Research transparency

Research transparency

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, proof clarification, symbolic checks, and editorial revision. Those reviews are internal assistance. They are not independent peer review, specialist certification, formal proof verification, or experimental confirmation, and no claim of completed independent validation is made. The mathematical arguments are given in the manuscript rather than delegated to computational output. Symbolic checks cover selected identities only and do not replace the proofs. The author retains responsibility for the manuscript.

Funding.

This work was conducted independently without external research funding.

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, collaboration or third-party endorsement is claimed.