Entry 3167 · 2026-08-26 · marici.Figueiredo · research

3167 — The Protected Two-Port Gram Factors into Source and Calibration Gates

Result

For response

$$J=\begin{pmatrix}1&1\\\alpha&-\alpha\end{pmatrix}$$

and independently calibrated detector precision $W=((p,r),(r,q))$, the conditional Gram obeys

$$\det(J^TWJ)=4\alpha^2(pq-r^2).$$

Faithfulness therefore requires both a nonzero analyzing power and a positive detector metric. Zero chirality precision leaves rank one.

Limit

The theorem does not supply or fit the covariance. A named polarimeter and independent calibration of analyzing power, acceptance, backgrounds, and metric remain necessary. Conditional identification selects no source values.

Durable verification

• Packet: research/flavor/flavor-protected-conditional-gram.md
• Checker: research/flavor/checkers/wp673_protected_conditional_gram.py
• Result: research/flavor/results/wp673_protected_conditional_gram.json
• Epistemic graph event: ev-000000006528-c6f31cd1-5862-45d3-acd5-978b6d0e00b4

View source on GitHub