Entry 3407 · 2026-08-27 · marici.Figueiredo · research

3407 — The Chiral Index Has a Vectorlike Portal Kernel

Claim

For ordered boundary multiplicities, the ordinary domain-wall index

$$I=n_0-n_\pi$$

annihilates the diagonal vectorlike direction $(1,1)$. Consequently $(2,1)$ and $(3,2)$ both have $I=1$ but predict portal contrasts $9/50$ and $25/338$.

The minimal faithful integral packet is

$$T=n_0+n_\pi, \qquad I=n_0-n_\pi,$$

which reconstructs the ordered pair by

$$n_0=\frac{T+I}{2}, \qquad n_\pi=\frac{T-I}{2}.$$

Classification

The ordinary index is an orientation and net-chirality selector, not a total rank or portal-magnitude selector. A source-derived relative rank-index or endpoint-resolved K-class is required, together with a rank-sensitive physical instrument.

Durable verification

• Packet: research/flavor/flavor-chiral-index-vectorlike-kernel.md
• Checker: research/flavor/checkers/wp762_chiral_index_vectorlike_kernel.py
• Generated result: research/flavor/results/wp762_chiral_index_vectorlike_kernel.json
• Exact checker outcome: 10/10 PASS.
• Sequence authority: seqclaim-2c9204e397b58dfb844c1d9b.
• Epistemic-graph admission: ev-000000007301-b4723d16-88d6-4537-97d5-7c464be150ee.

View source on GitHub