diff b34550f..b1f9bc4 univalent_inverse_power_v2.txt
diff --git a/univalent_inverse_power_v2.txt b/univalent_inverse_power_v2.txt
index a92cbeb..6aaf163 100644
--- a/univalent_inverse_power_v2.txt
+++ b/univalent_inverse_power_v2.txt
@@ -150,71 +150,6 @@ Three things to notice, because they are all part of the content.
exponent.
-0.6 WHY STRICTNESS IS THE WHOLE DIFFICULTY
-
-The machinery of the proof naturally produces a NON-STRICT inequality:
-it will say B_b(-1) <= 1/4. But that is exactly the conjectured value.
-A non-strict inequality at the conjectured value confirms the
-conjecture; it does not refute it. To refute it we need the strict
-version, and there is no slack anywhere: the conjecture sits precisely
-where the method's equality case sits.
-
-Here is the shape of the argument, in one sentence:
-
- If the operator in Part 1 grows by a factor 2^beta with beta >= 1/4,
- then averaging over maps produces a probability law (Part 2) and a
- potential whose critical points (Part 4) can be paired (Part 5), and
- the pairing forces a certain average signed Jacobian to be <= 0,
- while the moment identities force it to be > 0 unless beta = 1/4
- exactly; and the case beta = 1/4 forces an identically vanishing
- Jacobian, which a harmonic barrier (Part 6) forbids.
-
-The pairing in Part 4 matches each saddle of the potential to a peak of
-strictly larger value. "Strictly larger" is the crucial word and it is
-also the fragile one: the strictness may be arbitrarily small, one
-pair to the next. So no step of the argument is allowed to use a
-uniform positive gain. It must be handled by an equality analysis
-instead, which is what Parts 5 and 6 do.
-
-
-0.7 ROADMAP
-
- Part 1 Transfers the disk problem to the compact family K of
- half-plane maps. Builds one positive operator L whose
- exponential growth rate 2^beta controls ALL the disk means
- of THM 0.5. This is the only place where f is used; after
- this part, the question is purely about L.
-
- Part 2 Assumes beta >= 1/4 and builds a probability law on K whose
- weighted rebasings scale exactly as y^{-beta}. Differentia-
- ting that identity twice pins down two moments of the
- logarithmic derivative.
-
- Part 3 Introduces a potential V built from F and a target point
- xi, and proves that its positive superlevels are compact for
- almost every map and almost every target. Compactness is
- what makes critical points a finite, countable business.
-
- Part 4 Identifies the critical points of V with the solutions of a
- smooth equation G_F(z) = xi, computes the Hessian in terms of
- a signed Jacobian J_F, proves the index count (peaks at least
- as many as saddles above every level), and builds a
- measurable rank pairing.
-
- Part 5 Changes variables through G_F and compares the paired
- weights on a large box against a slightly larger box. The
- boxes' areas scale the same way, so the comparison survives
- and forces E J_F(i) <= 0, with equality only when J_F(i)
- vanishes identically.
-
- Part 6 Shows beta = 1/4 would force J_F = 0 for almost every F, and
- that no member of K has J_F = 0. Contradiction. So
- beta < 1/4, and Part 1 converts that into the theorem.
-
- Part 7 Honest accounting.
-
-
-================================================================
PART 1. A COMPACT MODEL, AND ONE OPERATOR
================================================================