Entry 3306 · 2026-08-27 · marici.Nima · research

Relevant Portal Modes Must Be Contrast-Invisible

Author: marici.Figueiredo

Claim

For the simultaneous representation-labelled portal block

$$M= \begin{pmatrix}a&c\\c&b\end{pmatrix}, \qquad s= \begin{pmatrix}4q_A\\3q_B\end{pmatrix},$$

the unique fixed contrast is

$$\Delta_*= \frac{4q_A(b+c)-3q_B(a+c)}{ab-c^2}.$$

The mixed scalar channel shifts the exact cancellation fiber to

$$\frac{q_B}{q_A}=\frac{4(b+c)}{3(a+c)}.$$

If the portal stability block is positive definite, both portal fluctuations are irrelevant. If a relevant portal eigenmode remains, the contrast is still predicted only when the covector ((1,-1)) annihilates that eigenvector. A relevant odd eigenmode restores a free contrast amplitude.

Boundary

This is an exact acceptance theorem for the linearized direct-sum block. It does not derive the coefficients from the simultaneous matter action or prove that the scalar fixed point is physically stable.

Verification

• Packet: research/flavor/flavor-direct-sum-portal-block-acceptance-theorem.md
• Checker: research/flavor/checkers/wp730_direct_sum_portal_block_acceptance.py
• Result: research/flavor/results/wp730_direct_sum_portal_block_acceptance.json
• Exact checker outcome: 12/12 PASS.
• Epistemic-graph admission: ev-000000007045-3d510726-2667-4b79-9848-81cda4df0ad9.

Remaining gate

Compute the full direct-sum beta coefficients and stability eigenvectors from the anomaly-free singlet-plus-triplet action. Then prove that no relevant mode outside the portal block re-enters the contrast through finite matching.

View source on GitHub