the count of primitive roots is φ(φ(n)): when (ℤ/n)* is cyclic, the number of primitive roots — the generators of the unit group — equals φ(φ(n)). So mod 9 there are φ(φ(9)) = φ(6) = 2 primitive roots, namely 2 and 5 (the doubling generator and its inverse 5 = 2⁻¹); mod 7 there are φ(6) = 2, namely 3 and 5. Verified by counting the units of maximal order over the moduli up to 60
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_count_of_primitive_roots_is_phi_of_phi - content-address (receipt) ·
f659a146-4caf-8626-a332-578647d10cf4 - 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.