Reference:

https://www.lifein19x19.com/viewtopic.php?f=15&t=18732dhu163, you try to reinvent the wheel. I have already provided suitable definitions for thickness:

The gap between a wall and extension:

See Joseki 1 - Fundamentals, p. 233.

First determine the farthest extension that is also a connection, which might be direct or indirect. This must be verified by reading. Then consider also alternatives.

Note that 'indirect connection' is a term defined on p. 120: An indirect connection does not ensure a 100% connection but makes cutting unattractive or at best equal for the opponent.

Definition of thickness by numbers:

See Joseki 2 - Strategy, p. 90.

Thickness of a player's group of stones has these properties:

- The stones are m-connected with each other.

- The stones are n-alive.

- The territory potential is estimated by letting the player make a small number of i = 0..t successive plays using the group's presence to get the greatest territory. For i = 0, count the territory in favour of the player. For every greater i, count the territory increment in favour of the player and divide by 2^i. Form the sum of the values calculated in all i steps.

Definition of influence by numbers:

See Joseki 2 - Strategy, p. 71.

In relation to a player's group of stones, an intersection's influence has all of these properties:

- The player's stone situated or else, if possible, placed on the intersection is m-connected to the group's stones.

- The opponent's stone situated or else, if possible, placed on the intersection is n-connected to at least one live string of his.

- The player's stone situated or else, if possible, placed on the intersection is p-alive.

- The opponent's stone situated or else, if possible, placed on the intersection is q-alive.

- The intersection is the player's t-territory.

From the number-dependent definitions, I have derived the following best informal definitions, where "connection" is "direct or indirect connection":

See Positional Judgement 2 - Dynamics, p. 206:

- Thickness: the group is connected and alive.

- Great thickness: the group retains its thickness even if the defender ignores at least one attacking move.

- Ordinary thickness: the group has thickness but not great thickness.

See also there for a definition of "ordinary influence stones", which are used for my important concept of influence stone difference.