I'm slightly puzzled by the mix of empiricism and its opposite here; there are a number of statements that sort of fit in well with the general context in which they're made, but which seem to be actually false.

The suggestion that "we say that one plus one is two" only because "we observe that there are two" when we put a one with another one is odd. I would claim to know that 600 plus 600 is 1200, and yet I've never made the corresponding observation. I'm not sure if you'd say that we really don't know that 600 plus 600 is 1200 (you would be mistaken if you did) or if you'd say that we come to know it through some other mechanism than in the one plus one case (but then it's odd that you chose to use the one plus one case as an example, if it's atypical of how we come to know mathematical facts). Mill's (and I assume Kitcher's) account of this stuff is considerably more complex. Perhaps yours is also, and this was just a summary so brief as to sound simply wrong. But in any case here the empiricism has gone overboard.

On the other hand, when discussing truth in a connected world and discussing "the question of how we will resolve the truth of the matter when (inevitably) there exists a point at which one encyclopedia says a statement is true and the other says the opposite", you say that "[t]ruth, in such a case, will come to depend not so much on the facts of the matter, but rather, through an examination of the process through which various types of knowledge are accumulated and interpreted". Again this seems just false on its face. If Wikipedia says that the airspeed of a swallow is such-and-such, and Britannica says that the airspeed of a swallow is something-else, we will resolve the dispute by appealing to more primary sources, records of swallow races, and actual experiment if need be. We will not do a sort of connectionist analysis of the communities that gave rise to the two conflicting articles, evaluating them for their diversity, the exponent in their scale-free degree equation, their openness, and so on. It would be beside the point: the truth of the matter will depend upon the airspeed of a swallow, not upon the relative structures of two networks of encyclopaediasts. Here empiricism has been left behind, or perhaps focused on the wrong thing.

(A small but important side-note; you say that scale-free networks "are very tightly connected - in a scale free network a piece of information can reach an entire network very quickly". This is actually not true. A scale-free network can in fact be disconnected; there may be pairs of nodes X, Y such that there is no path at all from X to Y, let alone a quick one. You are in fact talking about an important subset of scale-free networks, roughly those in which the average degree is significantly above one and the distribution is random. It might be good to say so.)

I think you are a bit quick to go from "every entity in the world is a distributed entity" (which is, I think, a salutary observation that our dividing up the universe into distinct 'things' is in some sense a convenient shorthand) to "were there no perceivers to recognize diamonds as being 'hard', there would be no 'hardness' for diamonds to have" (which is, I think, either false or uninteresting, depending how you mean it). It's quite true that the hardness of diamonds is a distributed property of a distributed thing, and that "diamonds are hard" (like pretty much any other true sentence) is true only in a sort of squishy sense, as a shorthand for a huge number of facts about the universal wave function. But, to the extent that it is true, it would still be true to exactly that same extent even in a universe in which evolution had been very unlucky, and there were no perceivers around to perceive it.