T. Gittings (2004) noticed that it might be possible to calculate unlinking numbers from minimum braids. Unfortunately, this is true only for KLs with n £ 10 crossings, including the link 4 1 4 (9₄²) and the Nakanishi-Bleiler example 5 1 4 (10₈) with an unlinking gap. 

The minimum braid unlinking gap is the positive difference between the unlinking number obtained from a minimum braid u_B(L) and unlinking number u(L) of a link L, i.e., 

The unlinking gap for minimum braids appears for n = 11. The following alternating links given in the Conway notation, followed by their minimum braids have the minimum braid unlinking gap: 
 
 

.5.2		A5bAbAb2			8*3.2		A3bAbAbAb2
.3.4		A4bAbAb3			8*3:2		A3bA2bAbAb
8*4		A4bAbAbAb			8*2.2:.2		A2bAbA2bAb2
.2.3.3 0		A3bA3bAb2			10*2		A2bAbAbAbAb

For the links .5.2, .3.4 the value of minimum braid unlinking gap is d_B = 2, and for other links from this list d_B = 1. Hence, minimum braid unlinking number is different from the unlinking number and represents a new KL invariant. 

Periodic tables of KLs can be established in three ways: starting with families of KLs given in the Conway notation, with minimum braids (Gittings, 2004), or with BFRs. Since we have established correspondence between BFRs and KLs in the Conway notation, it follows that the same patterns (with regard to all KL polynomial invariants and KL properties) will appear in all cases. For example, for every family of KLs is possible to obtain a general formula for Alexander polynomials, with coefficients expressed by numbers denoting tangles in Conway symbols, or from their corresponding parameters from minimum braids or from BFRs. The same holds not only for KL polynomials, but for all other properties of KLs: writhe, amphicheirality, number of projections, unlinking number, signature, periods, etc.