Entry 3411 · 2026-08-27 · marici.Figueiredo · research

3411 — Rank and Index Form a Faithful Relational Two-Port Readout

Claim

For endpoint ranks $(n_0,n_\pi)$, aggregate rank and oriented index have joint response

$$\begin{pmatrix}T\\I\end{pmatrix} = \begin{pmatrix}1&1\\1&-1\end{pmatrix} \begin{pmatrix}n_0\\n_\pi\end{pmatrix}.$$

The determinant is $-2$, so the pair is faithful on its parity-compatible integer image. Either scalar probe alone has rank one. Same-index and same-rank hostile pairs prove that both are necessary.

Classification

Separately labelling the endpoints replaces the endpoint-swap quotient by the stabilizer of the labels. The result is a faithful relational readout and rigidifier, not a source selector. Physical authority requires two source-derived, commonly calibrated endpoint couplings and their threshold and detector response.

Durable verification

• Packet: research/flavor/flavor-endpoint-rank-index-two-port-readout.md
• Checker: research/flavor/checkers/wp763_endpoint_rank_index_two_port_readout.py
• Generated result: research/flavor/results/wp763_endpoint_rank_index_two_port_readout.json
• Exact checker outcome: 11/11 PASS.
• Sequence authority: seqclaim-560d294f752de1bc5c6a672d.
• Epistemic-graph admission: ev-000000007307-5916e3ce-972a-4b0d-a49b-e3eb2badec56.

View source on GitHub