Reflective king and Anticirce

[WalterL-wL]

With Popeye v4.89 I tried to retrace a composition ser#5 by Maryan Kerhuel with a black reflective king and Anticirce (Phénix VIII/1995, basically also PDB P1205139). It covers a neutral superpawn (SBb6) and a royal white bishop (Lc8) instead of a white king, next to a black reflective king (brefK) on a8 and a bPa7. A refK under check can move like a king AND(!) like the checking piece(s). This shows as follows (German notation):

anfa
ford ser-#5
bedi Anticirce SchwarzerReflektierenderKoenig
Stei Weis Koeniglich Lc8   Schw Ka8 Ba7   Neut SBb6
Ende

Popeye presents a single solution (the standard is Anticirce type Calvet):
1.kLc8-g4 2.kLg4-d1 3.nSBb6-b8=nD 4.nDb8-e5 5.kLd1-f3#

Implying (and agreeing to) the following basic assumption in Popeye: The rebirth square of a black reflective king (brefK) is always e8, no matter what the actual move mode of his capturing move under (regular) Anticirce has been, like here, when capturing "as a bishop".
(In contrast, in the PDB version the rebirth square of the brefK seems to follow his actual move mode when capturing as a bishop/light square, and so would be c8, which is providently occupied in this version over there by a different 4th move ...4.nQb8-c8!...)

If this assumption for Popeye is correct, then the presented solution with 4.nQb8-e5 is false anyhow! Because the Qe5 does not occupy e8, but only threatens b8 and e8 from the distance. So, the square b8 correctly is no flight for the brefK, but then again as the bishop is the only white royal(!) piece the brefK can non the less capture it, immediately ending the game, without considering his (just) threatened rebirth square e8 (following the rule of Anticirce n.d.n.E.). So, there is actually NO checkmate of the brefK at all with this sequence of moves! A checkmate instead seems to require ...4.nQb8-e8... (but see as follows), in order to pre-occupy the rebirth square of the brefK, so he cannot capture the royal bishop! (And BTW, if the rebirth square would instead be defined as in the PDB version, then c8 is not even threatened here!)

But this opens the next issue up - in Popeye (when assuming ...4.nQb8-e8...) as well as in the PDB version of the solution (with ...4.nQb8-c8...)! What about the check by the Q, as soon as 5.kLd1-f3 is executed and thereby vacating the rebirth square of the wQ and thus "activating" the additional check by the Q on rank 8?? If the brefK can move as a king AND as the checking piece(s), why can't he capture the royal bishop by moving "as a queen"? In Popeye this should be clearcut, because his unitary rebirth square e8 is occupied! But in the PDB version the capture of the royal bishop by moving "as a queen" (which would need a vacant rebirth square d8) should even prevent the checkmate of the brefK there (UNLESS each check is separately handled without considering the other checks at the same time - just one check that cannot be parried in isolation should such result in checkmate; compare those "isolated cases" interpretation with the hypertransmuted king)!

Now, considering you change the condition to Anticirce type Cheylan
bedi Anticirce cheylan SchwarzerReflektierenderKoenig
then TWO solutions are presented by Popeye as follows:
1.kLc8-g4 2.kLg4-d1 3.nSBb6-b8=nD 4.nDb8-e5 5.kLd1-f3# (as before)
1.kLc8-g4 2.kLg4-d1 3.nSBb6-b8=nD 4.nDb8-e8 5.kLd1-f3#

WHY now TWO solutions - what makes the difference? The first solution is equally false (as before), and the second solution only shows up in type Cheylan, because the brefK must not capture the checking nQ on his own rebirth square e8 (in type Calvet this was not a problem, because he could do so)! The only logical answer seems to contradict the approach of "isolated cases" in Popeye insofar; else the second solution would also be shown for type Calvet: the royal bishop indeed cannot be captured by the brefK (neither moving as a bishop nor as a queen) because of his occupied rebirth square e8. But then again in type Calvet the queen could be legally captured by the brefK on e8, and such he would escape the (double) checks overall. So, the absence(!) of the second solution with type Calvet would rather confirm the 2nd assumption of a (regular) holistic approach in case of multiple checks instead of the "isolated cases" interpretation!

For a comparison with the similar transmuted king, where kings under check can ONLY(!) move like the checking piece(s) and NOT as a king, and by applying both assumptions from above accordingly (German notation):

In case you change the condition to transmuted king, Anticirce regular type Calvet:
bedi Anticirce SchwarzerTransmutierenderKoenig
a single correct solution is shown by Popeye as:
1.nSBb6-b8=nS 2.nSb8-d7 3.nSd7-f6 4.nSf6-e8 5.kLc8-b7#

If you further change the condition of transmuted king to Anticirce type Cheylan:
bedi Anticirce cheylan SchwarzerTransmutierenderKoenig
then again TWO solutions (here both seem correct) are presented:
1.nSBb6-b8=nS 2.nSb8-d7 3.nSd7-f6 4.nSf6-e8 5.kLc8-b7# (as before)
1.kLc8-g4 2.kLg4-d1 3.nSBb6-b8=nD 4.nDb8-e8 5.kLd1-f3#
This again raises the question, WHY this second solution is only presented under type Cheylan!? The only logical answer seems the same like above with the reflective king, confirming a (regular) holistic approach in case of multiple checks instead of the "isolated cases" interpretation!

Lots of dubieties here, but definitely at least ...4.nQb8-e5... seems wrong!

Thanks!