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Input data and context
% PT3m3
r1.y0.x2.y0.x2.y0.x2.u1
,1,0
Bar-Natan multicurve \(\mathrm{\widetilde{BN}}(T)\)
options -c0
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT3m3/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)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c2
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT3m3/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) s4(0) q^0 δ|^0: h^-3 q^-5 δ^1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c3
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT3m3/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)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c5
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT3m3/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)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c7
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT3m3/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)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c11
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT3m3/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)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
HF-minus multicurve \(\mathrm{HF}^-(T)\)
options -c2P.r1.pqm
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT3m3/cxHFr-c2P.r1.pqm', generated by kht++ v0.1-105-g07ddf05 on Tue Apr 7 14:55:13 2026 GMT
HFT multicurve \(\mathrm{HFT}(T)\)
options -c2P.r1.pqm
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT3m3/cxHFT-c2P.r1.pqm', generated by kht++ v0.1-105-g07ddf05 on Tue Apr 7 14:55:13 2026 GMT
1) r(0) q^0 δ|^0: h^ 0 q^ 0 δ^0 a——p——c~
2) s2(0) q^-1 δ|^0: h^-1 q^-2 δ^0 a——p——c~d—a~c—d~
3) s2(0) q^1 δ|^0: h^ 0 q^ 0 δ^0 a——p——c~d—a~c—d~
4) s2(0) q^-1 δ|^0: h^-1 q^-2 δ^0 a——p——b~c—a~b—c~
5) s2(0) q^1 δ|^0: h^ 0 q^ 0 δ^0 a——p——b~c—a~b—c~
Khovanov multicurve \(\mathrm{\widetilde{Kh}}(T)\)
options -c0
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT3m3/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
options -c2
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT3m3/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) s4(0) q^-1 δ|^1/2: h^-4 q^-6 δ^ 1 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) s4(0) q^1 δ|^1/2: h^-3 q^-4 δ^ 1 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c3
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT3m3/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
options -c5
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT3m3/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
options -c7
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT3m3/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
options -c11
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT3m3/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