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George Duke wrote on Tue, Jan 31, 2012 04:21 PM UTC:

Thanks Jorg, I got to rechecking not sovereign (Quintessence 3.5, 2) but
TABLE OF SOVEREIGN VALUES(II)Venator below. Corrections when several will
P/T         P/V   Mate#   be entried. Sovereign (Venator 3.5/5) would not
CANNON      4.5   3      be surprising Mate# turns out 4 or 6, not 5,     
CANNON PAWN 2.2   4      though '5' checks out the second test on paper
QUADRA-PAWN 2.0   3      only.  A generality: Mating Number  >=3, the 
HALF DUCK   4.5   2      set-up position of checkmate is attainable in
NAHBI       5.0   2      practice over the board.  However, mating
UNICORN     6.5   1      numbers 2 and 1 tend to need computer veri-
DABBABANTE  5.5   2      fication.  A subclass of '1's, (Rook 5.0/1)
SISSA       6.0   1      for one, of course are obvious cases without
WOLF        3.75  2      computer. For example, White Venators c4, d3,
PRIEST      4.25  2      d4, f4, f5, King c2, beat Black King d1. 
WATER ROOK  3.0   2      Checkmate. It's important to test the plausible last two or three moves.  A last move by White could be Venator g5-d4, delivering the Checkmate. So '5' is probably the right Mate# sovereign (Venator 3.5/5).  How can a mating number be '0'?  They belong not exclusively to cases of piece-types having negative value; it may have some value but not for check or checkmate, for eventual follow-up.

Jörg Knappen wrote on Tue, Jan 31, 2012 08:37 AM UTC:

Hi George,

I think the mating number of the quintessence is 2. Even a single
quintessence comes very close to a mate, but it cannot strike the final
blow to the enclosed King.

George Duke wrote on Mon, Jan 30, 2012 04:49 PM UTC:

If doing your own, fear not mistakes, shun not corrections. They are the essence of good CV-ing. Less exhibitionist NextChessesXXs for entire CVS not piece-types alone, submit to trial and error too. Chess herself undergoes revision -- adding Queen, Castling, stripping the King's Leap and Knight's Odds. Even some of the Mating Numbers stated are not entirely clear yet. 'Mate#' means with King alone. 'Each piece-type has a Mating Number' is the breakthrough realization.
Just a name/definition hanging in space without two numbers is unknowable.
The mathematical object is just not defined that limited way.
The Mate# is either 0, 1, 2, 3, or 4, or 5, with the one '5' listed
provisional.  Until you have stated a value/use, you have not invented
given p-t, however earnestly put into words or CV art. A '6' or more is certainly theoretically possible.  MN and PV, name and definition become the four pillars.  As for the piece-value column, there are over 25 documented tests and they need to be collated.  For now use two or more of your choosing.  The required numbers move the left side of a reaction, Name and Definition, to full SOVEREIGNTY on the right. Sovereign piece-type country, the world of Caissa herself reclaiming.

George Duke wrote on Mon, Jan 30, 2012 04:26 PM UTC:

For example, ''GIMEL'' has no meaning at all.  It remains as empty as
''LEMIG,'' undefined without credit of invention. ''GIMEL 4.0'' 
(I)_______________________ now defines a problemists' piece-type only.
TABLE OF SOVEREIGN VALUES  ''GIMEL 4.0, 4'' is a sovereign piece-type
P/T      P/Value   Mate#   proper. Acceptable to tag ''invented by...''
ROOK         5.0    1      Each piece-type must needs a computation
FALCON       5.0    1    of value to un-shackle blanket trivialization.
COMMONER     3.0    1    Without at least the other two columns left,
BISHOP       3.0    2    ordered pair, each indexing future and past,
KNIGHT       3.0    3    is an essential nullity.  Such jejune
CAMEL        2.5    3    cataloguing without number is not Emperor
ZEBRA        3.0    3    without clothes, it's Emperor stripped of
FERZ/MET     2.0    4    skin alive, a ghastly de-sentientation and
GRYPHON      4.0    1    and dis-corporation ('Stranger in a Strange
SQUIRREL     5.5    1    Land').  Each piece value should be read as
BENT HERO    4.5    1    range +/- 0.25 applicable to most likely 
QUINTESSENCE 4.0    3    environments.  Common sense applies in such
VENATOR      3.5    5    as no 6x6 or 75% piece-density to base
IMMOBILIZER 10.0    1    educated estimations.    The 
table above is preliminary, subject to /_\.   One key other compendium, articles M&Bxxs constantly re-name albeit 'undefineds' by above criterion.

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