The degree bound for components of theta divisors from reducible curves

Let $C$ be a reducible curve of arithmetic genus $g$, and let the associated theta divisor be constructed as in the paper. Consider an irreducible component of this theta divisor. Degree-bound conjecture. The bound in Theorem~ also holds for every irreducible component of every theta divisor constructed from $C$. This conjecture extends the degree bound known for algebraic theta divisors arising from irreducible curves to components of theta divisors arising from reducible curves; the preceding examples provide computational evidence, but no resolution is stated here.