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Input data and context
% 4_1
r1.x0.r2.y1.x2.u3.x0.u1
,1
% generated from braid [1,-2,1,-2]
% det=5,scraped from knotinfo on 23 Mai 2021
Bar-Natan multicurve \(\mathrm{\widetilde{BN}}(T)\)
options -c2-d
(diagram)
(metadata)
% file 'examples/braids/4_1/cxBNr-c2-d', generated by kht++ v0.1-26-g9b33898 on Mon Aug 23 16:10:46 2021 GMT
1) h^ 0 q^ 0 δ^ 0 ⬯
2) h^ 2 q^ 2 δ^-1 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^-2 q^ -4 δ^ 0 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^-1 q^ -2 δ^ 0 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
5) h^-5 q^ -8 δ^ 1 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
6) h^-4 q^ -6 δ^ 1 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
7) h^-8 q^-12 δ^ 2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c3-d
(diagram)
(metadata)
% file 'examples/braids/4_1/cxBNr-c3-d', generated by kht++ v0.1-26-g9b33898 on Mon Aug 23 16:10:46 2021 GMT
1) h^ 0 q^ 0 δ^ 0 ⬯
2) h^ 4 q^ 6 δ^-1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
3) h^-1 q^ -2 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
4) h^-3 q^ -4 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
5) h^-8 q^-12 δ^ 2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
6) h^-4 q^ -6 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c5-d
(diagram)
(metadata)
% file 'examples/braids/4_1/cxBNr-c5-d', generated by kht++ v0.1-26-g9b33898 on Mon Aug 23 16:10:46 2021 GMT
1) h^ 0 q^ 0 δ^ 0 ⬯
2) h^ 4 q^ 6 δ^-1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
3) h^-1 q^ -2 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
4) h^-3 q^ -4 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
5) h^-8 q^-12 δ^ 2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
6) h^-4 q^ -6 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c7-d
(diagram)
(metadata)
% file 'examples/braids/4_1/cxBNr-c7-d', generated by kht++ v0.1-26-g9b33898 on Mon Aug 23 16:10:46 2021 GMT
1) h^ 0 q^ 0 δ^ 0 ⬯
2) h^ 4 q^ 6 δ^-1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
3) h^-1 q^ -2 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
4) h^-3 q^ -4 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
5) h^-8 q^-12 δ^ 2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
6) h^-4 q^ -6 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c11-d
(diagram)
(metadata)
% file 'examples/braids/4_1/cxBNr-c11-d', generated by kht++ v0.1-26-g9b33898 on Mon Aug 23 16:10:46 2021 GMT
1) h^ 0 q^ 0 δ^ 0 ⬯
2) h^ 4 q^ 6 δ^-1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
3) h^-1 q^ -2 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
4) h^-3 q^ -4 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
5) h^-8 q^-12 δ^ 2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
6) h^-4 q^ -6 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
Khovanov multicurve \(\mathrm{\widetilde{Kh}}(T)\)
options -c2-d
(diagram)
(metadata)
% file 'examples/braids/4_1/cxKhr-c2-d', generated by kht++ v0.1-26-g9b33898 on Mon Aug 23 16:10:46 2021 GMT
1) h^-1 q^ -1 δ^ 1/2 ⬯~~S^2~>⬯<— r(∞) q^0 δ_^1/2
2) h^ 1 q^ 1 δ^-1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^6 δ|^-1
3) h^ 2 q^ 3 δ^-1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^8 δ|^-1
4) h^-3 q^ -5 δ^ 1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^0 δ|^0
5) h^-2 q^ -3 δ^ 1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^2 δ|^0
6) h^-2 q^ -3 δ^ 1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^2 δ|^0
7) h^-1 q^ -1 δ^ 1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^4 δ|^0
8) h^-6 q^ -9 δ^ 3/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-4 δ|^1
9) h^-5 q^ -7 δ^ 3/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-2 δ|^1
10) h^-5 q^ -7 δ^ 3/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-2 δ|^1
11) h^-4 q^ -5 δ^ 3/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^0 δ|^1
12) h^-9 q^-13 δ^ 5/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-8 δ|^2
13) h^-8 q^-11 δ^ 5/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-6 δ|^2
options -c3-d
(diagram)
(metadata)
% file 'examples/braids/4_1/cxKhr-c3-d', generated by kht++ v0.1-26-g9b33898 on Mon Aug 23 16:10:46 2021 GMT
1) h^-1 q^ -1 δ^ 1/2 ⬯~~(-S^2)~>⬯<— r(∞) q^0 δ_^1/2
2) h^ 3 q^ 5 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^8 δ|^-1
3) h^ 4 q^ 7 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^10 δ|^-1
4) h^-2 q^ -3 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^0
5) h^-1 q^ -1 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^2 δ|^0
6) h^ 0 q^ 1 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^4 δ|^0
7) h^-5 q^ -7 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^-4 δ|^1
8) h^-4 q^ -5 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^-2 δ|^1
9) h^-3 q^ -3 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^1
10) h^-9 q^-13 δ^ 5/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^-10 δ|^2
11) h^-8 q^-11 δ^ 5/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^-8 δ|^2
12) h^-3 q^ -5 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^0 δ|^0
13) h^-4 q^ -5 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^0 δ|^1
options -c5-d
(diagram)
(metadata)
% file 'examples/braids/4_1/cxKhr-c5-d', generated by kht++ v0.1-26-g9b33898 on Mon Aug 23 16:10:46 2021 GMT
1) h^-1 q^ -1 δ^ 1/2 ⬯~~(-S^2)~>⬯<— r(∞) q^0 δ_^1/2
2) h^ 3 q^ 5 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^8 δ|^-1
3) h^ 4 q^ 7 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^10 δ|^-1
4) h^-2 q^ -3 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^0
5) h^-1 q^ -1 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^2 δ|^0
6) h^ 0 q^ 1 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^4 δ|^0
7) h^-5 q^ -7 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^-4 δ|^1
8) h^-4 q^ -5 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^-2 δ|^1
9) h^-3 q^ -3 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^1
10) h^-9 q^-13 δ^ 5/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^-10 δ|^2
11) h^-8 q^-11 δ^ 5/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^-8 δ|^2
12) h^-3 q^ -5 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^0 δ|^0
13) h^-4 q^ -5 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^0 δ|^1
options -c7-d
(diagram)
(metadata)
% file 'examples/braids/4_1/cxKhr-c7-d', generated by kht++ v0.1-26-g9b33898 on Mon Aug 23 16:10:46 2021 GMT
1) h^-1 q^ -1 δ^ 1/2 ⬯~~(-S^2)~>⬯<— r(∞) q^0 δ_^1/2
2) h^ 3 q^ 5 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^8 δ|^-1
3) h^ 4 q^ 7 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^10 δ|^-1
4) h^-2 q^ -3 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^0
5) h^-1 q^ -1 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^2 δ|^0
6) h^ 0 q^ 1 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^4 δ|^0
7) h^-5 q^ -7 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^-4 δ|^1
8) h^-4 q^ -5 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^-2 δ|^1
9) h^-3 q^ -3 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^1
10) h^-9 q^-13 δ^ 5/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^-10 δ|^2
11) h^-8 q^-11 δ^ 5/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^-8 δ|^2
12) h^-3 q^ -5 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^0 δ|^0
13) h^-4 q^ -5 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^0 δ|^1
options -c11-d
(diagram)
(metadata)
% file 'examples/braids/4_1/cxKhr-c11-d', generated by kht++ v0.1-26-g9b33898 on Mon Aug 23 16:10:46 2021 GMT
1) h^-1 q^ -1 δ^ 1/2 ⬯~~(-S^2)~>⬯<— r(∞) q^0 δ_^1/2
2) h^ 3 q^ 5 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^8 δ|^-1
3) h^ 4 q^ 7 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^10 δ|^-1
4) h^-2 q^ -3 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^0
5) h^-1 q^ -1 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^2 δ|^0
6) h^ 0 q^ 1 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^4 δ|^0
7) h^-5 q^ -7 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^-4 δ|^1
8) h^-4 q^ -5 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^-2 δ|^1
9) h^-3 q^ -3 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^1
10) h^-9 q^-13 δ^ 5/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^-10 δ|^2
11) h^-8 q^-11 δ^ 5/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^-8 δ|^2
12) h^-3 q^ -5 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^0 δ|^0
13) h^-4 q^ -5 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^0 δ|^1
Khovanov type D structure \(\mathrm{\widetilde{CKh}}(L)\)
options -c2
(diagram)
(metadata)
% file 'examples/braids/4_1/cxCKh-c2', generated by kht++ v0.1-25-gc037710 on Sun May 23 19:28:24 2021 GMT
1) h^ 0 q^ 0 δ^0 ⬮
2) h^-2 q^-4 δ^0 ⬮——H—>⬮
3) h^ 1 q^ 2 δ^0 ⬮——H—>⬮
options -c3
(diagram)
(metadata)
% file 'examples/braids/4_1/cxCKh-c3', generated by kht++ v0.1-25-gc037710 on Sun May 23 19:28:24 2021 GMT
1) h^ 0 q^ 0 δ^0 ⬮
2) h^-2 q^-4 δ^0 ⬮——H—>⬮
3) h^ 1 q^ 2 δ^0 ⬮——H—>⬮
options -c5
(diagram)
(metadata)
% file 'examples/braids/4_1/cxCKh-c5', generated by kht++ v0.1-25-gc037710 on Sun May 23 19:28:24 2021 GMT
1) h^ 0 q^ 0 δ^0 ⬮
2) h^-2 q^-4 δ^0 ⬮——H—>⬮
3) h^ 1 q^ 2 δ^0 ⬮——H—>⬮
options -c7
(diagram)
(metadata)
% file 'examples/braids/4_1/cxCKh-c7', generated by kht++ v0.1-25-gc037710 on Sun May 23 19:28:24 2021 GMT
1) h^ 0 q^ 0 δ^0 ⬮
2) h^-2 q^-4 δ^0 ⬮——H—>⬮
3) h^ 1 q^ 2 δ^0 ⬮——H—>⬮
options -c11
(diagram)
(metadata)
% file 'examples/braids/4_1/cxCKh-c11', generated by kht++ v0.1-25-gc037710 on Sun May 23 19:28:24 2021 GMT
1) h^ 0 q^ 0 δ^0 ⬮
2) h^-2 q^-4 δ^0 ⬮——H—>⬮
3) h^ 1 q^ 2 δ^0 ⬮——H—>⬮