Entry 3619 · 2026-08-27 · marici.Figueiredo · research

The Oriented Incidence Does Not Determine the Fixed-Point Coefficients

The coupled flow

$$\beta_x=2x^2(-b+cx-dy), \qquad \beta_y=2y(ay-fx)$$

has a positive nonzero solution

$$x_*=\frac{ab}{ac-df}, \qquad y_*=\frac{bf}{ac-df}$$

when $ac-df>0$. The exact packet $(a,b,c,d,f)=(1,1,3,1,1)$ gives $(x_*,y_*)=(1/2,1/2)$ with local infrared stability exponents $1/2$ and $2$. Combined with WP820's selected unit charge contrast, it conditionally fixes a positive portal magnitude $e_*=1/\sqrt2$.

WP820's incidence does not determine the loop coefficients. The same charge packet with coefficients $(1,1,1,1,1)$ has no finite fixed point, while a threshold shift to $(1,1,4,1,1)$ moves it to $(1/3,1/3)$. The known WP805 chiral fixed point supplies common-action algebra but lies outside perturbative control and erases orientation in squared coupling coordinates.

Evidence

• Packet: research/flavor/flavor-same-incidence-gauge-yukawa-fixed-point-interface.md
• Checker: research/flavor/checkers/wp821_same_incidence_gauge_yukawa_fixed_point_interface.py
• Generated result: research/flavor/results/wp821_same_incidence_gauge_yukawa_fixed_point_interface.json
• Exact result: 22 of 22 checks passed.
• Ledger-sequence claim: seqclaim-34d5998dbf802a7cfa575fbd, value 3619.
• Graph admission: ev-000000007767-33b1a777-f2e0-421c-a3c8-cd5f7622cc87.

Claim boundary

The toy coefficient packet is a conditional algebraic construction, not a derived flavor theory. A complete matter-spectrum constructor, global basin, threshold-stable fixed point, physical16 descent, and calibrated detector remain open.

View source on GitHub