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Input data and context
% 8_2-2
s.l1.x0.x0.y1.y0.y0.y1.y0.y0.y1.u2
,1
% Symmetry 2 of a 2-bridge knot corresponding to the fraction 17/14 = [2,-2,2,-2,2,2] (Sakuma, Prop. 3.6, Case (1), symmetry 2).
% Simplifies with options '-qs' to l1.x2.l2.x3.x3.x4.x4.x3.x3.x4.x4.x3.y2.y1.y2.x3.y2.x4.y3.x4.y2.x3.x2.u1.y1.x0.x1.y0.y0.u2.y0.y0
Bar-Natan multicurve \(\mathrm{\widetilde{BN}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-2/cxBNr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ -4 q^-10 δ^-1 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^ -8 q^-16 δ^ 0 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^-12 q^-22 δ^ 1 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^ 0 q^ -4 δ^-2 ⬯<~S~~⬮<—⬮<~⬮<—⬮<~⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯—>⬯~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-2/cxBNr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ -4 q^-10 δ^-1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^ -8 q^-16 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^-12 q^-22 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^ 0 q^ -4 δ^-2 ⬯<~S~~⬮<—⬮<~⬮<—⬮<~⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯—>⬯~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-2/cxBNr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ -4 q^-10 δ^-1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^ -8 q^-16 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^-12 q^-22 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^ 0 q^ -4 δ^-2 ⬯<~S~~⬮<—⬮<~⬮<—⬮<~⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯—>⬯~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-2/cxBNr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ -4 q^-10 δ^-1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^ -8 q^-16 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^-12 q^-22 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^ 0 q^ -4 δ^-2 ⬯<~S~~⬮<—⬮<~⬮<—⬮<~⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯—>⬯~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-2/cxBNr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ -4 q^-10 δ^-1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^ -8 q^-16 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^-12 q^-22 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^ 0 q^ -4 δ^-2 ⬯<~S~~⬮<—⬮<~⬮<—⬮<~⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯—>⬯~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮
Khovanov multicurve \(\mathrm{\widetilde{Kh}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-2/cxKhr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ -6 q^-13 δ^-1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-8 δ|^-1
2) h^ -5 q^-11 δ^-1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-6 δ|^-1
3) h^ -4 q^ -9 δ^-1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-4 δ|^-1
4) h^-10 q^-19 δ^ 1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-14 δ|^0
5) h^ -9 q^-17 δ^ 1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-12 δ|^0
6) h^ -8 q^-15 δ^ 1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-10 δ|^0
7) h^-13 q^-23 δ^ 3/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-18 δ|^1
8) h^-12 q^-21 δ^ 3/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-16 δ|^1
9) h^ -9 q^-17 δ^ 1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— r(1/8) q^-80/9 δ|^0
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-2/cxKhr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ -6 q^-13 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-8 δ|^-1
2) h^ -5 q^-11 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-6 δ|^-1
3) h^ -4 q^ -9 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-4 δ|^-1
4) h^-10 q^-19 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-14 δ|^0
5) h^ -9 q^-17 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-12 δ|^0
6) h^ -8 q^-15 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-10 δ|^0
7) h^-13 q^-23 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-18 δ|^1
8) h^-12 q^-21 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-16 δ|^1
9) h^ -9 q^-17 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— r(1/8) q^-80/9 δ|^0
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-2/cxKhr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ -6 q^-13 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-8 δ|^-1
2) h^ -5 q^-11 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-6 δ|^-1
3) h^ -4 q^ -9 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-4 δ|^-1
4) h^-10 q^-19 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-14 δ|^0
5) h^ -9 q^-17 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-12 δ|^0
6) h^ -8 q^-15 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-10 δ|^0
7) h^-13 q^-23 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-18 δ|^1
8) h^-12 q^-21 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-16 δ|^1
9) h^ -9 q^-17 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— r(1/8) q^-80/9 δ|^0
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-2/cxKhr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ -6 q^-13 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-8 δ|^-1
2) h^ -5 q^-11 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-6 δ|^-1
3) h^ -4 q^ -9 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-4 δ|^-1
4) h^-10 q^-19 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-14 δ|^0
5) h^ -9 q^-17 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-12 δ|^0
6) h^ -8 q^-15 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-10 δ|^0
7) h^-13 q^-23 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-18 δ|^1
8) h^-12 q^-21 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-16 δ|^1
9) h^ -9 q^-17 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— r(1/8) q^-80/9 δ|^0
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-2/cxKhr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ -6 q^-13 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-8 δ|^-1
2) h^ -5 q^-11 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-6 δ|^-1
3) h^ -4 q^ -9 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-4 δ|^-1
4) h^-10 q^-19 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-14 δ|^0
5) h^ -9 q^-17 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-12 δ|^0
6) h^ -8 q^-15 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-10 δ|^0
7) h^-13 q^-23 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-18 δ|^1
8) h^-12 q^-21 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-16 δ|^1
9) h^ -9 q^-17 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— r(1/8) q^-80/9 δ|^0
Khovanov type D structure \(\mathrm{\widetilde{CKh}}(L)\)
options -c0
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-2/cxCKh-c0', generated by kht, version v0.1, on Sun Mar 7 15:45:53 2021 GMT
1) h^ 0 q^ -4 δ^-2 ⬮
2) h^-6 q^-16 δ^-2 ⬮——H—>⬮
3) h^-5 q^-14 δ^-2 ⬮——H—>⬮
4) h^-4 q^-12 δ^-2 ⬮——H—>⬮
5) h^-3 q^-10 δ^-2 ⬮——H—>⬮
6) h^-3 q^-10 δ^-2 ⬮——H—>⬮
7) h^-2 q^ -8 δ^-2 ⬮——H—>⬮
8) h^-1 q^ -6 δ^-2 ⬮——H—>⬮
9) h^ 1 q^ -2 δ^-2 ⬮——H—>⬮
options -c2
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-2/cxCKh-c2', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^ 0 q^ -4 δ^-2 ⬮
2) h^-6 q^-16 δ^-2 ⬮——H—>⬮
3) h^-5 q^-14 δ^-2 ⬮——H—>⬮
4) h^-4 q^-12 δ^-2 ⬮——H—>⬮
5) h^-3 q^-10 δ^-2 ⬮——H—>⬮
6) h^-3 q^-10 δ^-2 ⬮——H—>⬮
7) h^-2 q^ -8 δ^-2 ⬮——H—>⬮
8) h^-1 q^ -6 δ^-2 ⬮——H—>⬮
9) h^ 1 q^ -2 δ^-2 ⬮——H—>⬮
options -c3
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-2/cxCKh-c3', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^ 0 q^ -4 δ^-2 ⬮
2) h^-6 q^-16 δ^-2 ⬮——H—>⬮
3) h^-5 q^-14 δ^-2 ⬮——H—>⬮
4) h^-4 q^-12 δ^-2 ⬮——H—>⬮
5) h^-3 q^-10 δ^-2 ⬮——H—>⬮
6) h^-3 q^-10 δ^-2 ⬮——H—>⬮
7) h^-2 q^ -8 δ^-2 ⬮——H—>⬮
8) h^-1 q^ -6 δ^-2 ⬮——H—>⬮
9) h^ 1 q^ -2 δ^-2 ⬮——H—>⬮
options -c5
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-2/cxCKh-c5', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^ 0 q^ -4 δ^-2 ⬮
2) h^-6 q^-16 δ^-2 ⬮——H—>⬮
3) h^-5 q^-14 δ^-2 ⬮——H—>⬮
4) h^-4 q^-12 δ^-2 ⬮——H—>⬮
5) h^-3 q^-10 δ^-2 ⬮——H—>⬮
6) h^-3 q^-10 δ^-2 ⬮——H—>⬮
7) h^-2 q^ -8 δ^-2 ⬮——H—>⬮
8) h^-1 q^ -6 δ^-2 ⬮——H—>⬮
9) h^ 1 q^ -2 δ^-2 ⬮——H—>⬮
options -c7
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-2/cxCKh-c7', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^ 0 q^ -4 δ^-2 ⬮
2) h^-6 q^-16 δ^-2 ⬮——H—>⬮
3) h^-5 q^-14 δ^-2 ⬮——H—>⬮
4) h^-4 q^-12 δ^-2 ⬮——H—>⬮
5) h^-3 q^-10 δ^-2 ⬮——H—>⬮
6) h^-3 q^-10 δ^-2 ⬮——H—>⬮
7) h^-2 q^ -8 δ^-2 ⬮——H—>⬮
8) h^-1 q^ -6 δ^-2 ⬮——H—>⬮
9) h^ 1 q^ -2 δ^-2 ⬮——H—>⬮
options -c11
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-2/cxCKh-c11', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^ 0 q^ -4 δ^-2 ⬮
2) h^-6 q^-16 δ^-2 ⬮——H—>⬮
3) h^-5 q^-14 δ^-2 ⬮——H—>⬮
4) h^-4 q^-12 δ^-2 ⬮——H—>⬮
5) h^-3 q^-10 δ^-2 ⬮——H—>⬮
6) h^-3 q^-10 δ^-2 ⬮——H—>⬮
7) h^-2 q^ -8 δ^-2 ⬮——H—>⬮
8) h^-1 q^ -6 δ^-2 ⬮——H—>⬮
9) h^ 1 q^ -2 δ^-2 ⬮——H—>⬮