The one-term relation in the theory of chord diagrams, also called the framing-independence relation or 1T relation, sets a chord diagram to zero when it has a chord whose endpoints are consecutive in the cyclic order of the marked points. It is imposed for unframed knots in addition to the four-term relations (Chmutov and Duzhin 2005, p. 2).
Modulo the four-term relations, this is equivalent to setting a chord diagram to zero whenever it contains a chord that intersects no other chord (Bar-Natan 1995, author version, pp. 4, 18). Here intersection means alternation of the two pairs of endpoints in the cyclic order, independently of how the chords are drawn. Indeed, a chord that intersects no other chord separates all remaining chords into two parts. The cut-independence of multiplication in the algebra of chord diagrams moves either part away from the arc between its endpoints, leaving a representative with consecutive endpoints.
In particular, the degree-one chord diagram is zero in the unframed quotient. A weight system for unframed knots vanishes on every diagram satisfying the one-term relation.
