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Input data and context
% PT3m3
r1.l3.
y0.x2.y0.x2.y0.x2.
y0.x2.y0.x2.y0.x2.
y0.x2.
u1
,1
Bar-Natan multicurve \(\mathrm{\widetilde{BN}}(T)\)
options -c0
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT7m7/cxBNr-c0', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^ 0 q^ 0 δ^ 0 ⬮
2) h^-3 q^ -5 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^-5 q^ -9 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^-7 q^-13 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c2
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT7m7/cxBNr-c2', generated by kht++ v0.1-110-gad0cb61-dirty on Mon Jun 1 16:47:17 2026 GMT
1) h^ 0 q^ 0 δ^ 0 ⬮
2) s12(0) q^0 δ|^0: h^-7 q^-13 δ^1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) s8(0) q^0 δ|^0: h^-5 q^ -9 δ^1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) s4(0) q^0 δ|^0: h^-3 q^ -5 δ^1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c3
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT7m7/cxBNr-c3', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^ 0 q^ 0 δ^ 0 ⬮
2) h^-3 q^ -5 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^-5 q^ -9 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^-7 q^-13 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c5
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT7m7/cxBNr-c5', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^ 0 q^ 0 δ^ 0 ⬮
2) h^-3 q^ -5 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^-5 q^ -9 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^-7 q^-13 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c7
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT7m7/cxBNr-c7', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^ 0 q^ 0 δ^ 0 ⬮
2) h^-3 q^ -5 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^-5 q^ -9 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^-7 q^-13 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c11
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT7m7/cxBNr-c11', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^ 0 q^ 0 δ^ 0 ⬮
2) h^-3 q^ -5 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^-5 q^ -9 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^-7 q^-13 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
Khovanov multicurve \(\mathrm{\widetilde{Kh}}(T)\)
options -c0
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT7m7/cxKhr-c0', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^-1 q^ -1 δ^1/2 ⬮~~(-S^2)~>⬮<— r(0) q^0 δ|^1/2
2) h^-4 q^ -6 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-1 δ|^1/2
3) h^-3 q^ -4 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^1 δ|^1/2
4) h^-6 q^-10 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-1 δ|^1/2
5) h^-5 q^ -8 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^1 δ|^1/2
6) h^-8 q^-14 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s6(0) q^-1 δ|^1/2
7) h^-7 q^-12 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s6(0) q^1 δ|^1/2
options -c2
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT7m7/cxKhr-c2', generated by kht++ v0.1-110-gad0cb61-dirty on Mon Jun 1 16:47:17 2026 GMT
1) r(0) q^0 δ|^1/2: h^-1 q^ -1 δ^1/2 ⬮~~S^2~>⬮<—
2) s12(0) q^-1 δ|^1/2: h^-8 q^-14 δ^ 1 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) s12(0) q^1 δ|^1/2: h^-7 q^-12 δ^ 1 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) s8(0) q^-1 δ|^1/2: h^-6 q^-10 δ^ 1 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
5) s8(0) q^1 δ|^1/2: h^-5 q^ -8 δ^ 1 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
6) s4(0) q^-1 δ|^1/2: h^-4 q^ -6 δ^ 1 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
7) s4(0) q^1 δ|^1/2: h^-3 q^ -4 δ^ 1 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c3
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT7m7/cxKhr-c3', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^-1 q^ -1 δ^1/2 ⬮~~(-S^2)~>⬮<— r(0) q^0 δ|^1/2
2) h^-4 q^ -6 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-1 δ|^1/2
3) h^-3 q^ -4 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^1 δ|^1/2
4) h^-6 q^-10 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-1 δ|^1/2
5) h^-5 q^ -8 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^1 δ|^1/2
6) h^-8 q^-14 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s6(0) q^-1 δ|^1/2
7) h^-7 q^-12 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s6(0) q^1 δ|^1/2
options -c5
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT7m7/cxKhr-c5', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^-1 q^ -1 δ^1/2 ⬮~~(-S^2)~>⬮<— r(0) q^0 δ|^1/2
2) h^-4 q^ -6 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-1 δ|^1/2
3) h^-3 q^ -4 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^1 δ|^1/2
4) h^-6 q^-10 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-1 δ|^1/2
5) h^-5 q^ -8 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^1 δ|^1/2
6) h^-8 q^-14 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s6(0) q^-1 δ|^1/2
7) h^-7 q^-12 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s6(0) q^1 δ|^1/2
options -c7
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT7m7/cxKhr-c7', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^-1 q^ -1 δ^1/2 ⬮~~(-S^2)~>⬮<— r(0) q^0 δ|^1/2
2) h^-4 q^ -6 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-1 δ|^1/2
3) h^-3 q^ -4 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^1 δ|^1/2
4) h^-6 q^-10 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-1 δ|^1/2
5) h^-5 q^ -8 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^1 δ|^1/2
6) h^-8 q^-14 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s6(0) q^-1 δ|^1/2
7) h^-7 q^-12 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s6(0) q^1 δ|^1/2
options -c11
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT7m7/cxKhr-c11', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^-1 q^ -1 δ^1/2 ⬮~~(-S^2)~>⬮<— r(0) q^0 δ|^1/2
2) h^-4 q^ -6 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-1 δ|^1/2
3) h^-3 q^ -4 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^1 δ|^1/2
4) h^-6 q^-10 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-1 δ|^1/2
5) h^-5 q^ -8 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^1 δ|^1/2
6) h^-8 q^-14 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s6(0) q^-1 δ|^1/2
7) h^-7 q^-12 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s6(0) q^1 δ|^1/2