The day before, soak the 8 g (¼ oz) of shiitake in the cold water.
Strain into a saucepan and add the kombu. Heat gently and remove the kombu as soon as the first tiny bubbles form on the bottom.
Let cool, then measure out 80 g (⅓ cup).
Grate the zest of the lime and mix it with the lime juice and rice vinegar. Steep for 30 minutes, then strain.
In a small saucepan, combine the 80 g (⅓ cup) of broth, the soy sauce, and the rice syrup.
Immediately whisk in the agar while the mixture is still cold. Bring to a boil while whisking, then let barely simmer for 1 minute.
Wait 3 to 4 minutes, then pour in the lime-vinegar mixture and stir.
Immediately pour into a cold dish and refrigerate for 30 minutes.
Cut into cubes and blend with an immersion blender until you have a smooth, lump-free fluid gel.
Dissolve the rice syrup and salt in the water, then add the vinegar.
Peel the persimmons and cut them into brunoise.
Cut the peppers into brunoise as well.
Add the persimmon and pepper brunoise to the liquid and refrigerate for at least 2 hours.
Put the sesame seeds in a cold, dry skillet and toast over medium heat for 3 to 4 minutes, stirring.
Immediately transfer to a cold plate.
In a very hot skillet, toast each nori sheet on both sides until brittle and green. Crumble by hand.
Using a coffee grinder or blender, grind the 6 g (¼ oz) of shiitake into a powder.
Mix the shiitake powder, crumbled nori, sesame seeds, salt, and sugar to make furikake (a Japanese seasoning blend). Transfer to a large plate.
Make the binder by thinning the miso with the water and rice syrup.
Preheat a skillet over high heat, add the oil, and sear the tuna blocks for 15 seconds per side.
Immediately chill on a wire rack in the freezer for 8 minutes.
Using a pastry brush, coat each tuna block with the binder.
Roll in the furikake, pressing lightly.
Drain the persimmon-pepper pickle. Spoon 2 to 3 tablespoons onto each plate and press into a circle.
Slice the tuna blocks and divide among the plates.
Dot the tataki slices with the lime ponzu fluid gel.