No.772 (LS&MD)

The first pair alone would make a very good problem. The second pair is not quite as spectacular but still interesting and elegant, using the matrix in a completely different manner. So the result is a great HOTF problem.

The mechanism of all white pieces (including wK) works almost perfectly in all phases, beautifully unifying the two thematic pairs into one wholeness.

The question is, what makes a HOTF problem?
Two different themes which have some clearly related common feature(s) might be or, might not be, quite enough to make one problem as a whole.
wS acts as an active/passive hurdle for wLIs, reciprocating the checkmate/flightguard functions with each one of them.
The complexity and originality of “acting as a hurdle” would probably be not convincing enough to call it a “unifying idea” for a serious problem. But the efficient complexity and originality of white mechanism is very convincing, especially due to the passive roles of wK in all phases.
Looking only at the white pieces, we see a HOTF.

However, there is also Black, and it’s a black&white cooperative mechanism that makes a helpmate.

bRLa6 participates only in one phase of each thematic pair. In one solution it serves as a mere selfblocking passive “dummy”. In the other solution where it participates, it actually does not participate at all 🙂 (not even as a dummy) because that particular play would fulfill the stipulation also without bRLa6.
The same is about bBLb2 in the other two solutions.

Of course, the complexity, originality and beauty of the 1st pair of phases is motivated exactly by the thematic relation of bRa6/bBLb2 and wKf6.
So, these two black pieces do participate in the B&W HOTF mechanism, but only half employed and unfortunately without reciprocity.

bRBe4 and bRLd7 play beautifully, but each one in only one respective phase of the 1st thematic pair.
bBLe4 unconvincingly participates in the HOTF mechanism by closing the file after 1.Re2, and bRLd7 participates virtually by preventing the dual 1.LIc8, each one in one respective phase of the 2nd thematic pair.

bLIg8 and bRg2 are hardly the parts of any mechanism, being superfluous in 3 solutions each.
There is also a general question about the idle or non-thematic fairy pieces in some phases.

Still, mainly due to the unifying power of the white part of HOTF mechanism, the problem is quite impressive.
A strange esthetic perception sometimes “magnifies” the relevance of the trivial artificial “accidents”, missing at the same time the original thematic features.

For instance, bRg2 is motivated to act as a hurdle and plays 1.Re2. The pure arrival purpose would be better.
But for the constructional reasons, bLIg8 can’t be on e8,f8,h8, or replaced by bRL.
Move 1.LIg8-b8 is most essentially motivated by the arrival but after 1…LIa8+ 2.Kb3 LIf7#(3.LIg8-e6??), a “keen eye” would notice that the departure from g8 was “essentially” relevant.
And since the play by bLI can’t be purely motivated by the arrival, let’s spoil the possible purity of making a hurdle on e2.

But which essential relevance would such a “keen eye” miss?
Consider an illegal play 1.Kb3 LId8-a8(??) 2.LIg8-b8(??) – a bicolor Bristol, wLI “moves” to a8 over b8, enabling bLI to “move” to b8 over d8.
In the legal play 1.LIb8 LIa8+, bLI moves over d8 to b8, enabling wLI to move over b8 to a8.
It is an inversed motivation for an “inversed Bristol”, occupation and arrival instead of departure.
It is well known about the Lions, of course, but here it additionally thematically unifies 1st and 2nd pair, and also adds a hurdle function to wLId8 in the HOTF mechanism.

bBLh5(g4) would be yet another fairy piece 1/4 employed and the (annoying) “harmony” of impurity would be “lost” but personally, I wouldn’t hesitate if I were the author.