12 21
13 29
14 39
15 52
16 70
17 91
18 119
19 155
L = 21: 254 Hilbert functions
    136101 vc_DJNT  [DJNT, Proposition~1.2]
    13692 individual  Table tab:atlas, thm:S4
    136911 tail4  Proposition~\ref{prop:tails}(1)
    13683 individual  Table tab:atlas, thm:S4
    136821 individual  Table tab:atlas, thm:136821
    1368111 tail4  Proposition~\ref{prop:tails}(1)
    13674 individual  Table tab:atlas, thm:S4
    136731 individual  Table tab:atlas, thm:136731
    136722 individual  Table tab:atlas, thm:136722
    1367211 two_ones  Theorem~\ref{thm:136c211}
    13671111 tail4  Proposition~\ref{prop:tails}(1)
    13665 individual  Table tab:atlas, thm:S4
    136641 individual  Table tab:atlas, thm:136641
    136632 individual  Table tab:atlas, thm:136632
    1366311 individual  Table tab:atlas, thm:1366311
    1366221 individual  Table tab:atlas, thm:1366221
    13662111 septic  Lemma~\ref{lem:septic}
    136611111 tail4  Proposition~\ref{prop:tails}(1)
    13656 individual  Table tab:atlas, thm:S4
    136551 individual  Table tab:atlas, thm:136551
    136542 individual  Table tab:atlas, thm:136542
    1365411 individual  Table tab:atlas, thm:1365411
    136533 individual  Table tab:atlas, thm:136533
    1365321 individual  Table tab:atlas, thm:1365321
    13653111 septic  Lemma~\ref{lem:septic}
    1365222 individual  Table tab:atlas, thm:1365222
    13652211 individual  Table tab:atlas, thm:13652211
    136521111 longtail  Proposition~\ref{prop:tails}(2)
    1365111111 tail4  Proposition~\ref{prop:tails}(1)
    136452 individual  Table tab:atlas, thm:136452
    1364511 individual  Table tab:atlas, thm:1364511
    136443 individual  Table tab:atlas, thm:136443
    1364421 individual  Table tab:atlas, thm:1364421
    13644111 septic  Lemma~\ref{lem:septic}
    1364331 individual  Table tab:atlas, thm:1364331
    1364322 individual  Table tab:atlas, thm:1364322
    13643211 individual  Table tab:atlas, thm:13643211
    136431111 longtail  Proposition~\ref{prop:tails}(2)
    13642221 individual  Table tab:atlas, thm:13642221
    136422111 individual  Table tab:atlas, thm:136422111
    1364211111 longtail  Proposition~\ref{prop:tails}(2)
    13641111111 tail4  Proposition~\ref{prop:tails}(1)
    1363332 threepoints  Corollaries~\ref{cor:threepoints}, \ref{cor:fatpoint}
    13633311 individual  Table tab:atlas, thm:13633311
    13633221 individual  Table tab:atlas, thm:13633221
    136332111 individual  Table tab:atlas, thm:136332111
    1363311111 longtail  Proposition~\ref{prop:tails}(2)
    13632222 individual  Table tab:atlas, thm:13632222
    136322211 individual  Table tab:atlas, thm:136322211
    1363221111 individual  Table tab:atlas, thm:1363221111
    13632111111 longtail  Proposition~\ref{prop:tails}(2)
    136311111111 tail4  Proposition~\ref{prop:tails}(1)
    136222221 twopoints  Corollary~\ref{cor:twopoints}
    1362222111 twopoints  Corollary~\ref{cor:twopoints}
    13622211111 longtail  Proposition~\ref{prop:tails}(2)
    136221111111 longtail  Proposition~\ref{prop:tails}(2)
    1362111111111 tail4  Proposition~\ref{prop:tails}(1)
    13611111111111 tail4  Proposition~\ref{prop:tails}(1)
    13575 socle4  Corollary~\ref{cor:socle4}
    135741 socle5  Corollary~\ref{cor:socle5}
    135732 individual  Table tab:atlas, thm:135732
    1357311 quadrictails  Proposition~\ref{prop:quadrictails}
    1357221 quadrictails  Proposition~\ref{prop:quadrictails}
    13572111 quadrictails  Proposition~\ref{prop:quadrictails}
    135711111 longtail  Proposition~\ref{prop:tails}(2)
    13566 socle4  Corollary~\ref{cor:socle4}
    135651 socle5  Corollary~\ref{cor:socle5}
    135642 individual  Table tab:atlas, thm:135642
    1356411 quadrictails  Proposition~\ref{prop:quadrictails}
    135633 socle5plane  Corollary~\ref{cor:socle5plane}
    1356321 individual  Table tab:atlas, thm:1356321
    13563111 quadrictails  Proposition~\ref{prop:quadrictails}
    1356222 quadrictails  Proposition~\ref{prop:quadrictails}
    13562211 quadrictails  Proposition~\ref{prop:quadrictails}
    135621111 longtail  Proposition~\ref{prop:tails}(2)
    1356111111 longtail  Proposition~\ref{prop:tails}(2)
    135561 socle5  Corollary~\ref{cor:socle5}
    135552 individual  Table tab:atlas, thm:135552
    1355511 quadrictails  Proposition~\ref{prop:quadrictails}
    135543 individual  Table tab:atlas, thm:135543
    1355421 individual  Table tab:atlas, thm:1355421
    13554111 quadrictails  Proposition~\ref{prop:quadrictails}
    1355331 individual  Table tab:atlas, thm:1355331
    1355322 individual  Table tab:atlas, thm:1355322
    13553211 individual  Table tab:atlas, thm:13553211
    135531111 longtail  Proposition~\ref{prop:tails}(2)
    13552221 individual  Table tab:atlas, thm:13552221
    135522111 individual  Table tab:atlas, thm:13552221
    1355211111 longtail  Proposition~\ref{prop:tails}(2)
    13551111111 longtail  Proposition~\ref{prop:tails}(2)
    135453 individual  Table tab:atlas, thm:135453
    1354521 individual  Table tab:atlas, thm:1354521
    13545111 quadrictails  Proposition~\ref{prop:quadrictails}
    135444 individual  Table tab:atlas, thm:135444
    1354431 individual  Table tab:atlas, thm:radialturn
    1354422 individual  Table tab:atlas, thm:radialturn
    13544211 individual  Table tab:atlas, thm:13544211
    135441111 longtail  Proposition~\ref{prop:tails}(2)
    1354332 individual  Table tab:atlas, thm:radialturn
    13543311 individual  Table tab:atlas, thm:13543311
    13543221 individual  Table tab:atlas, thm:13543221
    135432111 individual  Table tab:atlas, thm:135432111
    1354311111 longtail  Proposition~\ref{prop:tails}(2)
    13542222 individual  Table tab:atlas, thm:13542222
    135422211 individual  Table tab:atlas, thm:135422211
    1354221111 individual  Table tab:atlas, thm:1354221111
    13542111111 longtail  Proposition~\ref{prop:tails}(2)
    135411111111 longtail  Proposition~\ref{prop:tails}(2)
    1353333 E6pencil  Theorem~\ref{thm:E6pencil}
    13533321 E6pencil  Theorem~\ref{thm:E6pencil}
    135333111 E6pencil  Theorem~\ref{thm:E6pencil}
    13533222 E6pencil  Theorem~\ref{thm:E6pencil}
    135332211 E6pencil  Theorem~\ref{thm:E6pencil}
    1353321111 E6pencil  Theorem~\ref{thm:E6pencil}
    13533111111 E6pencil  Theorem~\ref{thm:E6pencil}
    135322221 E6pencil  Theorem~\ref{thm:E6pencil}
    1353222111 E6pencil  Theorem~\ref{thm:E6pencil}
    13532211111 E6pencil  Theorem~\ref{thm:E6pencil}
    135321111111 E6pencil  Theorem~\ref{thm:E6pencil}
    1353111111111 E6pencil  Theorem~\ref{thm:E6pencil}
    135222222 surface  Theorem~\ref{thm:surfaces}(1)
    1352222211 surface  Theorem~\ref{thm:surfaces}(1)
    13522221111 surface  Theorem~\ref{thm:surfaces}(1)
    135222111111 surface  Theorem~\ref{thm:surfaces}(1)
    1352211111111 surface  Theorem~\ref{thm:surfaces}(1)
    13521111111111 surface  Theorem~\ref{thm:surfaces}(1)
    135111111111111 surface  Theorem~\ref{thm:surfaces}(1)
    134562 surface  Theorem~\ref{thm:surfaces}(1)
    1345611 surface  Theorem~\ref{thm:surfaces}(1)
    134553 surface  Theorem~\ref{thm:surfaces}(1)
    1345521 surface  Theorem~\ref{thm:surfaces}(1)
    13455111 surface  Theorem~\ref{thm:surfaces}(1)
    134544 surface  Theorem~\ref{thm:surfaces}(1)
    1345431 surface  Theorem~\ref{thm:surfaces}(1)
    1345422 surface  Theorem~\ref{thm:surfaces}(1)
    13454211 surface  Theorem~\ref{thm:surfaces}(1)
    134541111 surface  Theorem~\ref{thm:surfaces}(1)
    1345332 surface  Theorem~\ref{thm:surfaces}(1)
    13453311 surface  Theorem~\ref{thm:surfaces}(1)
    13453221 surface  Theorem~\ref{thm:surfaces}(1)
    134532111 surface  Theorem~\ref{thm:surfaces}(1)
    1345311111 surface  Theorem~\ref{thm:surfaces}(1)
    13452222 surface  Theorem~\ref{thm:surfaces}(1)
    134522211 surface  Theorem~\ref{thm:surfaces}(1)
    1345221111 surface  Theorem~\ref{thm:surfaces}(1)
    13452111111 surface  Theorem~\ref{thm:surfaces}(1)
    134511111111 surface  Theorem~\ref{thm:surfaces}(1)
    134454 surface  Theorem~\ref{thm:surfaces}(1)
    1344531 surface  Theorem~\ref{thm:surfaces}(1)
    1344522 surface  Theorem~\ref{thm:surfaces}(1)
    13445211 surface  Theorem~\ref{thm:surfaces}(1)
    134451111 surface  Theorem~\ref{thm:surfaces}(1)
    1344441 surface  Theorem~\ref{thm:surfaces}(1)
    1344432 surface  Theorem~\ref{thm:surfaces}(1)
    13444311 surface  Theorem~\ref{thm:surfaces}(1)
    13444221 surface  Theorem~\ref{thm:surfaces}(1)
    134442111 surface  Theorem~\ref{thm:surfaces}(1)
    1344411111 surface  Theorem~\ref{thm:surfaces}(1)
    1344333 surface  Theorem~\ref{thm:surfaces}(1)
    13443321 surface  Theorem~\ref{thm:surfaces}(1)
    134433111 surface  Theorem~\ref{thm:surfaces}(1)
    13443222 surface  Theorem~\ref{thm:surfaces}(1)
    134432211 surface  Theorem~\ref{thm:surfaces}(1)
    1344321111 surface  Theorem~\ref{thm:surfaces}(1)
    13443111111 surface  Theorem~\ref{thm:surfaces}(1)
    134422221 surface  Theorem~\ref{thm:surfaces}(1)
    1344222111 surface  Theorem~\ref{thm:surfaces}(1)
    13442211111 surface  Theorem~\ref{thm:surfaces}(1)
    134421111111 surface  Theorem~\ref{thm:surfaces}(1)
    1344111111111 surface  Theorem~\ref{thm:surfaces}(1)
    13433331 surface  Theorem~\ref{thm:surfaces}(1)
    13433322 surface  Theorem~\ref{thm:surfaces}(1)
    134333211 surface  Theorem~\ref{thm:surfaces}(1)
    1343331111 surface  Theorem~\ref{thm:surfaces}(1)
    134332221 surface  Theorem~\ref{thm:surfaces}(1)
    1343322111 surface  Theorem~\ref{thm:surfaces}(1)
    13433211111 surface  Theorem~\ref{thm:surfaces}(1)
    134331111111 surface  Theorem~\ref{thm:surfaces}(1)
    134322222 surface  Theorem~\ref{thm:surfaces}(1)
    1343222211 surface  Theorem~\ref{thm:surfaces}(1)
    13432221111 surface  Theorem~\ref{thm:surfaces}(1)
    134322111111 surface  Theorem~\ref{thm:surfaces}(1)
    1343211111111 surface  Theorem~\ref{thm:surfaces}(1)
    13431111111111 surface  Theorem~\ref{thm:surfaces}(1)
    1342222221 surface  Theorem~\ref{thm:surfaces}(1)
    13422222111 surface  Theorem~\ref{thm:surfaces}(1)
    134222211111 surface  Theorem~\ref{thm:surfaces}(1)
    1342221111111 surface  Theorem~\ref{thm:surfaces}(1)
    13422111111111 surface  Theorem~\ref{thm:surfaces}(1)
    134211111111111 surface  Theorem~\ref{thm:surfaces}(1)
    1341111111111111 surface  Theorem~\ref{thm:surfaces}(1)
    133455 surface  Theorem~\ref{thm:surfaces}(1)
    1334541 surface  Theorem~\ref{thm:surfaces}(1)
    1334532 surface  Theorem~\ref{thm:surfaces}(1)
    13345311 surface  Theorem~\ref{thm:surfaces}(1)
    13345221 surface  Theorem~\ref{thm:surfaces}(1)
    133452111 surface  Theorem~\ref{thm:surfaces}(1)
    1334511111 surface  Theorem~\ref{thm:surfaces}(1)
    1334442 surface  Theorem~\ref{thm:surfaces}(1)
    13344411 surface  Theorem~\ref{thm:surfaces}(1)
    1334433 surface  Theorem~\ref{thm:surfaces}(1)
    13344321 surface  Theorem~\ref{thm:surfaces}(1)
    133443111 surface  Theorem~\ref{thm:surfaces}(1)
    13344222 surface  Theorem~\ref{thm:surfaces}(1)
    133442211 surface  Theorem~\ref{thm:surfaces}(1)
    1334421111 surface  Theorem~\ref{thm:surfaces}(1)
    13344111111 surface  Theorem~\ref{thm:surfaces}(1)
    13343331 surface  Theorem~\ref{thm:surfaces}(1)
    13343322 surface  Theorem~\ref{thm:surfaces}(1)
    133433211 surface  Theorem~\ref{thm:surfaces}(1)
    1334331111 surface  Theorem~\ref{thm:surfaces}(1)
    133432221 surface  Theorem~\ref{thm:surfaces}(1)
    1334322111 surface  Theorem~\ref{thm:surfaces}(1)
    13343211111 surface  Theorem~\ref{thm:surfaces}(1)
    133431111111 surface  Theorem~\ref{thm:surfaces}(1)
    133422222 surface  Theorem~\ref{thm:surfaces}(1)
    1334222211 surface  Theorem~\ref{thm:surfaces}(1)
    13342221111 surface  Theorem~\ref{thm:surfaces}(1)
    133422111111 surface  Theorem~\ref{thm:surfaces}(1)
    1334211111111 surface  Theorem~\ref{thm:surfaces}(1)
    13341111111111 surface  Theorem~\ref{thm:surfaces}(1)
    13333332 surface  Theorem~\ref{thm:surfaces}(1)
    133333311 surface  Theorem~\ref{thm:surfaces}(1)
    133333221 surface  Theorem~\ref{thm:surfaces}(1)
    1333332111 surface  Theorem~\ref{thm:surfaces}(1)
    13333311111 surface  Theorem~\ref{thm:surfaces}(1)
    133332222 surface  Theorem~\ref{thm:surfaces}(1)
    1333322211 surface  Theorem~\ref{thm:surfaces}(1)
    13333221111 surface  Theorem~\ref{thm:surfaces}(1)
    133332111111 surface  Theorem~\ref{thm:surfaces}(1)
    1333311111111 surface  Theorem~\ref{thm:surfaces}(1)
    1333222221 surface  Theorem~\ref{thm:surfaces}(1)
    13332222111 surface  Theorem~\ref{thm:surfaces}(1)
    133322211111 surface  Theorem~\ref{thm:surfaces}(1)
    1333221111111 surface  Theorem~\ref{thm:surfaces}(1)
    13332111111111 surface  Theorem~\ref{thm:surfaces}(1)
    133311111111111 surface  Theorem~\ref{thm:surfaces}(1)
    1332222222 surface  Theorem~\ref{thm:surfaces}(1)
    13322222211 surface  Theorem~\ref{thm:surfaces}(1)
    133222221111 surface  Theorem~\ref{thm:surfaces}(1)
    1332222111111 surface  Theorem~\ref{thm:surfaces}(1)
    13322211111111 surface  Theorem~\ref{thm:surfaces}(1)
    133221111111111 surface  Theorem~\ref{thm:surfaces}(1)
    1332111111111111 surface  Theorem~\ref{thm:surfaces}(1)
    13311111111111111 surface  Theorem~\ref{thm:surfaces}(1)
    13222222221 surface  Theorem~\ref{thm:surfaces}(1)
    132222222111 surface  Theorem~\ref{thm:surfaces}(1)
    1322222211111 surface  Theorem~\ref{thm:surfaces}(1)
    13222221111111 surface  Theorem~\ref{thm:surfaces}(1)
    132222111111111 surface  Theorem~\ref{thm:surfaces}(1)
    1322211111111111 surface  Theorem~\ref{thm:surfaces}(1)
    13221111111111111 surface  Theorem~\ref{thm:surfaces}(1)
    132111111111111111 surface  Theorem~\ref{thm:surfaces}(1)
    1311111111111111111 surface  Theorem~\ref{thm:surfaces}(1)
Table tab:general at d = 21 (first row that applies):
   surface       Theorem~\ref{thm:surfaces}(1)            134
   E6pencil      Theorem~\ref{thm:E6pencil}                12
   socle4        Corollary~\ref{cor:socle4}                 2
   socle5        Corollary~\ref{cor:socle5}                 3
   socle5plane   Corollary~\ref{cor:socle5plane}            1
   quadrictails  Proposition~\ref{prop:quadrictails}       10
   tail4         Proposition~\ref{prop:tails}(1)            9
   longtail      Proposition~\ref{prop:tails}(2)           17
   septic        Lemma~\ref{lem:septic}                     3
   twopoints     Corollary~\ref{cor:twopoints}              2
   threepoints   Corollaries~\ref{cor:threepoints}, \ref{cor:fatpoint}   1
   verycompressed Theorem~\ref{thm:vc}                       0
   c1_link       Theorem~\ref{thm:13641}                    0
   pencils       Proposition~\ref{prop:pencils}             0
   vc_DJNT       [DJNT, Proposition~1.2]                    1
   two_ones      Theorem~\ref{thm:136c211}                  1
   general 196, individual 58, total 254
Checks:
  ok   the 254 O-sequences of length 21 are distinct and start with (1,3)
  ok   254 Hilbert functions of length 21
  ok   per-row counts of Table tab:general: surface 134, E6pencil 12, socle4 2, socle5 3, socle5plane 1, quadrictails 10, tail4 9, longtail 17, septic 3, twopoints 2, threepoints 1, vc_DJNT 1, two_ones 1
  ok   the rows of [Twenty points] that are not in Table tab:general cover nothing at d = 21 (verycompressed, c1_link, pencils)
  ok   the very compressed row [DJNT, Prop. 1.2] applies exactly to (1,3,6,10,1): ['136101']
  ok   (1,3,6,10,1) is a Hilbert function of length 21 not covered by an earlier row
  ok   196 assigned to general rows
  ok   Table tab:atlas has 58 distinct rows
  ok   the Hilbert functions not covered by a general row are exactly the 58 rows of Table tab:atlas
  ok   no row of Table tab:atlas is covered by a general row
  ok   Table tab:atlas by section: H(2) = 6 and s <= 5: 15, H(2) = 6 and s >= 6: 19, H(2) = 5: 24 (15 + 19 + 24)
  ok   the table order of Table tab:atlas follows the three sections
  ok   254 = 196 + 58
checks: 13
ALL CHECKS PASSED
