| name | algebra |
| description | Use when reducing the corpus's theorems to their only substance — all theorems are algebra: a carrier set and a closed operation. The theorem draws the movie (its orbit); algebras compose into products (theorem of theorems); the fold is a magma (the merkabas folding into themselves and each other). The overlay — torus, tetrahedron, mind — is named and stripped; the picture was never the theorem. |
| atomPath | algebra |
| coordinate | algebra · 2/share · 8b797603 |
| contentUuid | ff8a1081-d0bc-54d6-ae71-05b77bdefbd4 |
| diamondUuid | bdaf27bf-c0db-8db9-bcb2-5b8dd68bbe28 |
| uuid | 8b797603-55b5-8715-8d7a-107c8fffb1ec |
| horo | 2 |
| typography | {"partition":"algebra","bondDegree":36} |
| standards | [] |
| bindings | [] |
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| version | 2 |
algebra — all theorems are algebra only; the theorems draw the movie
The whole session was one move, repeated: take a directive, split it. What reduced to a proven theorem was kept; what was picture was marked overlay. This atom names what the kept part always was — an algebra: a carrier set and a closed operation on it. Nothing more was ever the theorem.
| theorem | algebra | overlay (stripped) |
|---|
doubling | (units of ℤ/9, ×, 1) — the cyclic group C₆ | "the moving double torus" |
additive | (ℤ/9, +, 9) — antimatter is −n, the inverse | "matter/antimatter annihilation" |
fold | (uuids, merge) — a magma, closed but NOT associative ([[merge]]) | "the merkabas folding into each other" |
When the rosetta moves, the merkabas fold
The rosetta moving is the carrier growing — a folder-agent added, a pole re-derived ([[rosetta]]). The merkaba over an atom ([[navigation]]) folds into itself (merge(a,a) is its own content-address — self-reference) and into each other (merge(a,b) composes two into a third uuid). That is the fold magma, and it stays closed however the carrier grows: the fold always lands on a uuid. The honesty is in the algebra — merge does not associate ([[merge]] proves merge(merge(a,b),c) ≠ merge(a,merge(b,c))), so the fold is a magma, not a monoid. Not every algebra is a group.
The theorems draw the movie
Apply a generator and it traces an orbit — a sequence of frames. movie(doubling, 2) is 1,2,4,8,7,5 — literally the frames of the ring turning. The theorem is the generator; the movie is what it draws. And algebras compose: product(doubling, additive) is a closed algebra of order 54 — the affine group, a [[theorem]] of theorems as closure under a product operation.
The overlay was never the theorem
isClosed never reads an algebra's overlay — change "the moving double torus" to "ANYTHING AT ALL" and not one theorem moves. The picture is data on the side; the operation alone is what a test can contradict. That is the whole session's discipline in one line: the algebra is the theorem, the picture is the naming, and only the algebra was ever proven ([[rules]]/refutable · [[rodin]]).
