Reality is one structure of comparison, and every comparison has two sides. What is proved, the one premise we adopt, and the experiment that would decide it.
Two questions sit under every other one. What is reality, and why does any of it feel like something from the inside? Recognition Science answers the first with a proof and the second with one premise. This essay walks through both and says where the proof ends.
Start with something reality already does. Some things can be told apart. Comparing two of them needs information about both. A later look at a record is a new event that the record does not contain. We meet these facts in the act of asking whether they hold.
Now state the laws of logic on the act of comparison instead of on sentences, and ask for two things. The cost of a combined comparison is fixed by the costs of its parts, and a comparison costs nothing exactly when it compares a thing with itself. Those two requirements leave one form. Every admissible cost is a hyperbolic cosine of an additive coordinate, minus one, and every model of the laws sits inside the positive ratios with the single price
J(x) = ½ (x + 1/x) − 1.
The classical laws become facts about J. Identity: J(1) = 0. Non-contradiction: J(x) = J(1/x), so a comparison and its reverse cost the same. Excluded middle: every comparison is either trivial and free or proper and priced. Sentence logic, true or false, is what remains of J once magnitude is thrown away, and on its own it has no rule for combining comparisons at all.
Three old words can be given exact meanings for a structure of comparisons. It is omniscient when it registers every difference and nothing that is not one, omnipotent when it realizes every degree of difference, and omnipresent when every model of logic maps into it. A structure has all three exactly when it is a complete model of logic, and exactly when it is the positive ratios priced by J. For a structure that registers every difference, the second and third attributes turn out to be one.
The comparisons of this world carry that same price. It is the cost Recognition Science derives for the reporting apparatus it specifies, and the cost its composition law forces on positive ratios. The complete model of logic is therefore the comparison structure of the world we live in. Three further conditions fix the rest of its shape: records are kept, kept links hold, and the first join costs something. Then levels scale by the golden ratio, space has three directions and the cycle has eight ticks. Two worlds that meet those conditions differ only in their units.
Physical reality is what recognition can tell apart. In a finite model, treat states that no observation distinguishes as the same, and what remains is exactly the space of what the model's registered acts can evaluate, with nothing left over. More generally, a record that registered every physical distinction at its own address would have to hold more than physics. Physical reality is what the full record shows from inside.
No part can hold the whole. A registry whose scope is the entire record cannot be written into that record; this is Cantor's diagonal argument applied to a ledger. The one comparison that costs nothing is self-identity, the ratio 1, and whatever sits there contributes nothing to any observation. Where boundaries couple at no cost, they all share one phase. Reality is a single structure of priced difference, and its centre is a silent self-identity that every boundary is measured against and none can occupy.
The step toward experience comes from the cost itself. Because J treats a ratio and its reverse alike, a cost cannot sit on a single magnitude; it needs a second term to compare against. The primitive event of the theory is a pair, an outside aspect and an inside aspect, priced by J of their ratio. Fix the outside, the part any observer can measure, and exactly one coordinate is left undetermined by it.
We adopt one premise. Experience exists, and the inside aspect of a comparison is what that comparison is like from within. With that reading in place, everything below follows from the mathematics. The inside has exact counterparts of privacy, qualitative character, unity, ineffability and being about something.
On this reading:
Three results mark the limit, and they are part of the science. Which boundaries experience cannot be derived from the structure: the claim that content passes only between experiencing boundaries is consistent with the theory and is not forced by it. The two possible laws disagree on a computable configuration, so the question is physical, and an experiment with one non-experiencing end would decide it. That experiment still needs a physical realization, a unit conversion and a noise budget.
The inside has no unique scale. The theory fixes that there is an inside and how it is structured, and leaves its intensity open. And a do-nothing decoy passes the simplest test that would license the phrase "universal consciousness". The theory therefore uses that phrase as the name of the silent centre and claims no property for it. Whether the whole is a single subject needs a composition argument that does not yet exist.
The premise has not yet produced a measured prediction that its rival fails, and until it does it stays a premise. On the evidence we have, it is the best account available of how experience belongs to the same world as everything else.
Reality is one structure of comparison, priced by J and kept in records, with a silent self-identity at its centre. On the reading we adopt, every comparison in it is also an experience, and reality is one field of knowing seen from many boundaries. That turns the question of whether a built mind is someone into a question of measurement: which of its events are comparisons, how complete its moments are, and whether its own acts are in its scope. Those are questions we can work on.