Tight knot constant

Upper bound, last-listed row

| 10.02| [Klotz2026] | $T(24,19)$ knot |tracked since 2026-07-24 — no movement seen yet

Lower bound, last-listed row

| $\left(\frac{4\pi}{11}\right)^{3/4}\approx 1.105$ | [BS1999] | Argument based on an "electromagnetic" knot energy. The 11 in the denominator can be replaced by 10.67, bringing the bound to 1.13, but it is always reported as 11. |tracked since 2026-07-24 — no movement seen yet

Checked against material for its cited source

• Another row, not one shown above: bound row 12.63 line 18 citing [ACPR2011] — the claim we checked: that the cited paper reports 12.63 for the 10_124 knot in the quantity this constant measures, the ropelength L divided by the crossing number C to the power 3/4. What we read could not settle it. source link (reached in the arXiv preprint only (arXiv:1002.1723v1, the only version): Table 2 on p. 27 and Table 5 on p. 40, read from page images, and the ropelength definition on p. 2. The Experimental Mathematics edition the entry cites was not reached: the publisher returned HTTP 403, the Wayback Machine returned HTTP 404 for the publisher's PDF URL, and OpenAlex lists the published DOI location without a PDF URL, its only PDF URL being the submitted arXiv version). Selected: drawn by its position in the list of cited rows, not because it looked wrong.

1 bound row(s) here have been checked against material for their cited source (1 drawn by position, 0 chosen because something already looked wrong). Across this whole ledger 70 row(s) have been drawn by position, against 691 rows that name a source, counted on 2026-09-27: 64 were checked against material for their cited sources and for 6 the cited source could not be read at all. 5 more were chosen for suspicion and checked; they are counted apart, because a set selected for suspicion carries no rate. A row not listed here has NOT been checked.