}.$$

Thus the anomaly probe identifies two spectra that the one-loop RG probe separates by exactly two. Both are asymptotically free at this order, so anomaly completion supplies neither one authorized beta system nor a nonzero ultraviolet normalization of the common portal coefficient.

Scope

This is a nonuniqueness theorem for the admitted local anomalies and fundamental-spinor parity test. It does not construct full Yukawa grammars, two-loop fixed points, mass generation for the chiral completion, finite thresholds, or a calibrated physical instrument. Phenomenological exclusion of high-charge singlets would be an additional probe, not an anomaly identity.

Durable verification

• Packet: research/flavor/flavor-spin5-anomaly-completion-beta-fiber.md
• Checker: research/flavor/checkers/wp879_spin5_anomaly_completion_beta_fiber.py
• Result: research/flavor/results/wp879_spin5_anomaly_completion_beta_fiber.json
• Exact result: 13 of 13 checks passed.
• Sequence claim: seqclaim-43ec6ab882c221f4c187191e, value 3793.
• Graph admission: ev-000000008189-dc1d7deb-656e-46fb-b427-f0f1430a4ce4.

View source on GitHub