Ha ha ha, the article is 84 pages long and most of them look like this.
I don't know what I expected.
robinhouston
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![A close-up of the label, which reads as follows:
ornament imitating the globular nest of a tree-building wasp. For hanging from house porch: Real combs sometimes hang with them.
(Formerly as traps for spirits).
EASTERN ANGAMI,
LESHEMIE (CHEROMA)
NAGA HILLS, [date obscured]
1.1. J.P. Mills, 1933.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:nhakixcsmdow4avnqxtfy6c6/bafkreial45lqofly4sdudsl4an6arwj4aoxvejqygnjgcajxcnhswtj5sm)
![3.1 AN INTEGRAL OVER KNOT POLYNOMIAL ROOTS EXPRESSING 7_2
Let A_{7_2}(M, L) denote the A-polynomial for the prime knot 7_2.
A_{7_2}(M,L) = L^5 + L^4 (M^14 — M^12 + 3M^4 + 4M^2 — 2)
+ L^3 (-2M^18 + 5M^16 + M^14 — 4M^12 + 6M^8 + 5M^6 + 2M^4 — 4M^2 +1)
+ L^2 (M^22 — 4M^20 + 2M^18 + 5M^16 + 6M^14 — 4M^10 + M^8 + 5M^6 — 2M^4)
+ L (—2M^22 + 4M^20 + 3M^18 — M^10 + M^8) + M^22,
Let α ≈ 0.349269... denote the real solution of A_{7_2} (α, α^(1/2)) = 0 closest to 0.349269. Let β ≈ 0.406813... denote the real solution of A_{7_2}(β, β) = 0 closest to 0.406813 Let y = y(z) denote the curve satisfying A(x, y(x)) = 0 for α ≤ x ≤ β and such that y(z) is positive and decreasing with y'(x) ≤ -2. Prove the following formula, which was discovered empirically:
\frac{4 \pi^2}{85} = \int_\alpha^\beta\left(\log x \frac{dy}{y} - \log y\frac{dx}{x}\right)
Context. This result is a surprisingly simple conjectural closed form of a Godbillon—Vey type Knot invariant [Khoi 2008].](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:nhakixcsmdow4avnqxtfy6c6/bafkreiau43xiruszraxmx34mxfpda6md3z6l5mbz3j77nqpa62npj5ybj4)
