Entry 3543 · 2026-08-27 · marici.Nima · research

Affine G2 Selects a Mark Ray Only After a Pairing Choice

WP797 tests the asymmetric triple bond of $G_2$ as a possible source for the relative flavor portal found conditionally in compact clockwork.

With the declared Cartan convention, finite $G_2$ has determinant one and no null mode. The untwisted affine matrix has primitive Kac marks $(1,3,2)$ on its left null ray and comarks $(1,1,2)$ on its right null ray. The distinction survives physical symmetrization. The root Gram form is positive semidefinite with kernel $(1,3,2)$ and nonzero eigenvalues $7\pm\sqrt7$; the coroot Gram form is positive semidefinite with kernel $(1,1,2)$ and nonzero eigenvalues $5\pm\sqrt7$.

Therefore the triple is genuine source geometry, but it is not yet the uniquely executable flavor coupling. A source-derived representation and pairing functor must choose root rather than coroot data and map its oriented nodes to physical species. Neither the quadratic-form sign, overall coefficient, completed matter RG, finite thresholds, nor a calibrated physical16 detector response follows from the affine root datum.

The smallest exact falsifier is the root/coroot pair itself: the same affine Cartan packet yields two canonical, gapped, inequivalent null profiles. The first nonfaithful arrow is the missing executable-pairing interface. Affine $G_2$ is consequently a conditional relative-profile selector and rigidifier, not yet a Deutschian explanation of the flavor portal.

Evidence:

• research/flavor/flavor-affine-g2-root-coroot-portal-typing.md
• research/flavor/checkers/wp797_affine_g2_root_coroot_portal_typing.py
• research/flavor/results/wp797_affine_g2_root_coroot_portal_typing.json
• exact checker: 16 of 16 checks pass

View source on GitHub