# B46: authoritative ordered generator list

For a proper triangle P, F(lambda,Xi)=G(P)+lambda*(Xi(P)-G(P)).
The 44 rational rows use normalized cyclic barycentric source weights, not unnormalized f=1+lambda*fX.
M_p minimizes the sum of the p-th powers of the distances to the three vertices.

| B46 position | Generator |
| ---: | --- |
| 1 | F(1,X598) |
| 2 | F(1,X4193) |
| 3 | F(1,X10523) |
| 4 | F(1,X12877) |
| 5 | F(1,X27277) |
| 6 | F(1,X27328) |
| 7 | F(1,X39141) |
| 8 | F(1,X59572) |
| 9 | F(1,X59639) |
| 10 | F(1,X66632) |
| 11 | F(-2/7,X2093) |
| 12 | F(-1/3,X2255) |
| 13 | F(1,X3794) |
| 14 | F(8/5,X3825) |
| 15 | F(-1/2,X4308) |
| 16 | F(1,X4342) |
| 17 | F(-2,X4438) |
| 18 | F(2/5,X4911) |
| 19 | F(-1/4,X5310) |
| 20 | F(-1/2,X5741) |
| 21 | F(-1/2,X6205) |
| 22 | F(-4/3,X7872) |
| 23 | F(5/11,X9597) |
| 24 | F(7/6,X10000) |
| 25 | F(1/2,X11164) |
| 26 | F(-1/2,X11373) |
| 27 | F(1,X10935) |
| 28 | F(1,X18236) |
| 29 | F(-27/2,X13725) |
| 30 | F(-2/7,X10324) |
| 31 | F(1/10,X10978) |
| 32 | F(5/12,X14997) |
| 33 | F(1,X10321) |
| 34 | M_(4-2 sqrt(2)) |
| 35 | M_(4+2 sqrt(2)) |
| 36 | F(1,X24211) |
| 37 | F(1,X24212) |
| 38 | F(1,X24217) |
| 39 | F(1,X35999) |
| 40 | F(1,X37280) |
| 41 | F(1,X43180) |
| 42 | F(1,X59689) |
| 43 | F(1,X68177) |
| 44 | F(1,X32979) |
| 45 | F(1,X37608) |
| 46 | F(1,X69251) |

R44 means B46 WITHOUT both power centers.
The proposed B44 means B46 WITHOUT F(-1/3,X2255) and X3794; it retains both powers and is NOT proved sufficient.
B46 is proved hull-equivalent to B76; the minimum subfamily size of that fixed reference is bounded by 44 and 46.
Neither exact minimum size nor equality with the maximal Heart is established.