the vortex and rosette unit groups are isomorphic cyclic groups of order 6: mapping 2^k mod 9 to 3^k mod 7 is a bijection of (ℤ/9)* onto (ℤ/7)* that preserves multiplication (an isomorphism, both ≅ ℤ/6), sending generator 2 to generator 3 and identity to identity. So the vortex and the rosette carry the same group structure — the shared 6+1 skeleton — while remaining distinct rings. Decidable by exhaustion
ab3e7c0b-4a21-8c31-a6a2-23155325ebb2Type anything and watch its uuidna recompute — deterministic, reproducible by anyone, no key. A theorem is alive when you interact with it. A content-address proves integrity, not truth. 0/7.
- theorem key ·
the_vortex_and_rosette_unit_groups_are_isomorphic - content-address (receipt) ·
6848f19f-8b5e-84e6-9682-1c4616f67c9d - status · decidable, re-verified on every build — recomputes from
src/
The 7D rosetta-ray vortex is plotted from this theorem's microdata (its content-address); the slowly rotating hero background is computed from its seven surrounding theorems' hues — the mesh, seen locally, in analog rotation of dimensions. Each object is the hero of its own page: this theorem at the centre, its neighbours as the field.
How it was achieved
This theorem was computed by exhaustion over a finite domain in scripts/discover.ts — a test: () => boolean that runs to completion, holding by full enumeration. It was gate-checked (its name and content hold the honesty floor — no over-reach), receipted and chained append-only, and it is re-verified on every build: if it ever stopped holding, the build would fail, not production. That is what achieved means here — not asserted, but recomputable.
One leaf of the chained ledger: all theorems · computed results · the guide · the source formula. The repo and the site cross-link both ways — this hero page points back to the formula that recomputes it. Verify by cloning and running npm run lean-claims. A content-address proves integrity, not truth. entails → 0/7.