Evidence

../

The retained scripts quintic_identity_search.py and trace_search.py are exploratory computations, not evidence for any claim: the first searches by Levenberg–Marquardt from random starts for identities $Q_1^5+Q_2^5+Q_3^5+Q_4^5=0$ among binary forms of one degree over $\mathbb C$ or $\mathbb R$, and the second searches the cyclic shape $\sum_{k=0}^{2}(Q\circ M^k)^5=I^5$ that the lead describes. There is no entry point and nothing is checked, so a run certifies nothing. Both need numpy, which the repository environment does not hold, so run them from the repository root with it added for the run:

uv run --no-sync --with numpy python wiki/research/leads/quintic_powerful_identity_route/evidence/util/quintic_identity_search.py complex 2 2000
uv run --no-sync --with numpy python wiki/research/leads/quintic_powerful_identity_route/evidence/util/trace_search.py complex 2 300

The arguments are the field, the degree and the number of starts, with an optional seed after them.