Something similar is described as the norm in ‘The Game of Wei - Chi’ by Daniele Pecorini & Tong Shu (Not a book I recommend).

The board is divided into four 10x9 rectangles + 10,10(tengen) using compass points. eg:
North 4,4 or N 4/4
East 10,8 or E 10/8
and just 10,10 for tengen

The system is rotationally symmetric so the clockwise shoulder hit of N4/4 is N5/3 and likewise for the other three quarters.

A good system for the opening and Joseki perhaps?

[Edit] The winds of change typically blow over the board from the corners.

That corner relative system was the norm from ancient until modern times in China. I got some interesting replies about this in another LifeIn19x19 thread: https://lifein19x19.com/viewtopic.php?f=17&t=11637

The “A1” coordinate system is a modern invention attributed to Oscar Korschelt, and bears clear similarities to the coordinate system conventions of chess.

A quite simple mechanism to record the game on a white paper is to use only numbers from 0 to 9 and + or - signs.

The center of the board is 0,0 and you record each move as x,y coordinates that are in the range -9,-9 lower-left corner of the board and +9,+9 in the top-right.

The hoshi points are always a twin of 6 values with different combination of signs.
-6,+6 for top left; +6,+6 for top right; -6,-6 for bottom-left and +6,-6 for bottom right.

The hoshi points on the side are always combination of 0 and 6 as above.
And so on…

Coming to the example mentioned in the original post, it would become (if I correctly understood the script, since there are still a lot of ambiguities imho):

(Black)

(White)

Description

(6,6)

(-6,6)

Top right hoshi, top left hoshi

(7,-7)

(-6,-6)

Lower right kosumi (rightmost), lower left hoshi

(-7,7)

(-6,7)

Invasion of the 3-3, inside block

(-7,6)

(-6,5)

Nobi, nobi

(-8,4)

(-1,6)

Keima, four-space extension (finishing the joseki)

(-4,-7)

(-7.-4)

Approach to the lower left hoshi, keima away

(0,-7)

(5,-7)

Three-space high extension, White approaches the lower right low.

You can notice how reflections or rotations of the board only changes signs and/or position of the same numbers. After a while you use it, the noticeable pairs (standard keima/big keima/corner approaches, low pincers, high pincers, …) would be easily recognizable.

Simple enough to be used without a game recording sheet. To record a game it is enough to get around a pencil and an paper envelope of your preferred pizza.

I just invented it now. But it seems to work quite well…

I like how the “simple coordinates” is both corner-relative and only use numbers, but I don’t like how they use apostrophes to disambiguate which corner.

Another variation (which would be convenient for pen and paper) is to draw lines around the number to indicate the closest corner or edge. Here is an example:

That’s an interesting phrase. Is it meant as like a combination of “back of the envelope/pizza box”, in the sense of whatever writing materials are at hand? Or is a “pizza-envelope” something like a calzone?

Continuing the experiment… for the lovers of corner relative notation a variation of the Cartesian system described above would be the following. Let define each corner as the origin of the relative Cartesian system as in the following picture:

Now the absolute value of the coordinate system is the same we use often to refers to the goban noticeable points starting from 1 and not 0. The only mark we add is the sign minus of x,y coordinates to specify which is the semi-axis we are referring to (essentially, to identify the corner we should look at). Each relative coordinate system has the boundaries at 1 and 10 as usual. So the center of the board can be written as (10,10) = (10,-10) = (-10,10) = (-10,-10).

Here, reflections of the board change only one sign in the pair but never exchange the numbers in each pair, while rotations of the same board position exchange numbers and change one sign.

The same example of the orginal post would become:

(Black)

(White)

Description

(-4,-4)

(4,-4)

Top right hoshi, top left hoshi

(-3,3)

(4,4)

San-San, lower left hoshi

(3,-3)

(4,-3)

Invasion of the 3-3, inside block

(3,-4)

(4,-5)

Nobi, nobi

(2,-6)

(9,-4)

Keima, four-space extension (finishing the joseki)

(6,3)

(3.6)

Approach to the lower left hoshi, keima away

(10,3)

(-5,3)

Three-space high extension, White approaches the lower right low.

… and most of the pairs shall become more familiar and easy to spot on the board.

Not a calzone… probably my English isn’t good enough.
It is a translation of an idiomatic phrase we use in Rome often said in local dialect. When you refer to a skecth or a note without any formal value written on the first piece of paper that you can grab around you we say literally: “taken on the piece of pizza paper” (that often is full of oil and not suitable for archiving purposes). This should highlight the emergency situation you are in taking that note…

This is essentially equivalent to the “simple coordinates” system, except that a hyphen (minus sign) is placed before the number instead of an apostrophe after it, and also “10” is used instead of “X”.

I think you might have some typos in your examples. Shouldn’t “top-left hoshi” be (4, -4)? I think kosumi means diagonal move. San-san would refer to the 33 point.

Your diagram shows a zero in each corner, but I think you are actually starting the counting at 1 or -1 in each corner.

Thank you for clarifying the phrase. It’s always nice to learn about idioms from other languages.

I think I’ll start calling calzones “pizza envelopes” now. I’ll just pretend that I misunderstood @ayaros’s reply as confirmation that that is literal translation from Italian.

I feel the original goal gets neglected here, though: one of the goals is to find a system that does not depend on knowing the exact coordinates of the move as a prior.

If this is the main goal, then it is an interesting challenge.

Essentially the objective should be the definition a sort of language which avoids numbers (since using numbers combines/fits quite automatically with local or global coordinates).

So, if this is the goal, now I understand better the complexity (evaluated by me as unreasonable at first reading) of Bugcat method in the original post.