Rank-zero part of the cross-strand witness in Theorem 3.9 #
The first divisor in the distinct-strand proof of Theorem 3.9 is reduced, after a path-pair slide, to a core chip plus a two-strand semibreak. This file records the normal-form calculation abstractly, so the eventual case split does not need to unfold a concrete banana divisor.
Two raw interior path chips on distinct strands form a semibreak divisor.
This is the raw-coordinate companion of
isSemibreak_two_distinct_strand_chips, used by the explicit path-firing
witnesses in Theorem 3.9.
Adding the left endpoint to a degree-two semibreak divisor has rank zero on a banana of genus at least three.
Adding the right endpoint to a degree-two semibreak divisor has rank zero on a banana of genus at least three.
The first rank-zero line of the distinct-strand witness in Theorem 3.9. If two interior chips on one raw path slide to its tail endpoint, adjoining an interior chip on a distinct strand gives a rank-zero divisor in genus at least three.
Two normalized chips at positions 1 and i slide to the left endpoint
and position i+1.
The left endpoint plus the difference between positions n-1 and j
is equivalent to the chip in complementary position n-1-j.
The first explicit divisor in the distinct-strand proof of corrected Theorem 3.9 has negative rank difference.