the order-6 unit group splits as reflection times trinity: by the Chinese remainder theorem the cyclic group of order 6 is C2 × C3, and in (ℤ/9)* this realizes as {1,8} × {1,4,7} — the order-2 factor {1, −1} is negation (8 ≡ −1 mod 9), the order-3 factor {1,4,7} is the trinity subgroup (the units ≡ 1 mod 3); the product map (s,r) ↦ s·r mod 9 is a bijective homomorphism, so every unit factors uniquely as a sign times a rotation. Decidable by exhaustion over ℤ/9
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_order_six_unit_group_splits_as_reflection_times_trinity - content-address (receipt) ·
90f30729-7598-890b-ae96-fa3747b3de16 - 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.