Everything you mentioned literally goes for both builds (Viral, HM, headshots).

That was my point, you and warframe builder are leaving out key elements of the builds so you're comparison isn't accurate.

It's not taking into account slash procs from hunter munitions, remove hunter munitions and you'll see no DPS changes. Nor does...

I'm referring to the fact that showing numbers isn't the be all end all if you're numbers aren't accurate. Leaving out the slash procs from both builds lowers the overall DPS, but has a more significant effect in lowering the actual numbers of a bladed rounds build.

And you are wrong, HC increases Slash proc damage

You even say it yourself

Wrong. I said base damage, base damage is unmodded damage it is the base or starting damage of the weapon. Modding with HC or serration does not change the base damage, it modifies based on the base damage. Amprex base damage is 22 this is used in the calculation. This is why bladed rounds has a bigger impact as it increases slash proc damage, HC does not. The whole reason viral+slash is so effective is because you're reducing the enemies health then taking advantage of that reduced health to bolster the true damage of slash procs. Increasing the damage that is bypassing shields and armor (something else you're not taking into account with your warframe builder numbers) is huge.

Why does Serration work and HC doesn't? They are literally the same thing.

I never said that HC doesn't work, I said it has diminishing returns. HC is sometimes the best mod to include in a build, but it well never have the same exact impact as Serration if you're including both. The more you build for one kind of damage the more your build suffers in general. This is especially true with HC, which provides additive damage with serration unlike like other sources which ad multiplicative damage. This is why a chroma that wants to be more efficient with the vex damage bonus should remove serration and slot in elemental, fire rate, crit, or multishot mods.