If something is already possible, or if a previous action already makes something possible, then a later action cannot be said to "enable" that thing to be possible.
Cassandra wrote:
$$
$$ ----------------------
$$ | O . O . X . 2 O O . O
$$ | O O O X 3 X O O O O O
$$ | X X X O X O O . O . .
$$ | X . X O O O O O . . .
$$ | . X X . . . . . . . .
$$ | X X . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$
$$ ----------------------
$$ | O . O . X . 2 O O . O
$$ | O O O X 3 X O O O O O
$$ | X X X O X O O . O . .
$$ | X . X O O O O O . . .
$$ | . X X . . . . . . . .
$$ | X X . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]
THEREAFTER,

is established on the board as a stone that cannot be captured. Thus, White's captured stone is considered "alive".

connects.
White's five stones in the corner remain uncaptured, due to Black's damezumari. Thus, these stones are also considered "alive".
This is wrong. White's captured stone is not deemed "alive" because the stone

is not actually "enabled" (made possible) by the captured stone (previously at

). The capture does not "enable"

because White could play

after a Black move that does not capture the 1 White stone. Also recognize that

is alive because the group with 2 eyes is uncapturable, not because the 1 White stone is capturable. Therefore, a move at

does not "confirm" (determine something unknown) the L&D status of any stones.
Cassandra wrote:
Sequence #2:
...
$$
$$ ----------------------
$$ | O . O . X 2 3 O O . O
$$ | O O O X . X O O O O O
$$ | X X X O X O O . O . .
$$ | X . X O O O O O . . .
$$ | . X X . . . . . . . .
$$ | X X . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$
$$ ----------------------
$$ | O . O . X 2 3 O O . O
$$ | O O O X . X O O O O O
$$ | X X X O X O O . O . .
$$ | X . X O O O O O . . .
$$ | . X X . . . . . . . .
$$ | X X . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]
White suspects that this time (after the obvious failure in sequence #1) Black wants to attack her stones in the corner, and so gives atari with

, causing damezumari temporarily.

captures, so resolving his damezumari.
I found the point you misunderstand. If the players are confirming the L&D of the 1 White stone then both White and Black have no reason to care whether the stones in the corner are attacked or captured because their capture
does NOT affect the status of the 1 White stone considered by itself.
If the players were attempting to confirm the L&D of the 5 white stones, then why is Black capturing a 6th stone? So then the players are assessing 6 stones, not 5 stones. I agree, the 6 stones considered together are alive. But the Japanese Rules show that the L&D status of stones is also considered separately.
Assessing the L&D status of the 1 White stone separate from the 5 White stones in the corner, the players will see that the 1 White stone is alive. That is, the capture of the 1 White stone enables White to place new uncapturable stones even without the 5 stones being captured. Since the new uncaptured stones are
already possible (already enabled) by the capture of the 1 stone, the capture of the 5 White stones is not "enabling."
Cassandra wrote:
Thus, ALL of White's captured stones are considered "alive".
Wrong. The 6 White stones together are alive. The 1 White stone by itself is alive. But the 5 White stones in the corner are dead because their capture does not "enable" any uncapturable stones that were not already enabled by the capture of the 1 White stone by itself.
White has dame and loses.
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The situation we are discussing is similar to Example 24:
https://www.nihonkiin.or.jp/match/kiyak ... 22_25.html
Considered as a whole, the 13 White stones are alive because at least 11 of the White stones have 2 eyes.
Considering

separately, it is alive because if Black captures

then White can connect at 'c' and

is uncapturable.
Considering

separately, it is dead because it can be captured and it's capture does not "enable" any new uncapturable stones that were not already "enabled." Playing a stone at 'c' is not "enabled" by

being captured. Therefore,

is dead and point 'b' is dame.
Similarly,

is alive and

are dead. After

is captured, playing stones at c and

are not enabled by the 5 stones being captured, they are already enabled by

being captured. So at least point 'b' is dame (as are others). In that area near with the 3 black stones, only point 'd' is territory.
$$
$$ ----------------------
$$ | Q b Q . X c . O O . O
$$ | Q Q Q X @ X O O O O O
$$ | X X X O d O O . O . .
$$ | X . X O O O O O . . .
$$ | . X X . . . . . . . .
$$ | X X . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$
$$ ----------------------
$$ | Q b Q . X c . O O . O
$$ | Q Q Q X @ X O O O O O
$$ | X X X O d O O . O . .
$$ | X . X O O O O O . . .
$$ | . X X . . . . . . . .
$$ | X X . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]