Simply doesn't go:

AkashicTome-1.4-16
TConstruct-1.16.5-3.0.4.171

Forge: 36.1.16

SlimeKnights/TinkersConstruct#4395
EnigmaticaModpacks/Enigmatica6#2351

"Whitelisted Items" = ["roots:runedtablet", "opencomputers:tool:4", "immersiveengineering:tool:3", "integrateddynamics:on_the_dynamics_of_integration", "theoneprobe:probenote", "evilcraft:origins_of_darkness", "draconicevolution:info_tablet", "charset:tablet", "antiqueatlas:antique_atlas", "occultism:dictionary_of_spirits", "tconstruct:materials_and_you", "tconstruct:puny_smelting", "tconstruct:mighty_smelting", "tconstruct:tinkers_gadgetry", "tconstruct:fantastic_foundry"]

It also does have that tag:

hope this gets fixed in the 1.18 version of the mod

edit; I found that there's a whitelist in the mod config, you can add the tconstruct books to that for now (and hopefully Vazkii fixes this soon)

Possible fix going forward, from the Tinkers dev:

I have tagged all my books under the item tag forge:books/guide and forge:books. Suggest to the other mods they should be using a tag check instead of a registry ID string match, way too many false positives in experience with registry ID check

SlimeKnights/TinkersConstruct#4395 (comment)

That does seem like a good idea.

Regarding this issue, in All the Mods 6 in MC1.16.5 with Akashic Tome v1.4-16, I've added the tinker's construct books to the "Whitelisted Items" list, and the Tome still will not allow any of them to be added.

To be clear:

"Whitelisted Items" = ["roots:runedtablet", "opencomputers:tool:4", "immersiveengineering:tool:3", "integrateddynamics:on_the_dynamics_of_integration", "theoneprobe:probenote", "evilcraft:origins_of_darkness", "draconicevolution:info_tablet", "charset:tablet", "antiqueatlas:antique_atlas", "occultism:dictionary_of_spirits", "tconstruct:materials_and_you", "tconstruct:puny_smelting", "tconstruct:mighty_smelting", "tconstruct:tinkers_gadgetry", "tconstruct:fantastic_foundry"]

But:

Possible fix going forward, from the Tinkers dev:

I have tagged all my books under the item tag forge:books/guide and forge:books. Suggest to the other mods they should be using a tag check instead of a registry ID string match, way too many false positives in experience with registry ID check

SlimeKnights/TinkersConstruct#4395 (comment)

Tiny update. I hadn't realized that items needed to be whitelisted when I made this report. However, I've gone back and whitelisted each book explicitly and they still don't go in.

I'm having the same problem, with a slight twist: I can add exactly one of the TiCo manuals to the Akashic Tome at once. The others will not be allowed to craft into the Akashic Tome until the added manual is removed. I would have added this as a separate issue, but I believe the two are related or possibly even the same issue.

I'm also seeing this while playing the ATM 6 modpack

Pretty sure this is a duplicate of #53.