Does anyone know of a game that was drawn under the mandatory 75 move rule?

You have been exchanging posts with MARattigan too long. I am not very interested in one particular kind of terminology or another, provided it is clear in context what is meant. I know scores of players who will understand the "subatomic move" when explained to them. For instance , I move Pa7 to a8, or I move a captured unit off the board and there is nothing strange about calling those actions "subatomic moves" - unless you claim a fixed understanding of the word move. In chess variants like MDR these changes can occur as isolated modular steps which makes some of them appear most similar to a normal chess move. The reason why your math article distinguishes move from action is to prevent you from entering the anatomy of the action. After all, it doesn't matter in this theory what the action looks like, the only state change it acknowledges is that of move. By the way, I regularly revise my terminology depending on context. Nothing I write really depends on it since I always explain what I mean.

Your last sentence almost literally repeats what I wrote in my posts: "the rules which apply to the category of subatomic moves do not apply to the category of full moves (and most certainly not to collections of full moves)". I could write exactly the same on physics. Though atoms and protons are both particles there is a clear distinction in the categories they belong to, and the laws that apply to them.

So in the final example I gave in #88 does that mean from your unproblematic standpoint that the position is dead when the rook is touched or not?

The link is interesting and I would prefer that the rules were couched in similar terms. There would need to be addenda describing how that would link to practical methods of playing chess. The latter could even legalise computer chess.

But the question is about FIDE rules, not the rules in the link. The rules in the link, for example, allow for games that are simultaneously drawn and won for one or other side, which wouldn't correspond with the FIDE rules. Also players could not resign or offer/accept draws. In particular touch move is not encompassed so it's irrelevant to my last few questions.

The issue I have with the term "subatomic move" is that it suggests that it is part of a "move" which is false if you use my definition. That is why I thought your view was different. Maybe your terminology is just confusing. Only in chess variants like MDR can you divide a full move in several partial moves. However a full move in MDR is not a pair of squares like in the definition I gave for regular chess. A full move is a series of several partial moves. Using the same terminology for both MDR and regular chess is just confusing.

The position is indeed  not dead. The article was never intended to replace all FIDE rules. It only gives a clear mathematical definition of legal moves, checkmate and when a draw can be claimed. Notably the actions of players are not included. The actions of players are not used to determine if a position is dead. A position does not depend on the state of the players, if you use the same definition of a position as in that article. 

I don't understand what you mean with that the rules allow games to be simultaneously drawn and won. Irregularities, time left etc are not included. So you can't judge these rules similarly as the FIDE rules. If we assume there are no irregularities and players got unlimited time, then how can games simultaneously be drawn and won?

That would be very inconvenient for most friendly games. Clocks are difficult to get hold of if you're playing on a travelling chess set on a train and anyway most people that play chess would probably not go to the expense of buying one.

All that is needed is to have an irregularities section in the basic rules saying that an illegal move has been made if a piece has been released on a square not in accordance with section 4 plus the rest of the gubbins in art.7.5.1. The releasing of the piece would then take the place of pressing the clock. Art. 7.5.1 could be profitably deleted. 

Yep, that would help against "illegal" moves as well besides a number of other (more off-beat) actions like tapping the table when you're done. Or would that count as an on-beat action ? When time-keeping is not an issue, there is a whole range of options. I only suggested the clock because it is a familiar chess appliance which has other useful functions and is potentially available in all environments.

There is another sort of move though which can't be handled that way, which is the "incomplete move". Though it is in itself illegal, there may still be a way to complete it legally. And you cannot know if a player intends to complete it or just slipped up. The most important one is taking an enemy piece of the board without moving your own piece there. This could happen when you suddenly see you could capture the unit in more than one way. I've seen players adding the captured unit to their booty while forgetting to complete the move. No problem when there is a clock to push or a table to tap. Some other interruptible moves are castling (if first moving the king) or promotions though these are not likely to make players forget midway about their status; hmmm may be when considering the promotion piece? Anyway, that's why the "incomplete move" has an individual identity in the MDR problem type.

But the dead position rule also doesn't depend on the touch move rule for it's interpretation, in just the same way as it doesn't depend on the 75 move rule. If you take the touch move rule into account in that position, why didn't you want to take the 75 move rule into account in the previous position discussed?

The actions of the players are as you say not included in the exposition in the link you gave. This is a bit of a drawback in a definition of chess, given that chess is a game that involves players. The only connection in the exposition is that in case of checkmate the player playing cₙ has lost the game and his opponent has won the game, from which one might understand that one of the players plays "white" and there is one other playing "black". It doesn't say that the player playing cᵢ rather than his opponent must choose a member of ValidMovesᵢ. In this respect it's faithful to the FIDE original, but that is obviously a failing in the FIDE original.

According to the definitions a game p₁p₂...pₙ can satisfy both the checkmate requirement and either or both of the threefold repetition and fifty-move rule requirements, in which case according to the accompanying text it is both won by one player and drawn. 

There is also nothing to suggest a game cannot continue after a dead position is reached, which conflicts with my reading of the FIDE rules, as does also that a game played on after a threefold repetition remains in a permanently drawn state even when the remaining positions are not also threefold repetitions.

It's also now out of date, of course.

I did think of the second type when I posted. In those cases is it an infringement of the rules governing use of clocks or a candidate for 7.5.1 (illegal move completion)? Strangely the only law I can find that prohibits pressing the clock prior to completing a legal move is

6.2.3 A player must press his clock with the same hand with which he made his move. It is forbidden
for a player to keep his finger on the clock or to ‘hover’ over it.

so the question is, if he uses the same hand to press the clock as he used to make the incomplete legal move, is there an infringement at all? He is obliged to complete it with the same hand.

At any rate, if you take it from the past tense "made" that he has no same hand with which he made his move, if it is an infringement, is it a violation of 6.2.3 or an illegal move?

1.5 If the position is such that neither player can possibly checkmate the opponent’s king, the game
is drawn (see Article 5.2.2).

5.2.2 The game is drawn when a position has arisen in which neither player can checkmate the
opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’. This
immediately ends the game, provided that the move producing the position Was in accordance with
Article 3 and Articles 4.2 — 4.7.

The above articles from FIDE LAWS OF CHESS TAKING EFFECT FROM 1 JANUARY 2018 perhaps answer the question. For the meaning of any terms involved see the same document e.g. here http://www.chessarbitersassociation.co.uk/Laws2018.pdf

or more authritatively here

https://www.fide.com/fide/handbook.html?id=208&view=article

In MDR terminology, an illegal move is one that is a full move but illegal in context, such as "self check", "illegal e.p. (by history)" or "illegal castling (by history)". Obviously, a complete rule set ought to be capable of dealing with all infringement formats, preferably in a uniform way. "Touching" is a bit of an oddball as it is the only common technical infringement that is really a fleeting action - not visible in a state change on the board.

I once said to Andrew Buchanan that I wasn't really interested to rewrite the FIDE laws with all the quirky bits relating to hands and clocks and arbiters. I prefer to concentrate on the interaction of game chess with composition chess, especially retrograde. That makes for instance the dead rule a target for me while I also have a mild interest in MDR. I'll be happy to leave the discussion on the typical game issues to others.

Well, let's agree to disagree on what the word "move" could mean in some context. I give you a point on "touching" since that is a fleeting action without a chess unit moving.

Going back to the origin of this debate, MARattigan suggested that an underway move might invoke a dead rule evaluation. He only mentioned "touching" but I generalized it to all subatomic action. For instance, the piece you select after you removed an opponent piece may determine whether or not death can still be avoided. Moving a king from e1 to g1 may be "deadly". According to MARattigans criterion the evaluator would have to step in at those points. That is how a subatomic state would become real in a chess game and could even be given the diagram of "game end".

Next, I argued against MARattigan point on the basis of the difference between the atomic and the subatomic universe and their laws. Concluding that, in the final analysis, the subatomic world may be dismissed alltogether in relation to the dead rule, precisely as you suggested. I only entered it in order to be able to dismiss it by agreeable argument. Just needed the discrete (sub)atomics to counter the time continuum.

Obviously, MDR served for me to show how many different infringements need to be taken into account when starting on subatomic phases. Their existence cannot be completely denied, since their handling is addressed in articles 4 and 7.5.1. The MDR inventors claim that their retro-type is based on remedies prescribed by the actual FIDE laws (15 years ago) - it's not just fairy! "Illegal moves as per 7.5.1" can be viewed as subatomic phases by virtue of the demand to complete or correct them until they become "full legal atomic moves". But it is a self-contained universe. In relation to the other chess rules the subatomics play no role whatsoever.

By the way, there is a big overlap between "illegal moves per 7.5.1" and "subatomic moves". If you object to the use of the word "moves" in the one, shouldn't you object to the other as well? By your definition?

@MARattigan No, but I could ask Veronika if you really want it.  As I recall, it was K+R vs. K+B.

I would be really interested if it's still available. I'm interested in whether it actually did draw under the 75 move rule or whether it should have been declared dead a ply or two before.

I think there may be even less agreement than you say.

Concerning this (White to play) position after White has touched the rook with intent:

Numquam says it is dead (#105).

You, I believe, would say it's not dead (subatomic).

I would say the laws are not precise enough to say either.

I don't believe you can validly decide what is to be atomic and what subatomic. That should be determined by the laws themselves. The laws are all in effect for the duration of the game and any event that is referred to in a law may possibly have consequences and a new evaluation is required. Unless the laws state it, there is no requirement that evaluations take place only on move boundaries.

You cannot for instance tell FIFA that, according to their rules, presentation of red and yellow cards, sendings off, offside decisions and all penalties should take place only at half and full time because you've arbitrarily decided that the atomic unit is the play in each direction.

It would, of course, be helpful if the laws gave a definite answer for each event.. 

Is a unique solution intended? If its meant to be halfway through a capture or promotion or both there are a lot of possibilities.

If that is what Numquam believes (edit: which I doubt), then I do not agree with him. The math article he referred to would not support Numquam either because "touches" are mere actions and not part of the dead rule which is defined in terms of positions and moves.

I agree with myself.

I do not disagree with you because I believe FIDE laws are incomplete anyway. But I do believe that the dead rule belongs conceptually to the full move laws and assume FIDE will confirm it in time. The following situation could arise (familiar?):

White touches the rook with the intention to move it. Hesitates when seeing the consequence. Then his flag falls. The arbiter looks on. What will he decide?

What I meant is that deadness applies to a position. The position in the diagram is not dead and after that rook move is made you get a dead position (stalemate). You are asking if a certain state is dead, but deadness is not defined for that state. So it may better to say that it is not a position and therefore deadness is not defined. 

That last question seems simple to me. Incomplete moves are not part of the game. That is why they are not written on the score sheet. The last position of the game is not a dead draw, so the player loses. The rules are complete enough to give a clear answer for that example. There is no doubt that deadness does not apply to states between two moves.

Compare the following situation: a player removes enemy piece with intent to capture. There is only one legal move to capture that piece, and that move is a ceheckmate. Once the enemy piece is touched, there is no other legal move. But making the move also requires moving the capturing piece to new square (and releasing it). Suppose flag falls with captured piece removed but capturing piece in starting square.

I understand that a move interrupted by flag fall before making it is parsed by retracting it to the position before the move started, and the outcome evaluated from that position. Correct?

Precisely my point. Positions are assumed to coincide with full move boundaries and with relevant knowledge of the preceding game, necessary to decide castling rights and such.

This definition is commonly used in composition chess but I am not sure it is well defined in the FIDE handbook.

It's not only the dead rule that doesn't apply to an inter-position state. Almost nothing applies, including the movement of pieces. Which is a good thing, or you could start a completely new move when in the middle of the previous one!

By the way, all this doesn't mean that FIDE somehow needs to decide about deadness in the "MARattigan state". In a context of formal mathematical systems, the statement MARattigan-state is dead would be considered a language/syntax error (type mismatch). That's the math way. No need to resolve.