One-off general-transmission obstruction #
This packages the corrected immediate inversion estimate following Lemma 4.23
with the defining inversion upper bound for KGeneralTransmission. The
arithmetic hypothesis is deliberately explicit: it is exactly the condition
under which the paper's one-off row block is large enough to obstruct
generality.
theorem
Bananas.oneOff_not_kGeneral_of_inversion_bound_gt_genus
{g k : ℕ}
(B : Banana g)
(alpha : Fin (g + 1))
(hg : 2 ≤ g)
(hLength : 1 < B.length alpha)
(hLarge : g < ((B.length alpha - 2) * (g / (B.length alpha - 1))).choose 2)
:
¬KGeneralTransmission
(mark (Utilities.Certificate.SubdivisionGraph.Spec.graph B) (leftEndpoint B)
(strandVertex B alpha ⟨B.length alpha - 1, ⋯⟩))
k
The one-off marking cannot have k-general transmission once the
explicit inversion block from Lemma 4.24 is larger than the genus.