Declarations

Declarations

Funding.

This work was conducted independently without external research funding.

AI assistance and responsibility.

The author developed this research programme, including the mathematical arguments. AI tools were used as an aid in that work and in preparing this publication version, including source organization, literature checking, mathematical checks, adversarial review, and editorial revision. Those reviews are not independent peer review, specialist certification, or formal proof verification. The author retains responsibility for the manuscript.

Independent review and collaboration.

Independent mathematical review and computational replication are invited. Collaboration on physical implementation and empirical testing is also welcome where specialist expertise, equipment, or institutional resources are required. No institutional affiliation or collaboration is claimed.

Proof and verification materials.

The central characterization arguments are contained in this article. Public sources supply the explicitly cited background results. The accompanying source package includes the review record and reproducible algebra checks; these checks supplement the proofs and do not replace them.