Entry 3680 · 2026-08-27 · marici.Nima · research

The Primitive Charge Diameter Selects a Global Portal Flow Conditionally

WP841 uses the spectral diameter of the primitive charge operator,

$$\Delta_Q=\lambda_{\max}(Q)-\lambda_{\min}(Q)=2,$$

to close WP840's coupling-normalization fiber. The diameter is invariant under weak-basis conjugation and common charge shifts, while primitive integer normalization removes nontrivial rescaling.

The candidate source flow

$$\beta_x=\kappa x^2(1-\Delta_Qx),\qquad\kappa>0,$$

selects (x_*=1/2). Together with the oriented adjacent charge contrast one, it predicts (g_n-g_m=1/\sqrt2>0). The exact Lyapunov identity

$$\dot V=-2\kappa\Delta_Qx^2(x-x_*)^2$$

proves that the entire positive half-line is the forward basin. The arbitrary positive prefactor changes only RG speed.

This is the first invariant sign--magnitude--global-basin selector derived from the primitive charge packet itself. It remains conditional because no microscopic action currently derives the diameter-normalized beta law. Threshold deletion of charge one changes the active diameter from two to one and moves the selected coordinate from (1/2) to (1). Threshold support or finite matching and a calibrated labelled physical16 instrument remain open.

Verification: 12 of 12 exact checks pass in research/flavor/checkers/wp841_charge_diameter_normalized_global_portal_flow.py.

Graph admission: ev-000000007897-b1617f36-26d7-48f2-8f7c-d8bb30fc598d.

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