user23305: The challenge is to create the longest list of half moves whereby an AI could re-create that list of moves perfectly, only given the ending board state and the number of moves.
As example I will first give a short example that does NOT work.
[FEN ""]

1. a3 a6 2. b3 

From that final board state, it is impossible to differentiate it from  1. b3 a6 2. a3.
And a short example that DOES work.
[FEN ""]
1. a3 a6 2. a4 a5 

There is no way to get this board state in exactly two moves other than what was done here.
Scoring will work like this.

+1 point per move.
+5 points if the game is complete, i.e. the last move in the sequence is checkmate.

This is my best solution so far.
[FEN ""]

1. a4 h5 2. a5 h4 3. a6 h3 4. axb7 hxg2 5. Rxa7 Rxh2 6. Rxa8 Rxh1 7. Rxb8 Rxg1 8. Rxc8 Rxf1 

This would score 21 points: 1 point for each of the 16 moves plus 5 points for ending in a checkmate for black.
Note: Opening pawns moving 2 spaces instead of one is necessary in this particular solution.  A 9 turn game where the pawns each move one space per turn would be undifferentiated from an identical game where pawns open with the two space move and then rooks spend an extra turn making their first capture. Also, the game cannot be extended by slipping in Bxg2 at any point in time for White, because it would be unclear, when looking back, when such a move had occurred, since there are several possible turns for such a move to occur.

user15543: Such a sequence of moves, where there is only one way to reach the given position on the given number of moves, are called Shortest Proof Games. There are many chess programs that solve such problems.
Long chess problems like this are usually checked with computers using these specially built chess programs, i.e. they are the A.I. that finds the solution you speak of in your answer. These problems have been composed by humans and computer-verified, meaning that there is only one possible solution no matter what you may think.
The longest problem that I know of that is computer verified, often shortened to “C+“, is 41.5 moves long according to the Die Schwalbe database.
[Title "Nicolas Dupont, PG In 41.5, FIDE Olympic Tourney 39 Khanty-Mansiysk, 2010, 3rd Prize,"]
[FEN ""]

1. e4 d5 2. e5 d4 3. e6 d3 4. exf7+ Kd7 5. a4 e5 6. a5 e4 7. a6 e3 8. axb7 e2 9. Ra6 exd1=B 10. Rb6 a5 11. h4 a4 12. h5 a3 13. h6 a2 14. hxg7 Ba3 15. f8=B a1=N 16. Bb4 c5 17. Rhh6 Kc7 18. Rhd6 h5 19. g4 h4 20. g5 Rh5 21. g6 Nh6 22. g8=B Nb3 23. g7 Nxd2 24. Bb3 Ne4 25. g8=N Nf6 26. Kd2 h3 27. Kc3 h2 28. Kc4 h1=B 29. Be1 d2 30. c3 Bc2 31. Ne7 Bh7 32. Nf5 d1=R 33. Ng3 Bcf5 34. f4 Nbd7 35. b8=N Qc8 36. Nc6 Qb7 37. Nb4 Bc6 38. Nh1 Rd5 39. Bd1 Kb8 40. b3 Bb2 41. Nc2 Ra3 42. Na1

By your system, this problem has a score of 83 points.
The longest computer verified one ending in checkmate that I know of is worth 59 points.
[Title "Silvio Baier, Die Schwalbe 4/24/2010"]
[FEN ""]

1. h4 a5 2. h5 Ra6 3. Rh4 Rg6 4. hxg6 h5 5. Rc4 h4 6. g4 h3 7. Bg2 h2 8. Bc6 Rh3 9. Bb5 Rb3 10. axb3 Nf6 11. Raa4 Ne4 12. Rab4 a4 13. d3 a3 14. dxe4 a2 15. Qd5 a1=R 16. Nd2 Ra8 17. Ba6 h1=R 18. Qa5 d5 19. Nf1 d4 20. Nf3 d3 21. Nd4 Rh8 22. f3 d2+ 23. Kf2 d1=N+ 24. Kg3 Ne3 25. g5 Nf5+ 26. Kg4 Nh6+ 27. Kh5 Ng8#

Your proof game in 8 moves is computer verified by Jacobi.


user4572: The current length record is an astounding 57.5 moves (115 half-moves).
[Title "Dmitri W. Pronkin & Andriy Frolkin, Die Schwalbe 06/1989, 1st Prize, PG in 57.5"]
[FEN ""]

1. a4 h5 2. a5 h4 3. a6 h3 4. axb7 hxg2 5. h4 d5 6. h5 d4 7. h6 d3 8. h7 dxc2 9. d4 a5 10. Bh6 c1=R 11. e4 Rc5 12. Ne2 Rh5 13. e5 c5 14. e6 Nc6 15. b8=R a4 16. Rb4 a3 17. Ra4 c4 18. b4 c3 19. b5 c2 20. b6 c1=R 21. b7 Rc4 22. b8=R Qa5+ 23. Rbb4 Bb7 24. Nbc3 O-O-O 25. exf7 e5 26. Rc1 Bc5 27. f8=R a2 28. Rf3 a1=R 29. Na2 g1=R 30. Rfa3 Rg6 31. f4 Re6 32. f5 g5 33. f6 g4 34. f7 g3 35. f8=R g2 36. Rf5 g1=R 37. Bf8 Rg7 38. Ng3 e4 39. Bd3 e3 40. O-O e2 41. Rcc3 e1=R 42. Bc2 R1e3 43. d5 Rdd7 44. d6 Rdf7 45. d7+ Kb8 46. Qd6+ Ka8 47. Qc7 Nge7 48. d8=R+ Nc8 49. Rdd3 Rhg8 50. h8=R Rae1 51. Rh6 R1e2 52. R1f2 Rce4 53. Kf1 Bd4 54. Rfc5 Ne5 55. Nf5 Nc4 56. Nd6 Nb2 57. Rbc4 Nb6 58. Qb8+

This length record was reportedly beaten in 2017 by Pronkin, Frolkin and Keym (to 58.5 moves) but unfortunately it turned that the longer problem had more than one solution. I do not know if the authors managed to make the problem sound.
Although this problem is not computer-checked, it has withstood human testing for 41 years, so it might as well be considered computer checked by the greatest computer of them all-the human mind.

23305: <p>The challenge is to create the longest list of half moves whereby an AI could re-create that list of moves perfectly, only given the ending board state and the number of moves.</p>
<p>As example I will first give a short example that does NOT work.</p>
<pre><code>[FEN &quot;&quot;]

1. a3 a6 2. b3 
</code></pre>
<p>From that final board state, it is impossible to differentiate it from  1. b3 a6 2. a3.</p>
<p>And a short example that DOES work.</p>
<pre><code>[FEN &quot;&quot;]
1. a3 a6 2. a4 a5 
</code></pre>
<p>There is no way to get this board state in exactly two moves other than what was done here.</p>
<p>Scoring will work like this.</p>
<ol>
<li>+1 point per move.</li>
<li>+5 points if the game is complete, i.e. the last move in the sequence is checkmate.</li>
</ol>
<p>This is my best solution so far.</p>
<pre><code>[FEN &quot;&quot;]

1. a4 h5 2. a5 h4 3. a6 h3 4. axb7 hxg2 5. Rxa7 Rxh2 6. Rxa8 Rxh1 7. Rxb8 Rxg1 8. Rxc8 Rxf1 
</code></pre>
<p>This would score 21 points: 1 point for each of the 16 moves plus 5 points for ending in a checkmate for black.</p>
<p>Note: Opening pawns moving 2 spaces instead of one is necessary in this particular solution.  A 9 turn game where the pawns each move one space per turn would be undifferentiated from an identical game where pawns open with the two space move and then rooks spend an extra turn making their first capture. Also, the game cannot be extended by slipping in Bxg2 at any point in time for White, because it would be unclear, when looking back, when such a move had occurred, since there are several possible turns for such a move to occur.</p>
 15543: <p>Such a sequence of moves, where there is only one way to reach the given position on the given number of moves, are called <a href="https://www.janko.at/Retros/Glossary/ShortestProofGame.htm" rel="nofollow noreferrer">Shortest Proof Games</a>. There are <a href="http://natch.free.fr/Natch.html" rel="nofollow noreferrer">many</a> <a href="http://lestourtereaux.free.fr/euclide/" rel="nofollow noreferrer">chess</a> <a href="https://wismuth.com/jacobi/" rel="nofollow noreferrer">programs</a> that solve such problems.</p>
<p>Long chess problems like this are usually checked with computers using these specially built chess programs, i.e. they are the A.I. that finds the solution you speak of in your answer. These problems have been composed by humans and computer-verified, meaning that there is only one possible solution no matter what you may think.</p>
<p>The longest problem that I know of that is computer verified, often shortened to “C+“, is <strong>41.5 moves</strong> long according to the <a href="https://pdb.dieschwalbe.de/P1108595" rel="nofollow noreferrer">Die Schwalbe database</a>.</p>
<pre><code>[Title &quot;Nicolas Dupont, PG In 41.5, FIDE Olympic Tourney 39 Khanty-Mansiysk, 2010, 3rd Prize,&quot;]
[FEN &quot;&quot;]

1. e4 d5 2. e5 d4 3. e6 d3 4. exf7+ Kd7 5. a4 e5 6. a5 e4 7. a6 e3 8. axb7 e2 9. Ra6 exd1=B 10. Rb6 a5 11. h4 a4 12. h5 a3 13. h6 a2 14. hxg7 Ba3 15. f8=B a1=N 16. Bb4 c5 17. Rhh6 Kc7 18. Rhd6 h5 19. g4 h4 20. g5 Rh5 21. g6 Nh6 22. g8=B Nb3 23. g7 Nxd2 24. Bb3 Ne4 25. g8=N Nf6 26. Kd2 h3 27. Kc3 h2 28. Kc4 h1=B 29. Be1 d2 30. c3 Bc2 31. Ne7 Bh7 32. Nf5 d1=R 33. Ng3 Bcf5 34. f4 Nbd7 35. b8=N Qc8 36. Nc6 Qb7 37. Nb4 Bc6 38. Nh1 Rd5 39. Bd1 Kb8 40. b3 Bb2 41. Nc2 Ra3 42. Na1
</code></pre>
<p>By your system, this problem has a score of 83 points.</p>
<p>The longest computer verified <a href="https://pdb.dieschwalbe.de/P1256159" rel="nofollow noreferrer">one</a> ending in checkmate that I know of is worth 59 points.</p>
<pre><code>[Title &quot;Silvio Baier, Die Schwalbe 4/24/2010&quot;]
[FEN &quot;&quot;]

1. h4 a5 2. h5 Ra6 3. Rh4 Rg6 4. hxg6 h5 5. Rc4 h4 6. g4 h3 7. Bg2 h2 8. Bc6 Rh3 9. Bb5 Rb3 10. axb3 Nf6 11. Raa4 Ne4 12. Rab4 a4 13. d3 a3 14. dxe4 a2 15. Qd5 a1=R 16. Nd2 Ra8 17. Ba6 h1=R 18. Qa5 d5 19. Nf1 d4 20. Nf3 d3 21. Nd4 Rh8 22. f3 d2+ 23. Kf2 d1=N+ 24. Kg3 Ne3 25. g5 Nf5+ 26. Kg4 Nh6+ 27. Kh5 Ng8#
</code></pre>
<p>Your proof game in 8 moves is computer verified by <a href="https://wismuth.com/jacobi/" rel="nofollow noreferrer">Jacobi</a>.</p>
<p><a href="https://i.stack.imgur.com/Kkeus.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Kkeus.png" alt="enter image description here" /></a></p>
 4572: <p>The <a href="https://pdb.dieschwalbe.de/P0000136" rel="nofollow noreferrer">current length record</a> is an astounding 57.5 moves (115 half-moves).</p>
<pre><code>[Title &quot;Dmitri W. Pronkin &amp; Andriy Frolkin, Die Schwalbe 06/1989, 1st Prize, PG in 57.5&quot;]
[FEN &quot;&quot;]

1. a4 h5 2. a5 h4 3. a6 h3 4. axb7 hxg2 5. h4 d5 6. h5 d4 7. h6 d3 8. h7 dxc2 9. d4 a5 10. Bh6 c1=R 11. e4 Rc5 12. Ne2 Rh5 13. e5 c5 14. e6 Nc6 15. b8=R a4 16. Rb4 a3 17. Ra4 c4 18. b4 c3 19. b5 c2 20. b6 c1=R 21. b7 Rc4 22. b8=R Qa5+ 23. Rbb4 Bb7 24. Nbc3 O-O-O 25. exf7 e5 26. Rc1 Bc5 27. f8=R a2 28. Rf3 a1=R 29. Na2 g1=R 30. Rfa3 Rg6 31. f4 Re6 32. f5 g5 33. f6 g4 34. f7 g3 35. f8=R g2 36. Rf5 g1=R 37. Bf8 Rg7 38. Ng3 e4 39. Bd3 e3 40. O-O e2 41. Rcc3 e1=R 42. Bc2 R1e3 43. d5 Rdd7 44. d6 Rdf7 45. d7+ Kb8 46. Qd6+ Ka8 47. Qc7 Nge7 48. d8=R+ Nc8 49. Rdd3 Rhg8 50. h8=R Rae1 51. Rh6 R1e2 52. R1f2 Rce4 53. Kf1 Bd4 54. Rfc5 Ne5 55. Nf5 Nc4 56. Nd6 Nb2 57. Rbc4 Nb6 58. Qb8+
</code></pre>
<p>This length record was reportedly beaten in 2017 by Pronkin, Frolkin and Keym (to 58.5 moves) but unfortunately it turned that the longer problem had more than one solution. I do not know if the authors managed to make the problem sound.</p>
<p>Although this problem is not computer-checked, it has withstood human testing for 41 years, so it might as well be considered computer checked by the greatest computer of them all-the human mind.</p>
