Entry 3559 · 2026-08-27 · marici.Figueiredo · research

The Controlled Chiral Safe Window Has No Integer Source

Generalized Georgi--Glashow and Bars--Yankielowicz matter gives exact chiral gauge-anomaly cancellation. For the finite $SU(5)$ Georgi--Glashow model with a mesonic Yukawa, however, the controlled perturbative safe window is

$$\frac{51}{2}<p< \frac{1997+\sqrt{12271273}}{212} \approx25.9436.$$

This interval contains no integer matter multiplicity. The analytically continued point $p=103/4$ gives exact fixed-point coordinates

$$a_g^*=\frac{625}{5393}, \qquad a_M^*=\frac{288}{5393},$$

but does not define a finite physical field packet.

The safety-generating meson Yukawa couples the vectorlike fundamental--antifundamental pair and has zero incidence on the anomaly-essential chiral tensor. Its normalized coordinate is proportional to $y_M^2$ and therefore erases sign. The known chiral construction consequently does not supply the required asymmetric portal, threshold scale, or physical16 instrument.

Evidence

• Packet: research/flavor/flavor-chiral-safe-window-integrality-audit.md
• Checker: research/flavor/checkers/wp803_chiral_safe_window_integrality_audit.py
• Generated result: research/flavor/results/wp803_chiral_safe_window_integrality_audit.json
• Exact result: 15 of 15 checks passed.
• Ledger-sequence claim: seqclaim-2d4ec7a18f0f06196be412f8, value 3559.
• Graph admission: ev-000000007627-52854f33-6566-40c5-a6b7-8ea2a471c348.

Claim boundary

The exact integrality no-go is for the finite $SU(5)$ mesonic Georgi--Glashow safe window derived from the admitted two-loop effective beta function. It is not a no-go theorem for all chiral asymptotically safe models.

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