What is even canonical form? Is it the minimal form normalized to a) first row or b) main diagonal?
My canonizer normalizes to first row. But then we look at antidiagonal of diagonally normalized DLK. Perhaps the mistery about 1, 5, 10 lies here?

What is even canonical form? Is it the minimal form normalized to a) first row or b) main diagonal?

There is a canonical form for DLS
a) normalized on the first row (format 1);
b) normalized in the main diagonal (format 2).

I wrote the algorithm for case a).

You can see the algorithm for case b) in the Belyshev’s program kanonizator_dlk_1.03.exe.
You said that you have the source of this program.

Example

CF DLS for format 1

0 1 2 3 4 5 6 7 8 9
1 2 0 4 5 3 7 9 6 8
9 7 6 2 3 8 5 1 4 0
7 5 1 8 6 9 2 0 3 4
3 9 8 6 7 4 1 2 0 5
2 4 5 9 8 1 0 3 7 6
4 8 3 0 2 6 9 5 1 7
8 6 7 5 9 0 3 4 2 1
6 3 9 1 0 7 4 8 5 2
5 0 4 7 1 2 8 6 9 3

CF DLS for format 2

0 2 6 9 5 7 8 4 3 1
8 1 5 6 3 2 4 9 0 7
4 5 2 0 8 9 1 3 7 6
7 6 4 3 9 8 2 5 1 0
3 0 9 7 4 6 5 1 2 8
2 4 1 8 7 5 9 0 6 3
1 7 0 4 2 3 6 8 9 5
9 3 8 1 6 4 0 7 5 2
6 9 3 5 1 0 7 2 8 4
5 8 7 2 0 1 3 6 4 9

Canonical form of these two sqares from Natalia is:
- normalized on first line in left, and main diagonal on right, alphanumeric

C9U8FR58nzyyyXZWiYTWAq4w:
0 1 2 3 4 5 6 7 8 9 A   0 8 1 6 7 9 A 5 2 4 3
1 2 0 4 6 9 7 8 A 3 5   8 1 0 7 A 4 5 2 3 6 9
3 A 8 9 1 6 2 5 0 7 4   6 3 2 4 8 A 1 9 0 5 7
9 5 7 A 3 8 4 1 2 6 0   4 9 5 3 6 2 7 8 1 A 0
7 8 3 6 9 A 5 2 4 0 1   5 2 6 A 4 3 9 1 7 0 8
5 4 9 0 8 7 1 6 3 A 2   9 7 4 0 2 5 8 A 6 3 1
8 6 A 5 2 4 3 0 9 1 7   2 A 3 9 1 7 6 0 4 8 5
6 0 5 8 A 1 9 4 7 2 3   A 0 9 2 3 8 4 7 5 1 6
A 7 6 2 5 0 8 3 1 4 9   3 5 A 1 9 0 2 6 8 7 4
2 9 4 1 7 3 0 A 6 5 8   1 4 7 8 5 6 0 3 A 9 2
4 3 1 7 0 2 A 9 5 8 6   7 6 8 5 0 1 3 4 9 2 A

CFyvKcBwTPKVXu6Fpsun7QtAC:
0 1 2 3 4 5 6 7 8 9 A   0 9 1 8 5 7 A 6 4 3 2
1 2 0 4 6 8 A 3 9 7 5   9 1 0 5 A 4 2 8 3 6 7
4 6 A 7 9 1 8 2 5 3 0   5 A 2 6 3 9 4 1 7 8 0
8 7 3 9 5 6 2 0 4 A 1   4 6 8 3 7 A 1 0 5 2 9
5 0 6 2 8 A 1 9 7 4 3   7 0 A 1 4 2 9 3 6 5 8
7 9 1 0 A 4 3 6 2 5 8   6 3 9 0 2 5 8 A 1 7 4
A 4 8 5 2 3 7 1 0 6 9   2 5 4 7 1 8 6 9 0 A 3
2 3 4 6 1 0 9 5 A 8 7   1 8 5 A 9 0 3 7 2 4 6
6 A 9 1 7 2 5 8 3 0 4   A 2 3 9 6 1 7 4 8 0 5
9 8 5 A 3 7 0 4 6 1 2   3 4 7 2 8 6 0 5 A 9 1
3 5 7 8 0 9 4 A 1 2 6   8 7 6 4 0 3 5 2 9 1 A

But if we chose minimal isotope in terms of the diagonally-normalized format, we end up with different isotope of the square.

CdryvS9qNEQjfXMJ9ZEKGsMp8:
0 1 2 3 4 5 6 7 8 9 A   0 2 1 4 5 7 8 3 6 A 9
7 2 9 0 5 6 A 4 1 8 3   3 1 A 0 7 8 9 5 2 6 4
3 9 1 A 6 8 2 0 5 7 4   4 A 2 9 8 6 1 0 7 3 5
1 A 4 7 8 9 5 6 2 3 0   2 9 5 3 6 A 7 8 1 4 0
5 7 8 6 3 2 0 A 9 4 1   7 3 6 8 4 1 0 9 A 5 2
A 6 5 8 0 4 9 3 7 1 2   9 8 7 6 0 5 A 4 3 2 1
6 4 0 2 9 A 8 1 3 5 7   8 5 0 1 A 9 6 2 4 7 3
9 8 A 1 7 0 3 5 4 2 6   A 6 9 2 3 0 4 7 5 1 8
4 5 7 9 A 3 1 2 6 0 8   5 7 3 A 9 4 2 1 8 0 6
8 3 6 4 2 1 7 9 0 A 5   6 4 8 5 1 2 3 A 0 9 7
2 0 3 5 1 7 4 8 A 6 9   1 0 4 7 2 3 5 6 9 8 A

CsyZ1miRTyLfs7BMM5XVLVes2:
0 1 2 3 4 5 6 7 8 9 A   0 2 1 5 6 8 9 A 3 4 7
3 2 5 1 0 9 8 4 A 7 6   5 1 8 2 0 4 3 6 7 A 9
6 5 1 7 3 A 2 9 4 8 0   9 8 2 A 5 7 1 4 6 3 0
1 9 7 8 5 6 A 2 3 0 4   2 4 A 3 8 9 7 1 5 0 6
4 6 0 A 9 7 5 1 2 3 8   6 9 0 7 4 A 8 2 1 5 3
5 8 4 2 7 3 0 6 9 A 1   8 3 6 1 A 5 0 9 4 7 2
A 3 6 5 1 0 4 8 7 2 9   7 5 9 8 2 0 6 3 A 1 4
9 7 3 6 8 2 1 A 0 4 5   4 A 5 9 3 1 2 7 0 6 8
7 A 9 4 6 8 3 0 5 1 2   A 7 4 6 9 3 5 0 8 2 1
2 0 8 9 A 4 7 5 1 6 3   1 0 3 4 7 6 A 8 2 9 5
8 4 A 0 2 1 9 3 6 5 7   3 6 7 0 1 2 4 5 9 8 A

And those isotopes have different rules.
Edit: Congrats, your original squares were actually in minimal diagonally-normalized form. no they were not.
Added: both of those squares are part of CBdLXkuMuUsLR2UMw31FGHxG64 orthogonal system.

Do you already understand everything? Congratulations!
But I didn’t understand anything.

To check the operation of your canonizer, you need to check it for DLS of order 10.
This is elementary logic!

See
https://boinc.progger.info/odlk/forum_thread.php?id=162&postid=6007

Thanks for the pointer. I created a custom canonizer to select minimal form in terms of main anti-diagonal of diagonally normalized square and now it is processing some of the squares from the CBdLXkuMuUsLR2UMw31FGHxG64 system. All would take about 25 hours (not optimized!), so I interrupted. I am not certain it is correct, because it already found 76. Here are some:

1 0 3 4 7 5 2 9 10 8 6
1 0 3 8 7 5 9 6 10 4 2
1 0 3 9 8 5 10 2 6 4 7
1 2 0 4 7 5 3 6 10 8 9
1 2 0 4 7 5 8 9 10 6 3
1 2 0 4 8 5 9 10 3 7 6
1 2 3 0 7 5 8 9 10 6 4
1 2 3 4 0 5 10 6 7 8 9
1 2 3 4 0 5 8 6 10 7 9
1 2 3 4 7 5 8 6 10 0 9

Quote from E. Vatutin:

As a result of constructing all X-shaped diagonal fillings for a DLC of order 11 and applying all possible combinations of M-transformations to them, it was established that they form 67 different equivalence classes (i.e., member a (11) of the sequence https://oeis.org/draft/A309283 in OEIS is 67). To determine it took 2.5 hours of computing time Core i7 4770 in 1 thread.

Why are even Rules an X filling interesting? They are used for generating strongly normalized DLK, which would be useful for enumerating all CF-DLS. But that is not feasible in order n>9 due to sheer size. The KanonizatorDLK by Belishev uses rules and hash table, and it is very fast. But also too complex for me to understand.

The KanonizatorDLK by Belishev uses rules and hash table, and it is very fast. But also too complex for me to understand.

Ask a question in the forum
https://dxdy.ru/topic15897.html
On this forum you can write in English.

This forum is sometimes visited by Belyshev.
Try to write him a PM (whitefox).

Decided to count unique isotopes of two squares:

#cnt_izo: 15360
CXhkDBcfWX6dt6i79CwuBkeNk
#cnt_izo: 7680
CF8117fZq9ujrxJ1JbiRkwz8j

How many unique isotopes does your program for DLS of order 10 give?

0 8 5 1 7 3 4 6 9 2
5 1 7 2 9 8 0 3 4 6
1 7 2 9 5 6 8 0 3 4
9 6 4 3 0 2 7 1 5 8
3 0 8 6 4 1 5 9 2 7
4 3 0 8 6 5 9 2 7 1
7 2 9 5 1 4 6 8 0 3
6 4 3 0 8 9 2 7 1 5
2 9 6 4 3 7 1 5 8 0
8 5 1 7 2 0 3 4 6 9

Belyshev’s program izomorf DLK10A gives 7680 unique isotopes.
You can see it, I sent you the izomorfDLK10A program.

What CF does your program gives for this DLS?

Belyshev’s program kanonizator_dlk_1.03 gives the following CF (format 2)

0 3 5 7 6 4 9 8 2 1
9 1 6 8 3 2 5 4 0 7
5 7 2 6 1 0 4 3 9 8
6 8 1 3 7 9 2 0 5 4
1 2 8 9 4 6 7 5 3 0
3 4 7 0 8 5 1 9 6 2
8 9 3 4 0 1 6 2 7 5
2 6 9 1 5 8 0 7 4 3
4 5 0 2 9 7 3 1 8 6
7 0 4 5 2 3 8 6 1 9

Take all the solutions of the PADLS TOTAL rule 51 subproject and find for them all the unique side diagonals (rules) using your program.
This will be a test of your program.

67 rules for SN DLS of order 11

№1 1 0 3 2 7 5 8 4 6 10 9
№2 1 0 3 2 7 5 8 4 9 10 6
№3 1 0 3 2 7 5 8 6 4 10 9
№4 1 0 3 2 7 5 8 6 9 10 4
№5 1 0 3 2 7 5 8 9 10 4 6
№6 1 0 3 2 7 5 8 9 10 6 4
№7 1 0 3 2 7 5 9 4 10 6 8
№8 1 0 3 2 7 5 9 4 10 8 6
№9 1 0 3 2 7 5 9 6 10 4 8
№10 1 0 3 2 7 5 9 6 10 8 4
№11 1 0 3 2 7 5 9 8 4 10 6
№12 1 0 3 2 7 5 9 10 4 8 6
№13 1 0 3 2 7 5 9 10 6 8 4
№14 1 0 3 4 2 5 7 9 10 6 8
№15 1 0 3 4 2 5 7 9 10 8 6
№16 1 0 3 4 2 5 8 6 7 10 9
№17 1 0 3 4 2 5 8 6 9 10 7
№18 1 0 3 4 2 5 8 9 10 6 7
№19 1 0 3 4 2 5 8 9 10 7 6
№20 1 0 3 4 7 5 2 6 9 10 8
№21 1 0 3 4 7 5 2 9 6 10 8
№22 1 0 3 4 7 5 2 9 10 6 8
№23 1 0 3 4 7 5 2 9 10 8 6
№24 1 0 3 4 7 5 8 9 10 2 6
№25 1 0 3 4 7 5 8 9 10 6 2
№26 1 0 3 4 7 5 9 2 10 8 6
№27 1 0 3 4 7 5 9 6 10 2 8
№28 1 0 3 4 7 5 9 6 10 8 2
№29 1 0 3 4 7 5 9 8 10 2 6
№30 1 0 3 4 7 5 9 8 10 6 2
№31 1 0 3 4 7 5 9 10 6 2 8
№32 1 0 3 4 7 5 9 10 6 8 2
№33 1 0 3 4 8 5 2 9 10 6 7
№34 1 0 3 4 8 5 2 9 10 7 6
№35 1 0 3 4 8 5 9 6 10 2 7
№36 1 0 3 4 8 5 9 6 10 7 2
№37 1 0 3 4 9 5 7 10 6 2 8
№38 1 0 3 4 9 5 8 6 10 2 7
№39 1 0 3 4 9 5 8 6 10 7 2
№40 1 0 3 4 9 5 10 6 7 2 8
№41 1 0 3 4 9 5 10 6 7 8 2
№42 1 0 3 8 7 5 9 6 10 2 4
№43 1 0 3 8 7 5 9 6 10 4 2
№44 1 0 3 8 9 5 10 2 7 4 6
№45 1 0 3 8 9 5 10 2 7 6 4
№46 1 2 0 4 7 5 3 6 10 8 9
№47 1 2 0 4 7 5 3 8 10 6 9
№48 1 2 0 4 7 5 8 9 10 3 6
№49 1 2 0 4 7 5 8 9 10 6 3
№50 1 2 0 4 8 5 9 6 10 3 7
№51 1 2 0 4 8 5 9 6 10 7 3
№52 1 2 0 4 8 5 9 10 3 7 6
№53 1 2 0 4 8 5 9 10 6 7 3
№54 1 2 0 4 8 5 10 9 6 3 7
№55 1 2 0 4 8 5 10 9 7 6 3
№56 1 2 3 0 7 5 8 6 10 4 9
№57 1 2 3 0 7 5 8 9 10 6 4
№58 1 2 3 0 7 5 8 10 4 6 9
№59 1 2 3 4 0 5 8 6 10 7 9
№60 1 2 3 4 0 5 8 9 10 6 7
№61 1 2 3 4 0 5 10 6 7 8 9
№62 1 2 3 4 7 5 0 9 10 8 6
№63 1 2 3 4 7 5 8 6 10 0 9
№64 1 2 3 4 7 5 9 10 6 0 8
№65 1 2 3 4 7 5 10 9 0 6 8
№66 1 2 3 8 7 5 9 6 10 0 4
№67 1 2 3 8 7 5 10 6 4 0 9

Found with Harry White.

Canonizer by Harry White for DLS of order 11 can be downloaded from here
https://yadi.sk/d/YPQ2hx_R0tOMWQ
Canonizer by Harry White for DLS of order 12 can be downloaded from here
https://yadi.sk/d/dbcljV5OkjXlXA

That's great! I found 65 of those 67 rules so far.
Unfortunately, there is no source to those programs.

Unfortunately, there is no source to those programs.

I will ask Harry White for sources.

Tomáš Brada
can you send me an ODLS for this DLS?

EUELx2zmrdPHyTGkGJhedf1cuDmJzqhw6hUme293TPB (13, 131106, >>248703)

I checked very slowly.

PS. https://boinc.tbrada.eu/forum_thread.php?id=3104&postid=4133

https://boinc.tbrada.eu/download/EUELx2zmrdPHyTGkGJhedf1cuDmJzqhw6hUme293TPB.txt
Note: there are many many more orthogonal mates than 248703 in the file.

Download sources from here
http://budshaw.ca/temp/canonizerSource.zip

https://boinc.tbrada.eu/download/EUELx2zmrdPHyTGkGJhedf1cuDmJzqhw6hUme293TPB.txt
Note: there are many many more orthogonal mates than 248703 in the file.

Thanks.

I downloaded 248703 squares.
These are the last

. . . . . . . 
E79gthK7jcFmd6aMopNvkSCmbRqmoBrKyrnvnR
EqFTGVj9WdodpgyzigaapVckbZbasBx1YGwAiZ3
EsM32FZkinwkBU2NVcrMF62HcSuCZN6Jno9uQ3
E5nQQhsvHq7tdghFA5yHoSarKoM83zTiTQjBVP9
EupGYCsh4MWx62Y4TjX4YpJpZkpwntkqdASQwWS
E4XGtTPYUmzUdNPpZPVLUf5xp8QS4giBBhoBQo
EzDfDvvs8ZiRr3Fvrmj4EanbcF9fbuzV41iDWL2
EviKBeoXQgiw3pmL1sEtg19gi8CiYnpu9h5QRW

 0  5  9  4 11 10  8  2  6  7  3  1
 6  1  7  2  5  4  9  3 10 11  0  8
11  6  2  8  0  1  4  9  5  3  7 10
10  8 11  3  1  2  7  0  4  5  6  9
 8  2  6 11  4  7  0  5  9 10  1  3
 7  0  4  1  3  5 10  8 11  2  9  6
 9  3 10  5  2 11  6  1  7  4  8  0
 5 10  3  9  6  8  2  7  1  0 11  4
 1  4  0  7 10  9  3 11  8  6  5  2
 3 11  8 10  7  6  1  4  0  9  2  5
 4  9  5  0  8  3 11  6  2  1 10  7
 2  7  1  6  9  0  5 10  3  8  4 11

D-transversals: 24752
ODLS: >>276464

Finding all ODLS for a given DLS is a big problem!

I improved the speed of my canonizer and also changed it to select diagonally-normalized squares minimal first in terms of the anti-diagonal. This makes it suitable for extraction of rules.

Can you post 596 rules for SN DLS of order 12 and 13?
I want to confirm the results by Harry White.

How many rules did you find for SN DLS of order 14?
I have found 278 rules so far.
I have very few CF ODLS of this order.

Can you post 596 rules for SN DLS of order 12 and 13?
I want to confirm the results by Harry White.
How many rules did you find for SN DLS of order 14?
I have found 278 rules so far.

I did not look for rules yet. But I can create a program to generate all rules.
What did found is that there is 23040*8 isomorphisms of order 12 and 13, and 322560*8 isomorphisms of order 14.

I have very few CF ODLS of order 14.

I could try enumerating orthogonal mates of F98aux31EFfDjHASPckbbhZCsweDB7qd3dcgExK6yTQ75FDD3, would that help? I need to modify my program. To enumerate all, it would take long time. Maybe for a boinc project?

Currently I am searching for all orthogonal mates, and their mates of DLK of order 12. Already 1048866 CF found.