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Abstract. Whether or not you like the formulas on this page, they describe the strongest truly computable knot invariant we know.
Handout: Elves.html, Elves.pdf, Elves.png.
A 4-hour version given at a time I knew a bit less is at LesDiablerets-1608.
A 2-hour version given a month ago is at Indiana-1611.
Sources: pensieve.