S_21_d119_Z2_chiral

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An open knot — it matches no entry in the public knot tables (KnotInfo, and Burton’s complete census of prime knots through 19 crossings), and it is not marked as a novelty. Its crossing number is proven to be exactly 21: the span of its Jones polynomial equals the 21 crossings of our diagram (Kauffman–Murasugi–Thistlethwaite). It is alternating, and the alternating prime knots are enumerated further than all prime knots: through c = 23 in the published literature (Rankin, Flint & Schermann 2004) and through c = 24 by a later run (Fontaine, Rankin & Flint 2007). Those tables are not public either, so a knot in that range may be unmatched only because it cannot be looked up. A knot counts as a novelty candidate here only beyond both boundaries: c ≥ 25, or c ≥ 21 together with a proof that it is not alternating.

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